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Register a new userMeasuring anisotropic stress with relativistic effects
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Added by
Daniel Sobral Blanco
Publication date
2021
fields
Physics
and research's language is
English
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One of the main goal of large-scale structure surveys is to test the consistency of General Relativity at cosmological scales. In the $Lambda$CDM model of cosmology, the relations between the fields describing the geometry and the content of our Universe are uniquely determined. In particular, the two gravitational potentials -- that describe the spatial and temporal fluctuations in the geometry -- are equal. Whereas large classes of dark energy models preserve this equality, theories of modified gravity generally create a difference between the potentials, known as anisotropic stress. Even though measuring this anisotropic stress is one of the key goals of large-scale structure surveys, there are currently no methods able to measure it directly. Current methods all rely on measurements of galaxy peculiar velocities (through redshift-space distortions), from which the time component of the metric is inferred, assuming that dark matter follows geodesics. If this is not the case, all the proposed tests fail to measure the anisotropic stress. In this letter, we propose a novel test which directly measures anisotropic stress, without relying on any assumption about the unknown dark matter. Our method uses relativistic effects in the galaxy number counts to provide a direct measurement of the time component of the metric. By comparing this with lensing observations our test provides a direct measurement of the anisotropic stress.
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We study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck data. Then, we analyze the role played by these parameters in the linear PS. In order for the anisotropic stress not to provoke deviations larger than $10%$ and $5%$ with respect to the $Lambda$CDM PS at $k sim 0.01 ,h/text{Mpc}$, the parameters have to be in the range $-0.30< g_0 < 0.32$, $0 leq c_g^2 < 0.01$ and $-0.15 < g_0 < 0.16$, $0 leq c_g^2 < 0.01$, respectively. Additionally, we compute the leading nonlinear corrections to the PS using standard perturbation theory in real and redshift space, showing that the differences with respect to the $Lambda$CDM are enhanced, especially for the quadrupole and hexadecapole RSD multipoles.
The effective anisotropic stress or gravitational slip $eta=-Phi/Psi$ is a key variable in the characterisation of the physical origin of the dark energy, as it allows to test for a non-minimal coupling of the dark sector to gravity in the Jordan frame. It is however important to use a fully model-independent approach when measuring $eta$ to avoid introducing a theoretical bias into the results. In this paper we forecast the precision with which future large surveys can determine $eta$ in a way that only relies on directly observable quantities. In particular, we do not assume anything concerning the initial spectrum of perturbations, nor on its evolution outside the observed redshift range, nor on the galaxy bias. We first leave $eta$ free to vary in space and time and then we model it as suggested in Horndeski models of dark energy. Among our results, we find that a future large scale lensing and clustering survey can constrain $eta$ to within 10% if $k$-independent, and to within 60% or better at $k=0.1 h/$Mpc if it is restricted to follow the Horndeski model.
We make precise the heretofore ambiguous statement that anisotropic stress is a sign of a modification of gravity. We show that in cosmological solutions of very general classes of models extending gravity --- all scalar-tensor theories (Horndeski), Einstein-Aether models and bimetric massive gravity --- a direct correspondence exists between perfect fluids apparently carrying anisotropic stress and a modification in the propagation of gravitational waves. Since the anisotropic stress can be measured in a model-independent manner, a comparison of the behavior of gravitational waves from cosmological sources with large-scale-structure formation could in principle lead to new constraints on the theory of gravity.
We study the imprints of an effective dark energy fluid in the large scale structure of the universe through the observed angular power spectrum of galaxies in the relativistic regime. We adopt the phenomenological approach that introduces two parameters ${Q,eta}$ at the level of linear perturbations and allow to take into account the modified clustering (or effective gravitational constant) and anisotropic stress appearing in models beyond $Lambda$CDM. We characterize the effective dark energy fluid by an equation of state parameter $w=-0.95$ and various sound speed cases in the range $10^{-6}leq c^2_sleq 1$, thus covering K-essence and quintessence cosmologies. We calculate the angular power spectra of standard and relativistic effects for these scenarios under the ${Q,eta}$ parametrization, and we compare these relative to a fiducial $Lambda$CDM cosmology. We find that, overall, deviations relative to $Lambda$CDM are stronger at low redshift since the behavior of the dark energy fluid can mimic the cosmological constant during matter domination era but departs during dark energy domination. In particular, at $z=0.1$ the matter density fluctuations are suppressed by up to $sim3%$ for the quintessence-like case, while redshift-space distortions and Doppler effect can be enhanced by $sim15%$ at large scales for the lowest sound speed scenario. On the other hand, at $z=2$ we find deviations of up to $sim5%$ in gravitational lensing, whereas the Integrated Sachs-Wolfe effect can deviate up to $sim17%$. Furthermore, when considering an imperfect dark energy fluid scenario, we find that all effects are insensitive to the presence of anisotropic stress at low redshift, and only the Integrated Sachs-Wolfe effect can detect this feature at $z=2$ and very large scales.
The observed galaxy distribution via galaxy redshift surveys appears distorted due to redshift-space distortions (RSD). While one dominant contribution to RSD comes from the Doppler effect induced by the peculiar velocity of galaxies, the relativistic effects, including the gravitational redshift effect, are recently recognized to give small but important contributions. Such contributions lead to an asymmetric galaxy clustering along the line of sight, and produce non-vanishing odd multipoles when cross-correlating between different biased objects. However, non-zero odd multipoles are also generated by the Doppler effect beyond the distant-observer approximation, known as the wide-angle effect, and at quasi-linear scales, the interplay between wide-angle and relativistic effects becomes significant. In this paper, based on the formalism developed by Taruya et al., we present a quasi-linear model of the cross-correlation function taking a proper account of both the wide-angle and gravitational redshift effects, as one of the major relativistic effects. Our quasi-linear predictions of the dipole agree well with simulations even at the scales below $20,h^{-1},$Mpc, where non-perturbative contributions from the halo potential play an important role, flipping the sign of the dipole amplitude. When increasing the bias difference and redshift, the scale where the sign flip happens is shifted to a larger scale. We derive a simple approximate formula to quantitatively account for the behaviors of the sign flip.
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