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Can Baryon Acoustic Oscillations Illuminate the Parity-Violating Galaxy 4PCF?
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Abstract
Measurements of the galaxy 4-Point Correlation Function (4PCF) from theSloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey (SDSS BOSS) have recently found strong statistical evidence for parity violation. If this signal is of genuine physical origin, it must stem from beyond-Standard Model physics, most likely during the very early Universe, prior to decoupling (z1,020). Since the Baryon Acoustic Oscillation (BAO) features imprint at decoupling, they are expected in the parity-odd galaxy 4PCF, and so detecting them would be an additional piece of evidence that the signal is genuine. We demonstrate in a toy parity-violating model how the BAO imprint on the parity-odd 4PCF. We then outline how to perform a model-independent search for BAO in the odd 4PCF, desirable since, if the signal is real, we may not know for some time what model of e.g. inflation is producing it. If BAO are detected in the parity-odd sector, they can be used as a standard ruler as is already done in the 2PCF and 3PCF. We derive a simple formula relating the expected precision on the BAO scale to the overall parity-odd detection significance. Pursuing BAO in the odd 4PCF of future redshift surveys such as DESI, Euclid, Spherex, and Roman will be a valuable additional avenue to determine if parity violation in the distribution of galaxies is of genuine cosmological origin.
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Polarization of the cosmic microwave background (CMB) is sensitive to new physics violating parity symmetry, such as the presence of a pseudoscalar “axionlike” field. Such a field may be responsible for early dark energy (EDE), which is active prior to recombination and provides a solution to the so-called Hubble tension. The EDE field coupled to photons in a parity-violating manner would rotate the plane of linear polarization of the CMB and produce a cross-correlation power spectrum of E- and B-mode polarization fields with opposite parities. In this Letter, we fit the EB power spectrum predicted by the photon-axion coupling of the EDE model with a potential V(ϕ)∝[1−cos(ϕ/f)]3 to polarization data from Planck. We find that the unique shape of the predicted EB power spectrum is not favored by the data and obtain a first constraint on the photon-axion coupling constant, g=(0.04±0.16)MPl−1 (68% C.L.), for the EDE model that best fits the CMB and galaxy clustering data. This constraint is independent of the miscalibration of polarization angles of the instrument or the polarized Galactic foreground emission. Our limit on g may have important implications for embedding EDE in fundamental physics, such as string theory.
We use the BOSS DR12 galaxy power spectrum to constrain compensated isocurvature perturbations (CIP), which are opposite-sign primordial baryon and dark matter perturbations that leave the total matter density unchanged. Long-wavelength CIP σ ( x ) enter the galaxy density contrast as δ g ( x ) ⊃ b σ σ ( x ), with b σ the linear CIP galaxy bias parameter. We parameterize the CIP spectra as P σσ = A ² P ℛℛ and P σℛ = ξ √ P σσ P ℛℛ , where A is the CIP amplitude and ξ is the correlation with the curvature perturbations ℛ. We find a significance of detection of Ab σ ≠ 0 of 1.8 σ for correlated CIP ( ξ = 1), consistent with no detection. For uncorrelated CIP ( ξ = 0), the constraints are instead more significantly shifted away from zero, although this may be due to large-scale data systematics which have a bigger impact on these type of CIP. The constraints on A depend on the assumed priors for the b σ parameter, which we estimate using separate universe simulations. Assuming b σ values representative of all halos we find σ A = 145 for correlated CIP and σ | A | = 475 for uncorrelated CIP. Our strongest uncorrelated CIP constraint is for b σ representative of the 33% most concentrated halos, σ | A | = 197, which is better than the current CMB bounds | A | ≲ 360. We also discuss the impact of the local primordial non-Gaussianity parameter f NL in CIP constraints. Our results demonstrate the power of galaxy data to place tight constraints on CIP, and motivate works to understand better the impact of data systematics, as well as to determine theory priors for b σ .
Isotropic functions of positions r1, r2, . . . , rN, i.e. functions invariant under simultaneous rotations of all the coordinates, are
conveniently formed using spherical harmonics and Clebsch-Gordan coefficients. An orthonormal basis of such functions provides
a formalism suitable for analyzing isotropic distributions such as those that arise in cosmology, for instance in the clustering of
galaxies as revealed by large-scale structure surveys. The algebraic properties of the basis functions are conveniently expressed
in terms of 6-j and 9-j symbols. The calculation of relations among the basis functions is facilitated by “Yutsis” diagrams for
the addition and recoupling of angular momenta.
The Nancy Grace Roman Space Telescope will conduct a High Latitude Spectroscopic Survey (HLSS) over a large volume at high redshift, using the near-IR grism (1.0–1.93 μ m, R = 435–865) and the 0.28 deg ² wide-field camera. We present a reference HLSS that maps 2000 deg ² and achieves an emission-line flux limit of 10 ⁻¹⁶ erg s ⁻¹ cm ⁻² at 6.5 σ , requiring ∼0.6 yr of observing time. We summarize the flowdown of the Roman science objectives to the science and technical requirements of the HLSS. We construct a mock redshift survey over the full HLSS volume by applying a semianalytic galaxy formation model to a cosmological N -body simulation and use this mock survey to create pixel-level simulations of 4 deg ² of HLSS grism spectroscopy. We find that the reference HLSS would measure ∼10 million H α galaxy redshifts that densely map large-scale structure at z = 1–2 and 2 million [O iii ] galaxy redshifts that sparsely map structures at z = 2–3. We forecast the performance of this survey for measurements of the cosmic expansion history with baryon acoustic oscillations and the growth of large-scale structure with redshift-space distortions. We also study possible deviations from the reference design and find that a deep HLSS at f line > 7 × 10 ⁻¹⁷ erg s ⁻¹ cm ⁻² over 4000 deg ² (requiring ∼1.5 yr of observing time) provides the most compelling stand-alone constraints on dark energy from Roman alone. This provides a useful reference for future optimizations. The reference survey, simulated data sets, and forecasts presented here will inform community decisions on the final scope and design of the Roman HLSS.
A stochastic gravitational-wave background is expected to emerge from the superposition of numerous gravitational-wave sources of both astrophysical and cosmological origin. A number of cosmological models can have a parity violation, resulting in the generation of circularly polarized gravitational waves. We present a method to search for parity violation in the gravitational-wave data. We first apply this method to the most recent, third, LIGO-Virgo observing run. We then investigate the constraining power of future A+LIGO−Virgo detectors, including KAGRA to the network, for a gravitational-wave background generated by early universe cosmological turbulence.
The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance–redshift relationship. The cosmological density fields traced by late-time galaxy formation are initially nearly Gaussian, and hence, all the cosmological information can be extracted from their two-point correlation function. Subsequent non-linear evolution under gravity, as well as halo and then galaxy formation, generates higher order correlation functions. Since the mapping of the initial to the final density field is, on large scales, invertible, it is often claimed that the information content of the initial field’s power spectrum is equal to that of all the higher order functions of the final, non-linear field. This claim implies that reconstruction of the initial density field from the non-linear field renders analysis of higher order correlation functions of the latter superfluous. We show that this claim is false when the N-point functions are used as standard rulers. Constraints available from joint analysis of the two and three-point correlation functions can, in some cases, exceed those offered by the initial power spectrum. We provide a mathematical justification for this claim and demonstrate it using a large suite of N-body simulations. In particular, we show that for the z = 0 real-space matter field in the limit of vanishing shot-noise, taking modes up to kmax = 0.2 h Mpc−1, using the bispectrum alone offers a factor of 2 reduction in the variance on the cosmic distance scale relative to that available from the linear power spectrum.
Galaxy shapes have been observed to align with external tidal fields generated by the large-scale structures of the Universe. While the main source for these tidal fields is provided by long-wavelength density perturbations, tensor perturbations also contribute with a non-vanishing amplitude at linear order. We show that parity-breaking gravitational waves produced during inflation leave a distinctive imprint in the galaxy shape power spectrum which is not hampered by any scalar-induced tidal field. We also show that a certain class of tensor non-Gaussianities produced during inflation can leave a signature in the density-weighted galaxy shape power spectrum. We estimate the possibility of observing such imprints in future galaxy surveys.
The existence of the cosmic neutrino background is a robust prediction of the hot big bang model. These neutrinos were a dominant component of the energy density in the early Universe and therefore played an important role in the evolution of cosmological perturbations. The energy density of the cosmic neutrino background has been measured using the abundances of light elements and the anisotropies of the cosmic microwave background. A complementary and more robust probe is provided by a distinct shift in the temporal phase of sound waves in the primordial plasma that is produced by fluctuations in the neutrino density. Here, we report on the first constraint on this neutrino-induced phase shift in the spectrum of baryon acoustic oscillations of the BOSS DR12 data. Constraining the acoustic scale using Planck data while marginalizing over the effects of neutrinos in the cosmic microwave background, we find a non-zero phase shift at greater than 95% confidence. Besides providing a new test of the cosmic neutrino background, our work is the first application of the baryon acoustic oscillation signal to early Universe physics. In the early Universe, fluctuations in the neutrino density produced a distinct shift in the temporal phase of sound waves in the primordial plasma. The size of this phase shift has now been constrained through baryon acoustic oscillation data.
We present the first application of the angle-dependent 3-Point Correlation Function (3PCF) to the density fields magnetohydrodynamic (MHD) turbulence simulations intended to model interstellar (ISM) turbulence. Previous work has demonstrated that the angle-averaged bispectrum, the 3PCF's Fourier-space analog, is sensitive to the sonic and Alfv\'enic Mach numbers of turbulence. Here we show that introducing angular information via multipole moments with respect to the triangle opening angle offers considerable additional discriminatory power on these parameters. We exploit a fast, order ( the number of grid cells used for a Fourier Transform) 3PCF algorithm to study a suite of MHD turbulence simulations with 10 different combinations of sonic and Alfv\'enic Mach numbers over a range from sub to super-sonic and sub to super-Alfv\'{e}nic. The 3PCF algorithm's speed for the first time enables full quantification of the time-variation of our signal: we study 9 timeslices for each condition, demonstrating that the 3PCF is sufficiently time-stable to be used as an ISM diagnostic. In future, applying this framework to 3-D dust maps will enable better treatment of dust as a cosmological foreground as well as reveal conditions in the ISM that shape star formation.
We outline here a new algorithm for evaluating Hankel (Fourier–Bessel) transforms numerically with enhanced speed, accuracy, and efficiency. A nonlinear change of variables is used to convert the one-sided Hankel transform integral into a two-sided cross-correlation integral. This correlation integral is then evaluated on a discrete sampled basis using fast Fourier transforms. The new algorithm offers advantages in speed and substantial advantages in storage requirements over conventional methods for evaluating Hankel transforms with large numbers of points.
The Chern-Simons Lagrangian has been studied previously in (2+1)-dimensional spacetime, where it is both gauge and Lorentz invariant. In 3+1 dimensions, this term couples the dual electromagnetic tensor to an external four-vector. If we take this four-vector to be fixed, the term is gauge invariant but not Lorentz invariant. In this paper, we examine both the theoretical consequences of such a modification and observational limits we can put on its magnitude. The Chern-Simons term would rotate the plane of polarization of radiation from distant galaxies, an effect which is not observed. From the observations we deduce that the magnitude of the vector is
A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to the continuum value much faster than with any alternative, all terms giving rise to a slower convergence exactly cancel. Explicit variance formulae are provided for both Poisson and multinomial point processes using techniques for spatial statistics reported by Ripley (1988). The formalism naturally includes most previously used statistical tools such as N-point correlation functions and their Fourier counterparts, moments of counts-in-cells, and moment correlators. For all these, and perhaps some other statistics our estimator provides a straightforward means for efficient edge corrections.
We introduce the Parity-Odd Power (POP) spectra, a novel set of observables for probing parity violation in cosmological N-point statistics. POP spectra are derived from composite fields obtained by applying nonlinear transformations, involving also gradients, curls, and filtering functions, to a scalar field. This compresses the parity-odd trispectrum into a power spectrum. These new statistics offer several advantages: they are computationally fast to construct, estimating their covariance is less demanding compared to estimating that of the full parity-odd trispectrum, and they are simple to model theoretically. We measure the POP spectra on simulations of a scalar field with a specific parity-odd trispectrum shape. We compare these measurements to semi-analytic theoretical calculations and find agreement. We also explore extensions and generalizations of these parity-odd observables.
We study a mechanism of generating the trispectrum (4-point correlation) of curvature perturbation through the dynamics of a spectator axion field and U(1) gauge field during inflation. Owing to the Chern-Simons coupling, only one helicity mode of gauge field experiences a tachyonic instability and sources scalar perturbations. Sourced curvature perturbation exhibits parity-violating nature which can be tested through its trispectrum. We numerically compute parity-even and parity-odd component of the sourced trispectrum. It is found that the ratio of parity-odd to parity-even mode can reach 𝒪(10%) in an exact equilateral momentum configuration. We also investigate a quasi-equilateral shape where only one of the momenta is slightly longer than the other three, and find that the parity-odd mode can reach, and more interestingly, surpass the parity-even one. This may help us to interpret a large parity-odd trispectrum signal extracted from BOSS galaxy-clustering data.
The propagation of gravitational waves can reveal fundamental features of the structure of spacetime. For instance, differences in the propagation of gravitational-wave polarizations would be a smoking gun for parity violations in the gravitational sector, as expected from birefringent theories like Chern-Simons gravity. Here we look for evidence of amplitude birefringence in the third catalog of detections by the Laser Interferometer Gravitational Wave Observatory and Virgo through the use of birefringent templates inspired by dynamical Chern-Simons gravity. From 71 binary-black-hole signals, we obtain the most precise constraints on gravitational-wave amplitude birefringence yet, measuring a birefringent attenuation of κ=−0.019−0.029+0.038 Gpc−1 at 100 Hz with 90% credibility, equivalent to a parity-violation energy scale of MPV≳6.8×10−21 GeV.
Gravitational parity violation arises in a variety of theories beyond general relativity. Gravitational waves in such theories have their propagation altered, leading to birefringence effects in both the amplitude and speed of the wave. In this work, we introduce a generalized, theory-motivated parametrization scheme to study parity violation in gravitational wave propagation. This parametrization maps to parity-violating gravity theories in a straightforward way. We find that the amplitude and velocity birefringence effects scale with an effective distance measure that depends on how the dispersion relation is modified. Furthermore, we show that this generic parametrization can be mapped to the parametrized-post-Einsteinian (ppE) formalism with convenient applications to gravitational wave observations and model-agnostic tests of general relativity. We derive a mapping to the standard ppE waveform of the gravitational wave response function, and also find a ppE waveform mapping at the level of the polarization modes, h+ and h×. Finally, we show how existing constraints in the literature translate to bounds on our new parity-violating parameters and discuss avenues for future analysis.
We show how the galaxy four-point correlation function can test for cosmological parity violation. The detection of cosmological parity violation would reflect previously unknown forces present at the earliest moments of the Universe. Recent developments both in rapidly evaluating galaxy N-point correlation functions and in determining the corresponding covariance matrices make the search for parity violation in the four-point correlation function possible in current and upcoming surveys such as those undertaken by Dark Energy Spectroscopic Instrument, the Euclid satellite, and the Vera C. Rubin Observatory. We estimate the limits on cosmic parity violation that could be set with these data.
Parity-violating physics in the early universe can leave detectable traces in late-time observables. While vector- and tensor-type parity violation can be observed in the B-modes of the cosmic microwave background, scalar-type signatures are visible only in the four-point correlation function (4PCF) and beyond. This work presents a blind test for parity violation in the 4PCF of the baryon oscillation spectroscopic survey (BOSS) CMASS sample, considering galaxy separations in the range [20,160] h−1 Mpc. The parity-odd 4PCF contains no contributions from standard ΛCDM physics and can be efficiently measured using recently developed estimators. Data are analyzed using both a nonparametric rank test (comparing the BOSS 4PCFs to those of realistic simulations) and a compressed χ2 analysis, with the former avoiding the assumption of a Gaussian likelihood. These find similar results, with the rank test giving a detection probability of 99.6% (2.9σ). This provides significant evidence for parity violation, from either cosmological sources or systematics. We perform a number of systematic tests: although these do not reveal any observational artifacts, we cannot exclude the possibility that our detection is caused by the simulations not faithfully representing the statistical properties of the BOSS data. Our measurements can be used to constrain physical models of parity violation. As an example, we consider a coupling between the inflaton and a U(1) gauge field and place bounds on the latter’s energy density, which are several orders of magnitude stronger than those previously reported. Upcoming probes such as DESI and Euclid will reveal whether our detection of parity violation is due to new physics, and strengthen the bounds on a variety of models.
We derive analytic covariance matrices for the N-point correlation functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary N and projected onto the isotropic basis functions given by spherical harmonics and Wigner 3j symbols. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a nonuniform window function. Our result is recently shown to facilitate NPCF analysis on a realistic survey data.
The current cosmological model requires new physics beyond the standard model of elementary particles and fields, such as dark matter and dark energy. Their nature is unknown and so is that of the initial fluctuations in the early Universe that led to the creation of the cosmic structure we see today. Polarized light of the cosmic microwave background (CMB) may hold the answer to these fundamental questions. Here, I discuss two phenomena that could be uncovered in CMB observations. First, if the physics behind dark matter and dark energy violates parity symmetry, their coupling to photons should have rotated the plane of linear polarization as the CMB photons have been travelling for more than 13 billion years. This effect is known as ‘cosmic birefringence’. A tantalizing hint of such a signal has been found with a statistical significance of 3σ. Second, the period of accelerated expansion in the very early Universe, called ‘cosmic inflation’, might have produced a stochastic background of primordial gravitational waves (as yet unobserved). These might have been generated by vacuum fluctuations in spacetime or by matter fields and could be measurable in the CMB polarization. The goal of observing these two phenomena will influence how data from future CMB experiments are collected, calibrated and analysed. The polarization of the cosmic microwave background (CMB) may shed light on the nature of dark matter and dark energy, and on the origin of all structures in the Universe. Discovering a signature of such new physics in the CMB will require new observational and calibration strategies for future CMB experiments. The current cosmological model includes at least three elements (the nature of dark matter and of dark energy, and the origin of all structures in the Universe) whose explanation requires new physics beyond the standard model (SM) of elementary particles and fields. The polarization of the cosmic microwave background (CMB), the afterglow of the primordial fireball Universe, is sensitive to new physics that violates parity symmetry and may shed new light on these three elements.Dark matter and dark energy might be a new pseudoscalar field (like a pion in the SM or an axion in the extension of the SM) that couples to photons in a parity-violating manner and that has rotated the plane of linear polarization of CMB photons as they have been travelling for more than 13 billion years, an effect dubbed ‘cosmic birefringence’.A tantalizing hint of cosmic birefringence has been found in the CMB polarization data of the Planck mission with a statistical significance of 3σ.Quantum-mechanical vacuum fluctuations in spacetime in the early Universe might have produced a stochastic background of primordial gravitational waves (GWs) that are scale-invariant, Gaussian and parity-symmetric.Matter fields, such as non-Abelian gauge fields, might have produced non-scale-invariant, non-Gaussian and parity-violating GWs that could be measured in the CMB polarization, with profound implications for the fundamental physics behind ‘cosmic inflation’, the period of accelerated expansion in the very early Universe.The goal of measuring cosmic birefringence and testing the statistical properties of primordial GWs will require new observational and calibration strategies for future CMB experiments. The current cosmological model includes at least three elements (the nature of dark matter and of dark energy, and the origin of all structures in the Universe) whose explanation requires new physics beyond the standard model (SM) of elementary particles and fields. The polarization of the cosmic microwave background (CMB), the afterglow of the primordial fireball Universe, is sensitive to new physics that violates parity symmetry and may shed new light on these three elements. Dark matter and dark energy might be a new pseudoscalar field (like a pion in the SM or an axion in the extension of the SM) that couples to photons in a parity-violating manner and that has rotated the plane of linear polarization of CMB photons as they have been travelling for more than 13 billion years, an effect dubbed ‘cosmic birefringence’. A tantalizing hint of cosmic birefringence has been found in the CMB polarization data of the Planck mission with a statistical significance of 3σ. Quantum-mechanical vacuum fluctuations in spacetime in the early Universe might have produced a stochastic background of primordial gravitational waves (GWs) that are scale-invariant, Gaussian and parity-symmetric. Matter fields, such as non-Abelian gauge fields, might have produced non-scale-invariant, non-Gaussian and parity-violating GWs that could be measured in the CMB polarization, with profound implications for the fundamental physics behind ‘cosmic inflation’, the period of accelerated expansion in the very early Universe. The goal of measuring cosmic birefringence and testing the statistical properties of primordial GWs will require new observational and calibration strategies for future CMB experiments.
We search for evidence of parity-violating physics in the Planck 2018 polarization data and report on a new measurement of the cosmic birefringence angle β. The previous measurements are limited by the systematic uncertainty in the absolute polarization angles of the Planck detectors. We mitigate this systematic uncertainty completely by simultaneously determining β and the angle miscalibration using the observed cross-correlation of the E- and B-mode polarization of the cosmic microwave background and the Galactic foreground emission. We show that the systematic errors are effectively mitigated and achieve a factor-of-2 smaller uncertainty than the previous measurement, finding β=0.35±0.14 deg (68% C.L.), which excludes β=0 at 99.2% C.L. This corresponds to the statistical significance of 2.4σ.
We present a configuration-space model of the large-scale galaxy 3-point correlation function (3PCF) based on leading-order perturbation theory and including redshift-space distortions (RSD). This model should be useful in extracting distance-scale information from the 3PCF via the baryon acoustic oscillation method. We include the first redshift-space treatment of biasing by the baryon-dark matter relative velocity. Overall, on large scales the effect of RSD is primarily a renormalization of the 3PCF that is roughly independent of both physical scale and triangle opening angle; for our adopted Ωm and bias values, the rescaling is a factor of ∼1.8. We also present an efficient scheme for computing 3PCF predictions from our model, important for allowing fast exploration of the space of cosmological parameters in future analyses.
Chiral symmetry is maximally violated in weak interactions [1], and such microscopic asymmetries in the early Universe might leave observable imprints on astrophysical scales without violating the cosmological principle. In this Letter, we propose a helicity measurement to detect primordial chiral violation. We point out that observations of halo-galaxy angular momentum directions (spins), which are frozen in during the galaxy formation process, provide a fossil chiral observable. From the clustering mode of large scale structure of the Universe, we construct a spin mode in Lagrangian space and show in simulations that it is a good probe of halo-galaxy spins. In the standard model, a strong symmetric correlation between the left and right helical components of this spin mode and galaxy spins is expected. Measurements of these correlations will be sensitive to chiral breaking, providing a direct test of chiral symmetry breaking in the early Universe.
Compensated isocurvature perturbations (CIPs) are opposite spatial fluctuations in the baryon and dark matter density. They can be generated for example in the curvaton model in the early Universe but are difficult to observe because their gravitational imprint nearly cancels. We therefore propose a new measurement method by searching for a spatial modulation of the baryon acoustic oscillation (BAO) scale that CIPs induce. We find that for a Euclid-like survey the sensitivity is marginally better than the WMAP cosmic microwave background (CMB) constraint, which exploits the CIP-induced modulation of the CMB sound horizon. For a cosmic-variance limited BAO survey using emission-line galaxies up to z∼7 the sensitivity is between stage 3 and stage 4 CMB experiments. These results include using CIP-galaxy cross-correlations, which improves the sensitivity by a factor of ∼2–3 for correlated CIPs. The method could be further improved with an optimal estimator, similarly to the CMB, and could provide a useful cross-check of other CIP probes. Finally, if CIPs exist, they can bias cosmological measurements made assuming no CIPs. In particular, they can act as a supersample fluctuation of the baryon density and bias measurements of the BAO scale. For modern BAO surveys, the largest 2σ CIP fluctuation allowed by Planck’s 95% bound could bias BAO measurements of H(z) by 2.2%, partially reducing the tension with the local H0 measurements from 3.1 σ to 2.3 σ.
The reconstruction of the initial conditions of the Universe is an important topic in cosmology, particularly in the context of sharpening the measurement of the baryon acoustic oscillation (BAO) peak. Non-linear reconstruction algorithms developed in recent years, when applied to late-time matter fields, can recover to a substantial degree the initial density distribution, however, when applied to sparse tracers of the matter field, the performance is poorer. In this paper, we apply the Shi et al. non-linear reconstruction method to biased tracers in order to establish what factors affect the reconstruction performance. We find that grid resolution, tracer number density, and mass assignment scheme all have a significant impact on the performance of our reconstruction method, with triangular-shaped-cloud mass assignment and a grid resolution of ~1-2h ⁻¹ Mpc being the optimal choice. We also show that our method can be easily adapted to include generic tracer biases up to quadratic order in the reconstruction formalism. Applying the reconstruction to halo and galaxy samples with a range of tracer number densities, we find that the linear bias is by far the most important bias term, while including non-local and non-linear biases only leads to marginal improvements on the reconstruction performance. Overall, including bias in the reconstruction substantially improves the recovery of BAO wiggles, down to k∼ 0.25 h Mpc ⁻¹ for tracer number densities between 2 × 10 -4 and 2× 10 ⁻³ (h ⁻¹ Mpc) ⁻³ . © 2018 The Author(s) Published by Oxford University Press on behalf of the Royal Astronomical Society.
Under the existence of chiral non-Gaussian sources during inflation, the trispectrum of primordial curvature perturbations can break parity. We examine signatures of the induced trispectrum of the cosmic microwave background (CMB) anisotropies. It is confirmed via harmonic-space analysis that such CMB trispectrum has nonvanishing signal in the domain, as a consequence of parity violation. When the curvature trispectrum is parametrized with Legendre polynomials, the CMB signal due to the Legendre dipolar term is enhanced at the squeezed configurations in space, yielding a high signal-to-noise ratio. A Fisher matrix computation results in a minimum detectable size of the dipolar coefficient in a cosmic-variance-limited-level temperature survey as . In an inflationary model where the inflaton field couples to the gauge field via a interaction, the curvature trispectrum contains such parity-odd dipolar term. We find that, in this model, the CMB trispectrum has a high signal-to-noise ratio compared with the CMB power spectrum or bispectrum, suggesting an advantage of measuring .
Though Fourier transforms (FTs) are a common technique for finding correlation functions, they are not typically used in computations
of the anisotropy of the two-point correlation function (2PCF) about the line of sight in wide-angle surveys because the line-of-sight
direction is not constant on the Cartesian grid. Here we show how FTs can be used to compute the multipole moments of the
anisotropic 2PCF. We also show how FTs can be used to accelerate the 3PCF algorithm of Slepian & Eisenstein. In both cases,
these FT methods allow one to avoid the computational cost of pair counting, which scales as the square of the number density
of objects in the survey. With the upcoming large data sets of Dark Energy Spectroscopic Instrument, Euclid, and Large Synoptic Survey Telescope, FT techniques will therefore offer an important complement to simple pair or triplet
counts.
We present a general method for calculating the bias and variance of
estimators for w(theta) based on galaxy-galaxy (DD), random-random (RR),
and galaxy-random (DR) pair counts and describe a procedure for quickly
estimating these quantities given an arbitrary two-point correlation
function and sampling geometry. These results, based conditionally upon
the number counts, are accurate for both high and low number counts. We
show explicit analytical results for the variances in the estimators
DD/RR, DD/DR, which turn out to be considerably larger than the common
wisdom Poisson estimate and report a small bias in DD/DR in addition to
that due to the integral constraint. Further, we introduce and recommend
an improved estimator (DD - 2DR + RR)/RR, whose variance is nearly
Poisson.
With particular reference to the pancake theory of galaxy formation, the
paper calculates the attenuation or amplification of adiabatic
perturbations of a Friedmann cosmology before, during, and after the era
of hydrogen recombination and matter-radiation decoupling. The
calculation is based on a modified two-fluid (baryon, photon) model
which maintains accuracy even when the mean free path of the photon
fluid becomes arbitrarily large. It is found that in addition to the
damping of radiative viscosity and heat conduction before recombination,
damping just during decoupling is important. Consequently there is no
'velocity overshoot' of perturbations to increased amplitude (as had
been previously proposed); this probably renders the standard pancake
model inconsistent with present limits on the microwave anisotropy.
Also, the smallest surviving mass scales ('pancake masses') are quite
large, e.g., 2 x 10 to the 16th solar masses, about 120 Mpc, for Omega =
0.1.
We show that the detection of acoustic oscillations in both upcoming cosmic microwave background (CMB) satellite experiments and large-redshift surveys can yield 5% determinations of H0 and Ωm, an order-of-magnitude improvement over CMB data alone. CMB anisotropies provide the sound horizon at recombination as a standard ruler. For reasonable baryon fractions, this scale is imprinted on the galaxy power spectrum as a series of spectral features. Measuring these features in redshift space determines the Hubble constant, which in turn yields Ωm once combined with CMB data. Since the oscillations in both power spectra are frozen-in at recombination, this test is insensitive to low-redshift cosmology.
We study the effect of primordial isocurvature perturbations on non-Gaussian properties of cosmic microwave background (CMB)
temperature anisotropies. We consider generic forms of the non-linearity of isocurvature perturbations which can be applied
to a wide range of theoretical models. We derive analytical expressions for the bispectrum and the Minkowski Functionals for
CMB temperature fluctuations to describe the non-Gaussianity from isocurvature perturbations. We find that the isocurvature
non-Gaussianity in the quadratic isocurvature model, where the isocurvature perturbation S is written as a quadratic function of the Gaussian variable σ, S=σ2−〈σ2〉, can give the same signal-to-noise ratio as fNL= 30 even if we impose the current observational limit on the fraction of isocurvature perturbations contained in the primordial
power spectrum α. We give constraints on isocurvature non-Gaussianity from Minkowski Functionals using the Wilkinson Microwave Anisotropy Probe (WMAP) 5-year data. We do not find a significant signal of isocurvature non-Gaussianity. For the quadratic isocurvature model,
we obtain a stringent upper limit on the isocurvature fraction α < 0.070 (95 per cent CL) for a scale-invariant spectrum which
is comparable to the limit obtained from the power spectrum.
Perturbations of the matter density in a homogeneous and isotropic cosmological model which leads to the formation of galaxies should, at later stages of evolution, cause spatial fluctuations of relic radiation. Silk assumed that an adiabatic connection existed between the density perturbations at the moment of recombination of the initial plasma and fluctuations of the observed temperature of radiation T/T=
m
/3
m
. It is shown in this article that such a simple connection is not applicable due to:(1)
The long time of recombination;
(2)
The fact that when regions withM15
M
become transparent for radiation, the optical depth to the observer is still large due to Thompson scattering;
(3)
The spasmodic increase of
m/m
in recombination.
As a result the expected temperature fluctuations of relic radiation should be smaller than adiabatic fluctuations. In this article the value of T/T arising from scattering of radiation on moving electrons is calculated; the velocity field is generated by adiabatic or entropy density perturbations. Fluctuations of the relic radiation due to secondary heating of the intergalactic gas are also estimated. A detailed investigation of the spectrum of fluctuations may, in principle, lead to an understanding of the nature of initial density perturbations since a distinct periodic dependence of the spectral density of perturbations on wavelength (mass) is peculiar to adiabatic perturbations. Practical observations are quite difficult due to the smallness of the effects and the presence of fluctuations connected with discrete sources of radio emission.
A method is described for the numerical calculation of Fourier transforms in variables that are the logarithms of the original variable and transform variable. The method involves only the application of two successive Fourier transforms and can also be applied to Bessel and spherical Bessel transforms. Numerical examples show that the method gives very accurate results up to large values of the transform variable.
Many inflationary theories introduce new scalar, vector, or tensor degrees of
freedom that may then affect the generation of primordial density
perturbations. Here we show how to search a galaxy (or 21-cm) survey for the
imprint of primordial scalar, vector, and tensor fields. These new fields
induce local departures to an otherwise statistically isotropic two-point
correlation function, or equivalently, nontrivial four-point correlation
functions (or trispectra, in Fourier space), that can be decomposed into
scalar, vector, and tensor components. We write down the optimal estimators for
these various components and show how the sensitivity to these modes depends on
the galaxy-survey parameters. New probes of parity-violating early-Universe
physics are also presented.
We investigate the effect of supersonic relative velocities between baryons
and dark matter, recently shown to arise generically at high redshift, on
baryonic acoustic oscillation (BAO) measurements at low redshift. The amplitude
of the relative velocity effect at low redshift is model-dependent, but can be
parameterized by using an unknown bias. We find that if unaccounted, the
relative velocity effect can shift the BAO peak position and bias estimates of
the dark energy equation-of-state due to its non-smooth, out-of-phase
oscillation structure around the BAO scale. Fortunately, the relative velocity
effect can be easily modeled in constraining cosmological parameters without
substantially inflating the error budget. We also demonstrate that the presence
of the relative velocity effect gives rise to a unique signature in the galaxy
bispectrum, which can be utilized to isolate this effect. Future dark energy
surveys can accurately measure the relative velocity effect and subtract it
from the power spectrum analysis to constrain dark energy models with high
precision.
We show that pairs of widely separated interferometers are advantageous for measuring the Stokes parameter V of a stochastic background of gravitational waves. This parameter characterizes asymmetry of amplitudes of right- and left-handed waves, and generation of the asymmetry is closely related to parity violation in the early universe. The advantageous pairs include the kilometer-size interferometers LIGO (Livingston)-LCGT and AIGO-Virgo, which are relatively insensitive to Omega(GW) (the simple intensity of the background). Using at least three detectors, information of the intensity Omega(GW) and the degree of asymmetry V can be separately measured.
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