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Decomposition of the dipole vector β in Galactic coordinates . The CMB dipole direction (l, b) = (263.99 @BULLET , 48.26 @BULLET ) is given as β , while two directions orthogonal to it (and each other) are denoted as β ⊥ and β × . The vector β × lies within the Galactic plane.
Source publication
Our velocity relative to the rest frame of the cosmic microwave background
(CMB) generates a dipole temperature anisotropy on the sky which has been well
measured for more than 30 years, and has an accepted amplitude of v/c =
0.00123, or v = 369km/s. In addition to this signal generated by Doppler
boosting of the CMB monopole, our motion also modul...
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Citations
... Einstein introduced gravity as a geometric property of spacetime in his General theory of relativity, which is the most celebrated theory of the last century in physics. Some recent observations in modern physics like Cosmic Microwave Background (CMB) [1,2], Type Ia supernova(SNeIa) [3,4], Baryon Acoustic Oscillations(BAOs) [5,6] has confirmed that our spatially flat homogeneous Universe that had undergone two accelerated expansion phases following the big bang: one that occurred before the radiation dominated era is known as cosmic inflation and the other one our Universe facing right now known as late time acceleration. This observational evidence strongly contradicts our fundamental understanding of gravity as an attracting force. ...
In the present article, we have explored the physical characteristics of extended f ( P ) gravity through the dynamical system analysis. We choose the function f ( P ) in the form of a polynomial of second order, i.e. f ( P ) = α P + β P 2 , where α and β are constant parameters. As an additional dark energy component, we take a canonical scalar field ϕ , and several types of interaction between the dark components are considered. After presenting the field equation for the corresponding cosmological setup, we introduce some dimensionless variables and formulate a nonlinear autonomous system. For the different interaction scenarios, we have investigated the phase space and their physical characteristics and the dynamics of the cosmological solution associated with each critical point. For the first interaction model, the results we obtained by the analysis of phase space reveals that the cosmological solution associated with critical points exhibits two different cosmological epochs, namely the de-sitter epoch and quintessence epoch. For the second interaction model, the solutions represent the quintessence era. We have also studied the dynamical stability properties of each critical point by linear stability theory and determined possible physical constraints to the parameters. The cosmological solutions support cosmic acceleration. Moreover, an analysis of statefinder parameter {r,s} in terms of the dynamical system variable is presented. Based on the mathematical prospects, the modified theory of gravitation based on the extension of f ( P ) cubic gravity has the potential to manifest an accelerated expansion during late-time evolution.
... Cosmological anisotropies of large magnitude include kinematic anisotropies due to our motion with respect to the primordial source of SGWB [58,[69][70][71][72][73][74]. For primordial sources of SGWB, we can expect a dipolar anisotropy with an amplitude one thousand smaller than the isotropic part of the background, as found in cosmic microwave background measurements [75][76][77][78]. Given that kinematic anisotropies of the SGWB are well motived, we mainly consider a kinematic dipole as specific target for our analysis, although it can be easily extended to discuss other anisotropies as well. ...
... The simple form of the SGWB anisotropy of equation (2.7) is all what we need to carry on our calculations. We include only the kinematic dipole contribution proportional to β, working under the hypothesis of small relative velocity among frames -supported by observations of the cosmic microwave background (CMB) dipolar anisotropy of the CMB temperature [75][76][77][78]. It is important to emphasize that kinematic effects are associated with deterministic -and not statistical -anisotropies. ...
High-precision astrometry offers a promising approach to detect low-frequency gravitational waves, complementing pulsar timing array (PTA) observations. We explore the response of astrometric measurements to a stochastic gravitational wave background (SGWB) in synergy with PTA data. Analytical, covariant expressions for this response are derived, accounting for the presence of a possible dipolar anisotropy in the SGWB. We identify the optimal estimator for extracting SGWB information from astrometric observations and examine how sensitivity to SGWB properties varies with the sky positions of stars and pulsars. Using representative examples of current PTA capabilities and near-future astrometric sensitivity, we demonstrate that cross-correlating astrometric and PTA data can improve constraints on SGWB properties, compared to PTA data alone. The improvement is quantified through Fisher forecasts for the SGWB amplitude, spectral tilt, and dipolar anisotropy amplitude. In the future, such joint constraints could play a crucial role in identifying the origin of SGWB signals detected by PTAs.
... A number of tests for consistency of this measurement with its kinematic interpretation are possible using CMB data alone. For ex-ample, measurements of the dipolar modulation of the higher multipole temperature fluctuations, expected from special relativistic aberration [6], generally agree in amplitude and direction with that of the dipole itself [7,8]. While such measurements, within measurement uncertainties, support the kinematic origin hypothesis, they do not exclude other scenarios, such as those in which large-scale isocurvature perturbations contribute to the CMB dipole [9][10][11][12][13]. ...
The dipole anisotropy induced by our peculiar motion in the sky distribution of cosmologically distant sources is an important consistency test of the standard FLRW cosmology. In this work, we formalize how to compute the kinematic matter dipole in redshift bins. Apart from the usual terms arising from angular aberration and flux boosting, there is a contribution from the boosting of the redshifts that becomes important when considering a sample selected on observed redshift, leading to non-vanishing correction terms. We discuss examples and provide expressions to incorporate arbitrary redshift selection functions. We also discuss the effect of redshift measurement uncertainties in this context, in particular in upcoming surveys for which we provide estimates of the correction terms. Depending on the shape of a sample's redshift distribution and on the applied redshift cuts, the correction terms can become substantial, even to the degree that the direction of the dipole is reversed. Lastly, we discuss how cuts on variables correlated with observed redshift, such as color, can induce additional correction terms.
... Finally, it is worth mentioning that the relativistic aberration and the Doppler effect associated with the motion of the observer w.r.t. the CMB frame also distorts the pattern of CMB anisotropies [20]. These signatures, first detected with the Planck satellite, are consistent with the kinematic interpretation of the dipole [68] and have been used to set an upper limit on the amplitude of the intrinsic dipole [22,35]. ...
Our peculiar velocity imprints a dipole on galaxy density maps derived from redshift surveys. The dipole gives rise to an oscillatory signal in the multipole moments of the observed power spectrum which we indicate as the finger-of-the-observer (FOTO) effect. Using a suite of large mock catalogues mimicking ongoing and future - and -selected surveys, we demonstrate that the oscillatory features can be measured with a signal-to-noise ratio of up to 7 (depending on the sky area coverage and provided that observational systematics are kept under control on large scales). We also show that the FOTO effect cannot be erased by correcting the individual galaxy redshifts. On the contrary, by leveraging the power of the redshift corrections, we propose a novel method to determine both the magnitude and the direction of our peculiar velocity. After applying this technique to our mock catalogues, we conclude that it can be used to either test the kinematic interpretation of the temperature dipole in the cosmic microwave background or to extract cosmological information such as the matter density parameter and the equation of state of dark energy.
... For the first case of GW sources from the early universe, the largest contribution to SGWB anisotropies is associated to kinematic Doppler effects, due to our motion with respect to the source of SGWB [40,63]. They are the GW analog to kinematic effects measured in the cosmic microwave background radiation [64][65][66][67][68]. Kinematic anisotropies in the SGWB are deterministically controlled by the isotropic part of the background, and the amplitude of the kinematic dipole is expected to be of order Oð10 −3 Þ smaller than the isotropic monopole. ...
... wheren is the GW direction, andv the relative velocity among frames. Since in this and the next section we are assuming a cosmological origin for the SGWB, we expect β to be of the same order of the value measured by cosmic microwave background: β ¼ 1.2 × 10 −3 [64][65][66][67][68]. With β being small, we can expand both quantities in (2.16) at first order in β, and plug the resulting expressions in the response functions of Eqs. ...
The circular polarization of the stochastic gravitational wave background (SGWB) is a key observable for characterizing the origin of the signal detected by Pulsar Timing Array (PTA) collaborations. Both the astrophysical and the cosmological SGWB can have a sizeable amount of circular polarization, due to Poisson fluctuations in the source properties for the former, and to parity violating processes in the early universe for the latter. Its measurement is challenging since PTA are blind to the circular polarization monopole, forcing us to turn to anisotropies for detection. We study the sensitivity of current and future PTA datasets to circular polarization anisotropies, focusing on realistic modelling of intrinsic and kinematic anisotropies for astrophysical and cosmological scenarios respectively. Our results indicate that the expected level of circular polarization for the astrophysical SGWB should be within the reach of near future datasets, while for cosmological SGWB circular polarization is a viable target for more advanced SKA-type experiments.
Published by the American Physical Society 2024
... However, in addition to intrinsic anisotropies, cosmological SGWB are expected to be characterized by a level of kinematic Doppler anisotropy similar to what has been observed by cosmic microwave background (CMB) experiments. According to CMB observations, our velocity with respect to the cosmic rest frame has a magnitude β ¼ v=c ¼ 1.23 × 10 −3 , and is directed towards ðl; bÞ ¼ ð264°; 48°Þ in galactic coordinates [26][27][28][29][30]. ...
Recent pulsar timing array (PTA) collaborations show strong evidence for a stochastic gravitational wave background (SGWB) with the characteristic Hellings-Downs interpulsar correlations. The signal may stem from supermassive black hole binary mergers, or early Universe phenomena. The former is expected to be strongly anisotropic, while primordial backgrounds are likely to be predominantly isotropic with small fluctuations. In the case the observed SGWB is of cosmological origin, our relative motion with respect to the SGWB rest frame is a guaranteed source of anisotropy, leading to O ( 10 − 3 ) energy density fluctuations of the SGWB. For such cosmological SGWB, kinematic anisotropies are likely to be larger than the intrinsic anisotropies, akin to the cosmic microwave background (CMB) dipole anisotropy. We assess the sensitivity of current PTA data to the kinematic dipole anisotropy, and we also forecast at what extent the magnitude and direction of the kinematic dipole can be measured in the future with an SKA-like experiment. We also discuss how the spectral shape of the SGWB and the location of the pulsars to monitor affect the prospects of detecting the kinematic dipole with PTA. In the future, a detection of this anisotropy may even help resolve the discrepancy in the magnitude of the kinematic dipole as measured by CMB and large-scale structure observations.
Published by the American Physical Society 2024
... For the first case of GW sources from the early universe, the largest contribution to SGWB anisotropies is associated to kinematic Doppler effects, due to our motion with respect to the source of SGWB [40,63]. They are the GW analog to kinematic effects measured in the cosmic microwave background radiation [64][65][66][67][68]. Kinematic anisotropies in the SGWB are deterministically controlled by the isotropic part of the background, and the amplitude of the kinematic dipole is expected to be of order O(10 −3 ) smaller than the isotropic monopole. ...
... wheren is the GW direction, andv the relative velocity among frames. Since in this and the next section we are assuming a cosmological origin for the SGWB, we expect β to be of the same order of the value measured by cosmic microwave background: β = 1.2 × 10 −3 [64][65][66][67][68]. ...
The circular polarization of the stochastic gravitational wave background (SGWB) is a key observable for characterising the origin of the signal detected by Pulsar Timing Array (PTA) collaborations. Both the astrophysical and the cosmological SGWB can have a sizeable amount of circular polarization, due to Poisson fluctuations in the source properties for the former, and to parity violating processes in the early universe for the latter. Its measurement is challenging since PTA are blind to the circular polarization monopole, forcing us to turn to anisotropies for detection. We study the sensitivity of current and future PTA datasets to circular polarization anisotropies, focusing on realistic modelling of intrinsic and kinematic anisotropies for astrophysical and cosmological scenarios respectively. Our results indicate that the expected level of circular polarization for the astrophysical SGWB should be within the reach of near future datasets, while for cosmological SGWB circular polarization is a viable target for more advanced SKA-type experiments.
... If the SGWB has cosmological origin, besides its intrinsic anisotropies, the signal is expected to be characterized by a Doppler anisotropy due to our relative motion with respect to the source rest frame. As found by cosmic microwave background (CMB) experiments [24][25][26][27], our velocity with respect to the cosmic rest frame has an amplitude of size β ¼ v=c ¼ 1.23 × 10 −3 with respect to the velocity of light, and points in the direction ðl; bÞ ¼ ð264°; 48°Þ. Correspondingly, the size of the dipolar kinematic anisotropy of a cosmological SGWB should be one-thousandth smaller than the amplitude of the isotropic part of the GW spectrum. ...
... In fact, kinematic anisotropies are a guaranteed property of a SGWB of primordial origin: their features are fully calculable, being determined by the properties of the isotropic part of the SGWB. If the SGWB has a cosmological origin related with early-universe physics, we can expect that the relative motion among frames induces an effect analog to the large dipolar anisotropy measured in the CMB [24][25][26][27], whose amplitude is a factor 1.2 × 10 −3 times smaller than the isotropic background. For the case of the CMB, the dipolar kinematic anisotropy is well larger in size than its intrinsic anisotropies. ...
Doppler anisotropies, induced by our relative motion with respect to the source rest frame, are a guaranteed property of stochastic gravitational wave backgrounds of cosmological origin. If detected by future pulsar timing array measurements, they will provide interesting information on the physics sourcing gravitational waves, which is hard or even impossible to extract from measurements of the isotropic part of the background only. We analytically determine the pulsar response function to kinematic anisotropies, including possible effects due to parity violation, to features in the frequency dependence of the isotropic part of the spectrum, as well as to the presence of extra scalar and vector polarizations. For the first time, we show how the sensitivity to different effects crucially depends on the pulsar configuration with respect to the relative motion among frames. Correspondingly, we propose examples of strategies of detection, each aimed at exploiting future measurements of kinematic anisotropies for characterizing distinct features of the cosmological gravitational wave background.
... If the SGWB has cosmological origin, besides its intrinsic anisotropies, the signal is expected to be characterised by a Doppler anisotropy due to our relative motion with respect to the source rest frame. As found by cosmic microwave background (CMB) experiments [24][25][26][27], our velocity with respect to the cosmic rest frame has an amplitude of size β = v/c = 1.23 × 10 −3 with respect to the velocity of light, and points in the direction (l, b) = (264 o , 48 o ). Correspondigly, the size of the dipolar kinematic anisotropy of a cosmological SGWB should be one-thousandth smaller than the amplitude of the isotropic part of the GW spectrum. ...
... In fact, kinematic anisotropies are a guaranteed property of a SGWB of primordial origin: their features are fully calculable, being determined by the properties of the isotropic part of the SGWB. If the SGWB has a cosmological origin related with early-universe physics, we can expect that the relative motion among frames induces an effect analog to the large dipolar anisotropy measured in the CMB [24][25][26][27], whose amplitude is a factor 1.2 × 10 −3 times smaller than the isotropic background. For the case of the CMB, the dipolar kinematic anisotropy is well larger in size than its intrinsic anisotropies. ...
Doppler anisotropies, induced by our relative motion with respect to the source rest frame, are a guaranteed property of stochastic gravitational wave backgrounds of cosmological origin. If detected by future pulsar timing array measurements, they will provide interesting information on the physics sourcing gravitational waves, which is hard or even impossible to extract from measurements of the isotropic part of the background only. We analytically determine the pulsar response function to kinematic anisotropies, including possible effects due to parity violation, to features in the frequency dependence of the isotropic part of the spectrum, as well as to the presence of extra scalar and vector polarizations. For the first time, we show how the sensitivity to different effects crucially depends on the pulsar configuration with respect to the relative motion among frames. Correspondingly, we propose examples of strategies of detection, each aimed at exploiting future measurements of kinematic anisotropies for characterizing distinct features of the cosmological gravitational wave background.
... The circles-in-the-sky searches for topology performed on WMAP [25,40,[42][43][44][45][46][47] and Planck data [49,61] (as well as a general unpublished search analogous to Ref. [46]) constrain the shortest non-trivial closed loop through the Earth to have a length greater than 98.5% of the diameter of the LSS. The translation of this limit to limits on the parameters characterizing the manifolds E i is underway; the results for the orientable manifolds E 1 -E 6 , E 11 , E 12 , and E 16 are in Ref. [62], and the non-orientable manifolds will be presented in an upcoming paper [63]. ...
If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies - , , , , and that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.
