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New analysis of SNeIa Pantheon Catalog: Variable speed of light as an alternative to dark energy
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Abstract
In A&A 412, 35 (2003) Blanchard, Douspis, Rowan-Robinson, and Sarkar (BDRS) slightly modified the primordial fluctuation spectrum and produced an excellent fit to WMAP's CMB power spectrum for an Einstein-de Sitter (EdS) universe, bypassing dark energy. Curiously, they obtained a Hubble value of , in sharp conflict with the canonical range . However, we will demonstrate that the reduced value of achieved by BDRS is fully compatible with the use of variable speed of light in analyzing the late-time cosmic acceleration observed in Type Ia supernovae (SNeIa). In arXiv:2412.04257 [gr-qc] we uncovered a hidden aspect in a generic class of scale-invariant actions: the dynamics of the dilaton can induce a variation in the speed of light as , causing c to vary alongside across spacetime. For an EdS universe with varying c, besides the effects of cosmic expansion, light waves emitted from distant SNeIa are further subject to a refraction effect, which alters the Lemaitre redshift relation to . Based on this new formula, we achieve a fit to the SNeIa Pantheon Catalog exceeding the quality of the CDM model. Crucially, our approach does not require dark energy and produces in strong alignment with the BDRS finding of . Hence, BDRS's analysis of the (early-time) CMB power spectrum and our variable-c analysis of the (late-time) Hubble diagram of SNeIa fully agree on two counts: (i) the dark energy hypothesis is avoided, and (ii) is reduced to , which also yields an age Gy for an EdS universe, without requiring dark energy. Most importantly, we will demonstrate that the late-time acceleration can be attributed to the declining speed of light in an expanding EdS universe, rather than to a dark energy component.
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We measure the speed of light with current observations, such as Type Ia Supernova, galaxy ages, radial BAO mode, as well as simulations of forthcoming redshift surveys and gravitational waves as standard sirens. By means of a Gaussian Process reconstruction, we find that the precision of such measurements can be improved from roughly 6% and to about 2–2.5% when the gravitational wave simulations are considered, and to 1.5–2% when redshift survey are included in the analysis as well. This result demonstrates that we will be able to perform a cosmological measurement of a fundamental physical constant with significantly improved precision, which will help us underpinning if its value is truly consistent with local measurements, as predicted by the standard model of Cosmology.
The possible time variation of the fundamental constants of nature has been an active subject of research in modern physics. In this paper, we propose a new method to investigate such possible time variation of the speed of light c using the updated Hubble diagram of high-redshift standard candles including Type Ia Supernovae (SNe Ia) and high-redshift quasars (based on UV–X relation). Our findings show that the SNe Ia Pantheon sample, combined with currently available sample of cosmic chronometers, would produce robust constraints on the speed of light at the level of c / c 0 = 1.03 ± 0.03. For the Hubble diagram of UV+X-ray quasars acting as a new type of standard candle, we obtain c / c 0 = 1.19 ± 0.07. Therefore, our results confirm that there is no strong evidence for deviation from a constant speed of light up to z ∼ 2. Moreover, we discuss how our technique might be improved at much higher redshifts ( z ∼ 5), focusing on future measurements of the acceleration parameter X ( z ) with gravitational waves (GWs) produced by binary neutron star mergers. In particular, in the framework of the second-generation space-based GW detector, DECi-hertz Interferometer Gravitational Wave Observatory, the speed of light is expected to be constrained with a precision of Δ c / c = 10 ⁻³ .
The co-varying physical couplings (CPC) framework states that physical parameters like the speed of light in vacuum c, the Newtonian constant G, and the cosmological constant Λ could indeed vary with the spacetime coordinates xμ. Here, we assume a temporal variation, that is, c(t), G(t) and Λ(t). We show that the McVittie spacetime, a black hole in an expanding universe, is a solution of the CPC framework providing naturally an important parameter of the model. Then, we calculate the shadow angular radius of this black hole at cosmological distances. A black hole shadow in the CPC context could be either larger or smaller than the same shadow in the standard cosmology. It depends on how the set {c, G, Λ} varies with time or with the cosmic expansion.
We consider the theory of quantum gravity in which gravity emerges as a result of the symmetry-breaking transition in the quantum vacuum. The gravitational tetrads, which play the role of the order parameter in this transition, are represented by the bilinear combinations of the fermionic fields. In this quantum gravity scenario the interval ds in the emergent general relativity is dimensionless. Several other approaches to quantum gravity, including the model of superplastic vacuum and BF theories of gravity support this suggestion. The important consequence of such metric dimension is that all the diffeomorphism invariant quantities are dimensionless for any dimension of spacetime. These include the action S, cosmological constant Λ, scalar curvature R, scalar field Φ, wave function ψ, etc. The composite fermion approach to quantum gravity suggests that the Planck constant ℏ can be the parameter of the Minkowski metric. Here, we extend this suggestion by introducing two Planck constants, bar ℏ and slash /h, which are the parameters of the correspondingly time component and space component of the Minkowski metric, gMinkμν=diag(−ℏ2,/h2,/h2,/h2). The parameters bar ℏ and slash /h are invariant only under SO(3) transformations, and, thus, they are not diffeomorphism invariant. As a result they have non-zero dimensions—the dimension of time for ℏ and dimension of length for /h. Then, according to the Weinberg criterion, these parameters are not fundamental and may vary. In particular, they may depend on the Hubble parameter in the expanding Universe. They also change sign at the topological domain walls resulting from the symmetry breaking.
The possible time variation of the fundamental constants of nature has been an active subject of research since the large-number hypothesis was proposed by Dirac. In this paper, we propose a new method to investigate a possible time variation of the speed of light ( c ) along with the fine-structure constant ( α ) using Strong Gravitational Lensing (SGL) and Type Ia Supernovae (SNe Ia) observations. We assume a general approach to describe the mass distribution of lens-type galaxies, the one in favor of the power-law index model (PLAW). We also consider the runaway dilaton model to describe a possible time-variation of α . In order to explore the results deeply, we split the SGL sample into five sub-samples according to the lens stellar velocity dispersion and three sub-samples according to lens redshift. The results suggest that it is reasonable to treat the systems separately, but no strong indication of varying c was found.
A powerful test of fundamental physics consists on probing the variability of fundamental constants in Nature. Although they have been measured on Earth laboratories and in our Solar neighbourhood with extremely high precision, it is crucial to carry out these tests at the distant Universe, as any significant variation of these quantities would immediately hint at new physics. We perform a cosmological measurement of the speed of light using the latest Type Ia Supernova and cosmic chronometer observations at the redshift range 0 < z < 2. Our method relies on the numerical reconstruction of these data in order to circumvent a priori assumptions of the underlying cosmology. We confirm the constancy of the speed of light at such redshift range, reporting two ∼ 5% precision measurements of c = (3.20 ± 0.16) × 10 ⁵ km s ⁻¹ in z ≃ 1.58, and c = (2.67 ± 0.14) × 10 ⁵ km s ⁻¹ in z ≃ 1.36, depending on the reconstruction method, at a 1σ confidence level.
In this paper, we implement a new method to test the invariance of the speed of light ( c ) as a function of redshift, by combining the measurements of galaxy cluster gas mass fraction, H ( z ) from cosmic chronometers, and Type-Ia supernovae (SNe Ia). In our analyses, we consider both a constant depletion factor (which corresponds to the ratio by which the cluster gas mass fraction is depleted with respect to the universal baryonic mean) and one varying with redshift. We also consider the influence of different H 0 estimates on our results. We look for a variation of c , given by c ( z ) = c 0 (1+ c 1 z ). We find a degeneracy between our final results on c variation and the assumptions on the gas mass fraction depletion factor. Most of our analyses indicate negligible variation of the speed of light.
Even though there have been various models of the time-varying speed of light (VSL), they remain out of the mainstream because of their possible violation of physics laws built into fundamental physics. In order to be the VSL as a viable theory, it should inherit the success of special relativity including Maxwell equations and thermodynamics at least. For this purpose, we adopt the assumption that the speed of light, c, i.e., c[a], varies for the scale factor, a. The background FLRW universe can be defined by the constant cosmic time hypersurface using physical quantities such as temperature, density, c, etc. It is because they evolve in cosmic time and the homogeneity of the Universe demands that they must equal at the equal cosmic time. The variation of c accompanies the joint variations of all related physical constants in order to satisfy the Lorentz invariance, thermodynamics, Bianchi identity, etc. We dub this VSL model as a "minimally extended VSL (meVSL)". We derive cosmological observables of meVSL and obtain the constraints on the variation of c by using current cosmological observations. Interestingly, both the cosmological redshift z and all geometrical distances except the luminosity distance of meVSL are the same as those of general relativity. However, the Hubble parameter of meVSL is rescaled as H(z) = (1+z)-b/4 H(GR)(z), where H(GR)(z) denotes the Hubble parameter obtained from general relativity. Thus, it might be used as an alternative solution for the tension of the Hubble parameter measurements. In this manuscript, we provide the main effects of the meVSL model on various cosmological observations including BBN, CMB, SZE, BAO, SNe, GWs, H, SL, and Δα. Compared to previous VSL models, meVSL might provide alternative solutions for various late time problems of the standard ΛCDM model. This is the main motivation for proposing the meVSL model.
The simplest ΛCDM model provides a good fit to a large span of cosmological data but harbors large areas of phenomenology and ignorance. With the improvement of the number and the accuracy of observations, discrepancies among key cosmological parameters of the model have emerged. The most statistically significant tension is the 4σ to 6σ disagreement between predictions of the Hubble constant, H 0, made by the early time probes in concert with the 'vanilla' ΛCDM cosmological model, and a number of late time, model-independent determinations of H 0 from local measurements of distances and redshifts. The high precision and consistency of the data at both ends present strong challenges to the possible solution space and demands a hypothesis with enough rigor to explain multiple observations - whether these invoke new physics, unexpected large-scale structures or multiple, unrelated errors. A thorough review of the problem including a discussion of recent Hubble constant estimates and a summary of the proposed theoretical solutions is presented here. We include more than 1000 references, indicating that the interest in this area has grown considerably just during the last few years. We classify the many proposals to resolve the tension in these categories: early dark energy, late dark energy, dark energy models with 6 degrees of freedom and their extensions, models with extra relativistic degrees of freedom, models with extra interactions, unified cosmologies, modified gravity, inflationary models, modified recombination history, physics of the critical phenomena, and alternative proposals. Some are formally successful, improving the fit to the data in light of their additional degrees of freedom, restoring agreement within 1-2σ between Planck 2018, using the cosmic microwave background power spectra data, baryon acoustic oscillations, Pantheon SN data, and R20, the latest SH0ES Team Riess, et al (2021 Astrophys. J. 908 L6) measurement of the Hubble constant (H 0 = 73.2 1.3 km s-1 Mpc-1 at 68% confidence level). However, there are many more unsuccessful models which leave the discrepancy well above the 3σ disagreement level. In many cases, reduced tension comes not simply from a change in the value of H 0 but also due to an increase in its uncertainty due to degeneracy with additional physics, complicating the picture and pointing to the need for additional probes. While no specific proposal makes a strong case for being highly likely or far better than all others, solutions involving early or dynamical dark energy, neutrino interactions, interacting cosmologies, primordial magnetic fields, and modified gravity provide the best options until a better alternative comes along.
A number of works have claimed detections of a turn-over in the spectral lag data for individual Gamma-Ray Bursts (GRBs), caused by an energy-dependent speed of light, which could be a possible manifestation of Lorentz invariance violation (LIV). Here, we stack the spectral lag data from a total of 37 GRBs (with a total of 91 measurements), to verify if the combined data is consistent with a unified model consisting of intrinsic astrophysical emission, along with another contribution due to LIV. We then carry out Bayesian model comparison to ascertain if this combined spectral lag data shows a preference for an energy-dependent speed of light, as compared to only an intrinsic astrophysical emission mechanism. We do not find a decisive evidence for such an energy-dependent speed of light for two different models of LIV. When we assume a constant intrinsic lag coupled with an unknown intrinsic scatter, we do not find any evidence for LIV. However, when we use GRB-dependent parameters to model the intrinsic emission, we get decisive evidence for LIV violation. We then carry out a search for LIV Standard Model Extension using this dataset as well as an independent search using a separate dataset consisting of rest-frame spectral lags. Finally, none of the models considered here with any of the aforementioned assumptions provide a good fit to the stacked spectral lag data, indicating that there is still missing Physics in the model for intrinsic spectral lags.
The Hubble constant (H 0) tension between Type Ia Supernovae (SNe Ia) and Planck measurements ranges from 4 to 6 σ. To investigate this tension, we estimate H 0 in the ΛCDM and w 0 w a CDM models by dividing the Pantheon sample, the largest compilation of SNe Ia, into 3, 4, 20 and 40 bins. We fit the extracted H 0 values with a function mimicking the redshift evolution: g(z) = H 0 (z) =H 0 /(1+z) α , where α indicates an evolutionary parameter andH 0 = H 0 at z = 0. We set the absolute magnitude of SNe Ia so that H 0 = 73.5 km s −1 Mpc −1 , and we fix fiducial values for Ω ΛCDM 0m = 0.298 and Ω w0waCDM 0m = 0.308. We find that H 0 evolves with redshift, showing a slowly decreasing trend, with α coefficients consistent with zero only from 1.2 to 2.0 σ. Although the α coefficients are compatible with 0 in 3 σ, this however may affect cosmological results. We measure locally a variation of H 0 (z = 0) − H 0 (z = 1) = 0.4 km s −1 Mpc −1 in 3 and 4 bins. Extrapolating H 0 (z) to z = 1100, the redshift of the last scattering surface, we obtain values of H 0 compatible in 1 σ with Planck measurements independently of cosmological models and number of bins we investigated. Thus, we have reduced the H 0 tension from 54% to 72% for the ΛCDM and w 0 w a CDM models, respectively. If the decreasing trend of H 0 (z) is real, it could be due to astrophysical selection effects or to modified gravity.
Astrophysical observations provide a unique opportunity to test possible signatures of Lorentz invariance violation (LIV), due to the high energies and long distances involved. In quantum theory of gravity, one may expect the modification of the dispersion relation between energy and momentum for photons, which can be probed with the time lag (the arrival time delay between light curves in different energy bands) of gamma-ray bursts (GRBs). In this paper, by using the detailed time delay measurements of GRB 160625B at different energy bands, as well as 23 time delay GRBs covering the redshift range of z = 0.168–2.5 (which were measured at different energy channels from the light curves), we propose an improved model-independent method (based on the newly compiled sample of H ( z ) measurements) to probe the energy-dependent velocity due to the modified dispersion relation for photons. In the framework of a more complex and reasonable theoretical expression to describe the time delays, our results imply that the intrinsic time lags can be better described with more GRB time delay data. More importantly, through direct fitting of the time delay measurements of a sample of GRBs, our limit on the LIV energy scale is comparable to that with unknown constant for the intrinsic time lag, much lower than the Planck energy scale in both linear LIV and quadratic LIV cases.
Probing the speed of light is an important test of general relativity, but the measurements of c using objects in the distant universe have been almost completely unexplored. In this paper, we propose an idea to use the multiple measurements of galactic-scale strong gravitational lensing systems with Type Ia supernovae acting as background sources to estimate the speed of light. This provides an original method to measure the speed of light using objects located at different redshifts that emitted their light in a distant past. Moreover, we predict that strongly lensed Type Ia supernovae observed by the Large Synoptic Survey Telescope (LSST) would produce robust constraints on Δc/c at the level of 10⁻³. We also discuss whether future surveys such as LSST may succeed in detecting any hypothetical variation of c predicted by theories in which fundamental constants have a dynamical nature. © 2018. The American Astronomical Society. All rights reserved..
We examine a method to detect the light speed variation from gamma ray burst data observed by the Fermi Gamma-ray Space Telescope (FGST). We suggest new criteria to determine the characteristic time for low energy photons by the energy curve and the average energy curve respectively, and obtain similar results compared with those from the light curve. We offer a new criterion with both the light curve and the average energy curve to determine the characteristic time for low energy photons. We then apply the new criteria to the GBM NaI data, the GBM BGO data, and the LAT LLE data, and obtain consistent results for three different sets of low energy photons from different FERMI detectors.
In this paper we aim to investigate a deformed relativistic dynamics so-called Symmetrical Special Relativity (SSR) with a universal minimum speed related to a cosmic background field that plays the role of a variable vacuum energy density associated to the temperature of the expanding universe with a cosmic inflation in its early time and an accelerated expansion for its very far future time. In this scenario, we show that both the speed of light and the universal minimum speed present an explicit dependence on the background temperature of the expanding universe. Although finding both the speed of light and the minimum speed in the early universe with very high temperature and also in the very old one with very low temperature being respectively much larger and much smaller than its current value, our approach does not violate the postulates of SSR which claims that both the speed of light and the minimum speed are invariant in a kinematics point of view. Moreover, it is shown that the high value of the speed of light and the quasi zero value of the minimum speed in the early universe was drastically decreased and increased respectively before the beginning of the inflationary period. So we are led to conclude that the theory of Varying Speed of Light (VSL) should be questioned as a possible solution of the horizon problem for the hot universe. Furthermore we will show that both the speed of light and the minimum speed are respectively increased to infinite and decreased to zero in a future horizon given by a ultra-cold universe governed by a rapid accelerated expansion. So we conclude that both universal speeds have the same variations in the early time and the future cosmic time governed by the vacuum energy.
We present optical light curves, redshifts, and classifications for 361 spectroscopically confirmed Type Ia supernovae (SNeIa) discovered by the Pan-STARRS1 (PS1) Medium Deep Survey. We detail improvements to the PS1 SN photometry, astrometry and calibration that reduce the systematic uncertainties in the PS1 SN Ia distances. We combine the subset of 276 PS1 SN Ia () with distance estimates of SN Ia from SDSS, SNLS, various low-z and HST samples to form the largest combined sample of SN Ia consisting of a total of 1049 SN Ia ranging from , which we call the 'Pantheon Sample'. Photometric calibration uncertainties have long dominated the systematic error budget of every major analysis of cosmological parameters with SNIa. We have reduced these calibration systematics to the point where they are similar in size to the other major sources of known systematic uncertainties: the nature of the intrinsic scatter of SNIa and modeling of selection effects. When combining Planck 2015 CMB measurements with the Pantheon SN sample, we find and for the wCDMmodel. When the SN and CMB constraints are combined with constraints from BAO and local H0 measurements, the analysis yields the most precise measurement of dark energy to date: and for the w0waCDM model. Tension with a cosmological constant previously seen in an analysis of PS1 and low-z SNe has diminished after an increase of in the statistics of the PS1 sample, improved calibration and photometry, and stricter light-curve quality cuts. We find the systematic uncertainties in our measurements of dark energy are almost as large as the statistical uncertainties, primarily due to limitations of modeling the low-redshift sample. This must be addressed for future progress in using SN Ia to measure dark energy.
The observational evidence for the recent acceleration of the universe demonstrates that canonical theories of cosmology and particle physics are incomplete-if not incorrect-and that new physics is out there, waiting to be discovered. A key task for the next generation of laboratory and astrophysical facilities is to search for, identify and ultimately characterize this new physics. Here we highlight recent developments in tests of the stability of nature's fundamental couplings, which provide a direct handle on new physics: a detection of variations will be revolutionary, but even improved null results provide competitive constraints on a range of cosmological and particle physics paradigms. A joint analysis of all currently available data shows a preference for variations of and at about the two-sigma level, but inconsistencies between different sub-sets(likely due to hidden systematics) suggest that these statistical preferences need to be taken with caution. On the other hand, these measurements strongly constrain Weak Equivalence Principle violations. Plans and forecasts for forthcoming studies with facilities such as ALMA, ESPRESSO and the ELT, which should clarify these issues, are also discussed, and synergies with other probes are briefly highlighted. The goal is to show how a new generation of precision consistency tests of the standard paradigm will soon become possible.
Since Lorentz invariance plays an important role in modern physics, it is of interest to test the possible Lorentz invariance violation (LIV). The time-lag (the arrival time delay between light curves in different energy bands) of Gamma-ray bursts (GRBs) has been extensively used to this end. However, to our best knowledge, one or more particular cosmological models were assumed {\it a priori} in (almost) all of the relevant works in the literature. So, this makes the results on LIV in those works model-dependent and hence not so robust in fact. In the present work, we try to avoid this problem by using a model-independent approach. We calculate the time delay induced by LIV with the cosmic expansion history given in terms of cosmography, without assuming any particular cosmological model. Then, we constrain the possible LIV with the observational data, and find weak hints for LIV.
We describe an alternative way to use future Baryon Acoustic Oscillation observations to perform non-mainstream research. We focus on the so-called Varying Speed of Light theories, in which the speed of light is made to vary in time. Using prescriptions from future BAO surveys (BOSS, DESI, WFirst-2.4 and SKA), we show that, within such surveys, a 1% Varying Speed of Light (VSL) signal could be detected at 3 sigmas confidence level, in the redshift interval [0.75, 1.45]. Smaller signals will be hardly detected. We also discuss some possible problems related to such kinds of observation, in particular, the degeneracy between a VSL signal and a non-null spatial curvature.
In this paper, based on a 2.29 GHz VLBI all-sky survey of 613 milliarcsecond ultra-compact radio sources with , we describe a method of identifing the sub-sample which can serve as individual standard rulers in cosmology. If the linear size of the compact structure is assumed to depend on source luminosity and redshift as , only intermediate-luminosity quasars ( W/Hz W/Hz) show negligible dependence (, ), and thus represent a population of such rulers with fixed characteristic length l=11.42 pc. With a sample of 120 such sources covering the redshift range , we confirm the existence of dark energy in the Universe with high significance, and obtain stringent constraints on both the matter density and the Hubble constant km sec Mpc. Finally, with the angular diameter distances measured for quasars extending to high redshifts (), we reconstruct the function using the technique of Gaussian processes. This allows us to identify the redshift corresponding to the maximum of the function: and the corresponding angular diameter distance Mpc. Similar reconstruction of the expansion rate function H(z) based on the data from cosmic chronometers and BAO gives us km sec Mpc. These measurements are used to estimate the speed of light at this redshift: km/s. This is the first measurement of the speed of light in a cosmological setting referring to the distant past.
It is postulated in Einstein's relativity that the speed of light in vacuum is a constant for all observers. However, the effect of quantum gravity could bring an energy dependence of light speed. Even a tiny speed variation, when amplified by the cosmological distance, may be revealed by the observed time lags between photons with different energies from astrophysical sources. From the newly detected long gamma ray burst GRB 160509A, we find evidence to support the prediction for a linear form modification of light speed in cosmological space.
The effect of quantum gravity can bring a tiny light speed variation which is detectable through energetic photons propagating from gamma ray bursts (GRBs) to an observer such as the space observatory. Through an analysis of the energetic photon data of the GRBs observed by the Fermi Gamma-ray Space Telescope (FGST), we reveal a surprising regularity of the observed time lags between photons of different energies with respect to the Lorentz violation factor due to the light speed energy dependence. Such regularity suggests a linear form correction of the light speed where E is the photon energy and is the Lorentz violation scale measured by the energetic photon data of GRBs. The results support an energy dependence of the light speed in cosmological space.
We develop a new model-independent method to probe the constancy of the speed
of light c. In our method, the degeneracy between the cosmic curvature and
the speed of light can be eliminated, which makes the test more natural and
general. Combining the independent observations of Hubble parameter H(z) and
luminosity distance , we use the model-independent smoothing technique,
Gaussian processes, to reconstruct them and then detect variation of the speed
of light. We find no signal of deviation from the present value of the speed of
light . Moreover, to demonstrate the improvement in probing the constancy
of the speed of light from future experiments, we produce a series of simulated
data. The Dark Energy Survey will be able to detect at
confidence level. If the errors are reduced to one-tenth of the
expected DES ones, it is easy to detect a variation
at confidence level.
In [1] a new method to measure the speed of light through Baryon Acoustic
Oscillations (BAO) was introduced. Here, we describe in much more detail the
theoretical basis of that method, its implementation, and give some newly
updated results about its application to the forecast data. In particular, we
will show that SKA will be able to detect a 1% variation (if any) in the speed
of light at 3 level. Smaller signals will be hardly detected by
already-planned future galaxy surveys, but we give indications about what
sensitivity requirements should a survey ful?ll in order to be successful.
The spontaneous breaking of local Lorentz invariance in the early Universe, associated with a first order phase transition at a critical time t c , generates a large increase in the speed of light and a superluminary communication of information occurs, allowing all regions in the Universe to be causally connected. This solves the horizon problem, leads to a mechanism of monopole suppression in cosmology and can resolve the flatness problem. After the critical time t c , local Lorentz (and diffeomorphism) invariance is restored and light travels at its presently measured speed. The kinematical and dynamical aspects of the generation of quantum fluctuations in the superluminary Universe are investigated. A scale invariant prediction for the fluctuation density amplitude is obtained.
In this letter we describe a new method to use Baryon Acoustic Oscillations
(BAO) to derive a constraint on the possible variation of the speed of light.
The method relies on the fact that there is a simple relation between the
angular diameter distance maximum and the Hubble function (H)
evaluated at the same maximum-condition redshift, which includes speed of light
c. We note the close analogy of the BAO probe with a laboratory experiment:
here we have which plays the role of a standard (cosmological) ruler,
and , with the dimension of time, as a (cosmological) clock. We
evaluate if current or future missions such as Euclid can be sensitive enough
to detect any variation of c.
A variable speed of light (VSL) cosmology is developed with a spontaneous breaking of Lorentz in-variance in the early universe. A non-minimal electromagnetic coupling to curvature and the resulting quantum electrodynamic vacuum polarization dispersive medium can produce c ≫ c0 in the early uni-verse, where c0 is the measured speed of light today. Higher derivative curvature contributions to the effective gravitational action and quantum gravity vacuum polarization can produce a dispersive medium and a large increase in the speed of gravitational waves cg ≫ cg0 in the early universe, where cg0 is the speed of gravitational waves today. The initial value problems of cosmology are solved: the horizon and flatness problems. The model predicts primordial scalar and tensor fluctuation spectral indices ns = 0.96 and nt = −0.04, respectively.
The varying speed of light (VSL) theory is controversial. It succeeds in
explaining some cosmological problems, but on the other hand it is excluded by
mainstream physics because it will shake the foundation of physics. In the
present paper, we devote ourselves to test whether the speed of light is
varying from the observational data of the type Ia Supernova, Baryon Acoustic
Oscillation, Observational H(z) data and Cosmic Microwave Background (CMB).
We select the common form with the contribution of dark energy
and matter, where is the current value of speed of light, n is a
constant, and consequently construct a varying speed of light dark energy model
(VSLDE). The combined observational data show a much trivial constraint
at 68.3\% confidence level, which indicates that the
speed of light may be a constant with high significance. By reconstructing the
time-variable c(t), we find that the speed of light almost has no variation
for redshift . For high-z observations, they are more sensitive
to the VSLDE model, but the variation of speed of light is only in order of
. We also introduce the geometrical diagnostic to show the
difference between the VSLDE and CDM model. The result shows that the
current data are difficult to differentiate them. All the results show that the
observational data favor the constant speed of light.
The varying speed of light (VSL) model describes how the speed of light in a vacuum changes with cosmological redshift. Despite numerous models, there is little observational evidence for this variation. While the speed of light can be accurately measured by physical means, cosmological methods are rarely used. Previous studies quantified the speed of light at specific redshifts using Gaussian processes and reconstructed the redshift-dependent function c(z). It is crucial to quantify the speed of light across varying redshifts. We use the latest data on angular diameter distances and Hubble parameters H(z) from baryon acoustic oscillation and cosmic chronometer measurements in the redshift interval . The speed of light c(z) is determined using Gaussian and deep Gaussian processes to reconstruct H(z), , and . Furthermore, we conduct comparisons across three distinct models, encompassing two renowned VSL models. We get the result of the parameters constraints in the models (1) for the ‘c-c’ model, . (2) For the ‘c-cl’ model, and n=0.05535 \pm\, ^{0.00008}_{0.00007}. (3) For the ‘c-CPL’ model, and . Based on our findings, it may be inferred that Barrow’s classical VSL model is not a suitable fit for our data. In contrast, the widely recognized Chevallier–Polarski–Linder (CPL) VSL model, under some circumstances, as well as the universal ‘c is constant’ model, demonstrate a satisfactory ability to account for our findings.
The Friedmann-Lemaître-Robertson-Walker model establishes the correlation between redshifts and distances. It has a metric expansion of space. As a result, the wavelength of photons propagating through the expanding space is stretched, creating the cosmological redshift, z. It also relates the frequency of light detected by a local observer to that emitted from a distant source. In standard cosmology (i.e., a constant speed light model), this relation is given by a factor 1/(1 + z). However, this ratio is modified in the minimally extended varying speed of light model (meVSL, c = c0ab/4) as 1/(1 + z)1 − b/4. This time dilation effect is detected as the observed rate of the time variation in the intensity of emitted radiation. The spectra of type Ia supernovae (SNe Ia) provide a reliable way to measure the apparent aging rate of distant objects. We use data on 13 high-redshift (0.28 ≤ z ≤ 0.62) SNe Ia to obtain b = 0.198 ± 0.415 at the 1-σ confidence interval. The current data is too sparse to give meaningful constrain on the meVSL and cannot distinguish the meVSL model from the standard model.
At least one dimensionless physical constant (i.e., a physically observable) must change for the cosmic time to make the varying speed of light (VSL) models phenomenologically feasible. Various physical constants and quantities also should be functions of cosmic time to satisfy all known local laws of physics, including special relativity, thermodynamics, and electromagnetism. Adiabaticity is another necessary condition to keep the homogeneity and isotropy of three-dimensional space. To be a self-consistent theory, one should consider cosmic evolutions of physical constants and quantities when one derives Einstein’s field equations and their solutions. All these conditions are well satisfied in the so-called minimally extended varying speed of light (meVSL) model. Unlike other VSL models, we show that the redshift-drift formula of the meVSL model is the same as a standard model. Therefore, we cannot use this as an experimental tool to verify the meVSL. Instead, one can still use the cosmological chronometers (CC) as a model-independent test of the meVSL. The current CC data cannot distinguish meVSL from the standard model (SM) when we adopt the best-fit values (or Gaussian prior) of H0 and Ωm0 from the Planck mission. However, the CC data prefer the meVSL when we choose Pantheon22 data.
In standard cosmology, redshift is related to scale factor by z = a−1 − 1. Varying speed of light cosmologies also have applied this relationship, in which c does not explicitly appear, with the assumption that ℏ∝c. Measured redshift is not a comparison of an observed spectrum with the spectrum as it was emitted at a distant location, but a comparison with a reference spectrum generated more locally. This distinction suggests decomposition into two parts: (a) change during the flight of a photon, and (b) difference in physics at the time of emission and at the time of observation of a photon associated with an electron transition between specific bound states of an atom. Based on atomic units consistent with data and a relativistic atomic model, redshift is given by z = β(θ)θa−1 − 1, where θ = c/c0, with c0 the present value of c, and β is a function of the atomic parameters describing the transition. The modified form appears to have a modest effect (a difference in scale factor < 2 %) for redshifts that are not much greater than 10. However, the modification can have a major effect for an early universe with c significantly larger than the present. The simplified form z = θa−1 − 1, which results from a non-relativistic model, provides an approximation for redshift that is not transition-specific.
The Co-varying Physical Couplings (CPC) framework is a modified gravity set up assuming Einstein Field Equations wherein the quantities {G, c, Λ} are promoted to spacetime functions. Bianchi identity and the requirement of stress-energy tensor conservation entangle the possible variations of the couplings {G, c, Λ}, which are forced to co-vary as dictated by the General Constraint (GC). In this paper we explore a cosmological model wherein G, c and Λ are functions of the redshift respecting the GC of the CPC framework. We assume a linear parameterization of Λ in terms of the scale factor a. We use the ansatz with σ = constant to deduce the functional forms of c = c(z) and G = G(z). We show that this varying-{G, c, Λ} model fits SNe Ia data and H(z) data with σ = 3. The model parameters can be constrained to describe dark energy at the background level.
Previous researches on high-energy photon events from gamma-ray bursts (GRBs) suggest a light speed variation v(E)=c(1−E/ELV) with ELV=3.6×1017 GeV, together with a pre-burst scenario that hight-energy photons come out about 10 seconds earlier than low-energy photons at the GRB source. However, in the Lorentz symmetry violating scenario with an energy dependent light speed considered here, high-energy photons travel slower than low-energy photons due to the light speed variation, so that they are usually detected after low-energy photons in observed GRB data. Here we find three high-energy photon events which were observed earlier than low-energy photons from Fermi Gamma-ray Space Telescope (FGST), and analysis on these photon events supports the pre-burst scenario of high energy photons from GRBs and the energy dependence of light speed listed above.
The invariance of the speed of light in the distant universe has profound significance for fundamental physics. In this paper, we propose a new model-independent method to test the invariance of the speed of light c at different redshifts by combining the strong gravitational lensing (SGL) systems and the observations of type-Ia supernovae (SNe Ia). All the quantities used to test the deviation of c come from the direct observations, and the absolute magnitudes of SNe Ia need not to be calibrated. Our results show that the speed of light in the distant universe is no obvious deviation from the constant value c0 within the uncertainty based on current observations. Moreover, we conclude that the currently compiled SGL and SNe Ia Pantheon samples may achieve much higher precision Δc/c ∼ 10−2 for the deviation of c than all previously considered approaches. The forthcoming data from the Legacy Survey of Space and Time and Wide-Field InfraRed Space Telescope will achieve more stringent testing for deviation of the SOL (at the level of Δc/c ∼ 10−3) by using our model-independent method. Finally, we discuss the potential ways in which our technique might be improved, focusing on the treatment of possible sources of systematic uncertainties.
We have used the recently published varying physical constants (VPC) approach in an attempt to resolve the primordial lithium abundance problem. The value of the ratio of ⁷Li to hydrogen ⁷Li/H = 1.400 ( ± 0.023) × 10⁻¹⁰ we have calculated using this approach is about four times lower than that estimated using the standard lambda cold dark matter (ΛCDM) cosmological model, and is consistent with the most agreed observational value of 1.6 ( ± 0.3) × 10⁻¹⁰. In the VPC approach Einstein equations are modified to include the variation of the speed of light c, gravitational constant G and cosmological constant Λ using the Einstein-Hilbert action. Application of this approach to cosmology naturally leads to the variation of the Plank constant ℏ and the Boltzmann constant kB as well. They approach fixed values at the scale factor a ≪ 1: c = c0/e, G = G0/e³, ℏ = ℏ0/e and kB = kB0/e5/4, where e is the Euler's number (= 2.7183). Since the VPC cosmology reduces to the same form as the ΛCDM cosmology at very small scale factors, we could use an existing Big-Bang nucleosynthesis (BBN) code AlterBBN with the above changes to calculate the light element abundances under the VPC cosmology. Among other abundances we have calculated at baryon to photon ratio η = 6.1 × 10⁻¹⁰ are: ⁴He/H = 0.2478 ( ± 0.0041), D/H = 2.453 ( ± 0.041) × 10⁻⁵, ³He/H = 2.940 ( ± 0.049) × 10⁻⁵.
We have shown that the varying physical constant model is consistent with the recently published variational approach wherein Einstein equations are modified to include the variation of the speed of light c, gravitational constant G, and cosmological constant Λ using the Einstein–Hilbert action. The general constraint resulting from satisfying the local conservation laws and contracted Bianchi identities provides the freedom to choose the form of the variation of the constants as well as how their variations are related. When we choose {\dot{G}}/G = 3\,\underset{\raise0.3em\hbox{\smash{\scriptscriptstyle\cdot}}}{\dot{c}} /c,\,c = {c_0}\,{\rm{exp}}\,[({a^\alpha} - 1)],\,G = {G_0}\,{\rm{exp}}\,[3({a^\alpha} - 1)], and , where a is the scale factor and α = 1.8, we are able to show that the resulting model: (a) fits the supernova 1a observational data marginally better than the Lambda cold dark matter (ΛCDM) model; (b) determines the first peak in the power spectrum of the cosmic microwave background temperature anisotropies at a multipole value of ; (c) calculates the age of the Universe as 14.1 Gyr; and (d) finds the BAO acoustic scale to be 145.2 Mpc. These numbers are within less than 3 per cent of the values derived using the ΛCDM model. Surprisingly, we find that the dark-energy density is negative in a Universe that has significant negative curvature and whose expansion is accelerating at a faster rate than that predicted by the ΛCDM model.
We develop an action principle to construct the dynamics that gives rise to a minimal generalization of Einstein’s equations, where the speed of light ([Formula: see text]), the gravitational constant ([Formula: see text]) and the cosmological constant ([Formula: see text]) are allowed to vary. Our construction preserves general covariance of the theory, which yields a general dynamical constraint on [Formula: see text], [Formula: see text] and [Formula: see text]. This action is general and can be applied to describe different cosmological solutions. We apply this formulation to the initial condition puzzles of the early universe and show that it generates a dynamical mechanism to obtain the homogeneous and flat universe we observe today. We rewrite the conditions necessary to solve the horizon and flatness problems in this framework, which does not necessarily lead to an accelerated expansion as in inflation. Then, we show how the dynamics of the scalar field that represents [Formula: see text] or [Formula: see text] (and [Formula: see text]) can be used to solve the problems of the early universe cosmology by means of different ways to [Formula: see text]-inflate the horizon in the early universe. By taking [Formula: see text], we show that the dynamics of the scalar field representing [Formula: see text] can be described once a potential is given.
Phantom dark energy (w<−1) can produce amplified cosmic acceleration at late times, thus increasing the value of H0 favored by CMB data and releasing the tension with local measurements of H0. We show that the best fit value of H0 in the context of the CMB power spectrum is degenerate with a constant equation-of-state parameter w, in accordance with the approximate effective linear equation H0+30.93w−36.47=0 (H0 in km sec−1 Mpc−1). This equation is derived by assuming that both Ω0mh2 and dA=∫0zrecdzH(z) remain constant (for an invariant CMB spectrum) and equal to their best fit Planck/ΛCDM values as H0, Ω0m, and w vary. For w=−1, this linear degeneracy equation leads to the best fit H0=67.4 km sec−1 Mpc−1 as expected. For w=−1.22, the corresponding predicted CMB best fit Hubble constant is H0=74 km sec−1 Mpc−1, which is identical with the value obtained by local-distance ladder measurements, while the best fit matter density parameter is predicted to decrease, since Ω0mh2 is fixed. We verify the above H0−w degeneracy equation by fitting a wCDM model with fixed values of w to the Planck TT spectrum, showing also that the quality of fit (χ2) is similar to that of ΛCDM. However, when including SnIa, baryon acoustic oscillation, or growth data, the quality of fit becomes worse than ΛCDM when w<−1. Finally, we generalize the H0−w(z) degeneracy equation for the parametrization w(z)=w0+w1z/(1+z) and identify analytically the full w0−w1 parameter region (straight line) that leads to a best fit H0=74 km sec−1 Mpc−1 in the context of the Planck CMB spectrum. This exploitation of H0−w(z) degeneracy can lead to immediate identification of all parameter values of a given w(z) parametrization that can potentially resolve the H0 tension.
Because of the high energies and long distances to the sources, astrophysical observations provide a unique opportunity to test possible signatures of Lorentz invariance violation (LIV). Superluminal LIV enables the decay of photons at high energy. The high altitude water Cherenkov (HAWC) observatory is among the most sensitive gamma-ray instruments currently operating above 10 TeV. HAWC finds evidence of 100 TeV photon emission from at least four astrophysical sources. These observations exclude, for the strongest of the limits set, the LIV energy scale to 2.2×1031 eV, over 1800 times the Planck energy and an improvement of 1 to 2 orders of magnitude over previous limits.
We present a novel method to reconstruct the temporal evolution of the speed of light c ( z ) in a flat Friedmann-Robertson-Walker (FRW) Universe using astronomical observations. After validating our pipeline with mock datasets, we apply our method to the latest baryon acoustic oscillations (BAO) and supernovae observations, and reconstruct c ( z ) in the redshift range of z ∈ [0,1.5]. We find no evidence of a varying speed of light, although we see some interesting features of Δ c ( z ), the fractional difference between c ( z ) and c 0 (the speed of light in the International System of Units), eg, Δ c ( z ) < 0 and Δ c ( z ) > 0 at 0.2 ≲ z ≲ 0.5 and 0.8 ≲ z ≲ 1.3, respectively, although the significance of these features is currently far below statistical importance.
In this paper, the Lorentz invariance violation (LIV) is introduced in the calculations of photon propagation in the universe. LIV is considered in the photon sector, and the mean-free path of the γγ → e⁺e⁻ interaction is calculated. The corresponding photon horizon, including LIV effects, is used to predict major changes in the propagation of photons with energy above 10¹⁸ eV. The flux of GZK photons on Earth, considering LIV, is calculated for several source models of ultra-high-energy cosmic rays (UHECRs). The predicted flux of GZK gamma-rays is compared to the new upper limits on the photon flux obtained by the Pierre Auger Observatory in order to impose upper limits on the LIV coefficients of order n = 0, 1, and 2. The limits on the LIV coefficients derived here are more realistic than previous works and in some cases more restrictive. The analysis resulted in LIV upper limits in the photon sector of δγ,0limit ∼ -10⁻²⁰,δγ,1limit ∼ -10⁻³⁸eV⁻², δγ,2limit ∼ -10⁻⁵⁶eV⁻²in the astrophysical scenario, which best describes UHECR data. © 2018. The American Astronomical Society. All rights reserved.
Many varying speed of light (VSL) theories have been developed recently. Here we address the issue of their observational verification in a fully comprehensive way. By using the most updated cosmological probes, we test three different candidates for a VSL theory (Barrow & Magueijo, Avelino & Martins, and Moffat). We consider many different Ansätze for both the functional form of c(z) and the dark energy dynamics. We compare these results using a reliable statistical tool such as the Bayesian evidence. We find that the present cosmological data are perfectly compatible with any of these VSL scenarios, but for the Moffat model there is a higher Bayesian evidence ratio in favor of VSL rather than the c = constant ΛCDM scenario. Moreover, in such a scenario, the VSL signal can help to strengthen constraints on the spatial curvature (with indication toward an open universe), to clarify some properties of dark energy (exclusion of a cosmological constant at 2σ level), and is also falsifiable in the near future owing to peculiar issues that differentiate this model from the standard one. Finally, we apply an information prior and entropy prior in order to put physical constraints on the models, though still in favor Moffat's proposal. © 2017. The American Astronomical Society. All rights reserved.
We investigate a new method to recover (if any) a possible varying speed of light (VSL) signal from cosmological data. It comes as an upgrade by Salzano, Dąbrowski, and Lazkoz [Phys. Rev. Lett.114, 101304 (2015); Phys. Rev. D 93, 063521 (2016)], where it was argued that such a signal could be detected at a single redshift location only. Here, we show how it is possible to extract information on a VSL signal on an extended redshift range. We use mock cosmological data from future galaxy surveys (BOSS, DESI, WFirst-2.4 and SKA): the sound horizon at decoupling imprinted in the clustering of galaxies (baryon acoustic oscillations) as an angular diameter distance, and the expansion rate derived from those galaxies recognized as cosmic chronometers. We find that, given the forecast sensitivities of such surveys, a ∼1% VSL signal can be detected at 3σ confidence level in the redshift interval z∈[0.,1.55]. Smaller signals (∼0.1%) will be hardly detected (even if some lower possibility for a 1σ detection is still possible). Finally, we discuss the degeneration between a VSL signal and a non-null spatial curvature; we show that, given present bounds on curvature, any signal, if detected, can be attributed to a VSL signal with a very high confidence. On the other hand, our method turns out to be useful even in the classical scenario of a constant speed of light: in this case, the signal we reconstruct can be totally ascribed to spatial curvature and, thus, we might have a method to detect a 0.01-order curvature in the same redshift range with a very high confidence.
The varying speed of light (VSL) has been used in cosmological models in which the physical constants vary over time. On the other hand, the Dvali, Gabadadze and Porrati (DGP) brane world model, especially its normal branch has been extensively discussed to justify the current cosmic acceleration. In this article we show that the normal branch of DGP in VSL cosmology leads to a self-accelerating behavior and therefore can interpret cosmic acceleration. Applying statefinder diagnostics demonstrate that our result slightly deviates {\Lambda}CDM model.
We revisit the possibility that the Planck mass is spontaneously generated in scale invariant scalar-tensor theories of gravity, typically leading to a "dilaton." The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally Weyl-scale invariant and argue that, as a consequence, the fifth force effects are dramatically suppressed and such models are viable. We discuss possible obstructions to maintaining scale invariance and how these might be resolved.
In this paper we extend a new method to measure possible variation of the speed of light by using Baryon Acoustic Oscillations and the Hubble function presented in our earlier paper [V. Salzano, M. P. D\c{a}browski, and R. Lazkoz, Phys. Rev. D93, 063521 (2016)] onto an inhomogeneous model of the universe. The method relies on the fact that there is a simple relation between the angular diameter distance maximum and the Hubble function (H) evaluated at the same maximum-condition redshift, which includes speed of light c. One limit of such method was the assumption of null spatial curvature (even if we showed that even a non-zero curvature would have negligible effects). Here, we move one step further: we explicitly assume a model with intrinsic non-null curvature, and calculate the exact relation between and H in this case. Then, we evaluate if current or future missions such as SKA can be sensitive enough to detect any such kind of spatial variation of c which can perhaps be related to the recently observed spatial variation of the fine structure constant (an effect known as -dipole).
Big Bang models of the Universe predict rapid domination by curvature, a paradox known as the flatness problem. Solutions to this problem usually leave the Universe exactly flat for every practical purpose. Explaining a nearly but not exactly flat current Universe is a new problem, which we label the quasi-flatness problem. We show how theories incorporating time-varying coupling constants could drive the Universe to a late-time near-flat attractor. A similar problem may be posed with regards to the cosmological constant Λ, the quasi-lambda problem, and we exhibit a solution to this problem as well.