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Register a new userA relativistic signature in large-scale structure
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Added by
Daniele Bertacca DR.
Publication date
2015
fields
Physics
and research's language is
English
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In General Relativity, the constraint equation relating metric and density perturbations is inherently nonlinear, leading to an effective non-Gaussianity in the dark matter density field on large scales - even if the primordial metric perturbation is Gaussian. Intrinsic non-Gaussianity in the large-scale dark matter overdensity in GR is real and physical. However, the variance smoothed on a local physical scale is not correlated with the large-scale curvature perturbation, so that there is no relativistic signature in the galaxy bias when using the simplest model of bias. It is an open question whether the observable mass proxies such as luminosity or weak lensing correspond directly to the physical mass in the simple halo bias model. If not, there may be observables that encode this relativistic signature.
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We show how the non-linearity of general relativity generates a characteristic non-Gaussian signal in cosmological large-scale structure that we calculate at all perturbative orders in a large scale limit. Newtonian gravity and general relativity provide complementary theoretical frameworks for modelling large-scale structure in $Lambda$CDM cosmology; a relativistic approach is essential to determine initial conditions which can then be used in Newtonian simulations studying the non-linear evolution of the matter density. Most inflationary models in the very early universe predict an almost Gaussian distribution for the primordial metric perturbation, $zeta$. However, we argue that it is the Ricci curvature of comoving-orthogonal spatial hypersurfaces, $R$, that drives structure formation at large scales. We show how the non-linear relation between the spatial curvature, $R$, and the metric perturbation, $zeta$, translates into a specific non-Gaussian contribution to the initial comoving matter density that we calculate for the simple case of an initially Gaussian $zeta$. Our analysis shows the non-linear signature of Einsteins gravity in large-scale structure.
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.
We discuss the relation between the output of Newtonian N-body simulations on scales that approach or exceed the particle horizon to the description of General Relativity. At leading order, the Zeldovich approximation is correct on large scales, coinciding with the General Relativistic result. At second order in the initial metric potential, the trajectories of particles deviate from the second order Newtonian result and hence the validity of 2LPT initial conditions should be reassessed when used in very large simulations. We also advocate using the expression for the synchronous gauge density as a well behaved measure of density fluctuations on such scales.
The recent measurement of the gravitational redshifts of galaxies in galaxy clusters by Wojtak et al. has opened a new observational window on dark matter and modified gravity. By stacking clusters this determination effectively used the line of sight distortion of the cross-correlation function of massive galaxies and lower mass galaxies to estimate the gravitational redshift profile of clusters out to 4 Mpc/h. Here we use a halo model of clustering to predict the distortion due to gravitational redshifts of the cross-correlation function on scales from 1 - 100 Mpc/h. We compare our predictions to simulations and use the simulations to make mock catalogues relevant to current and future galaxy redshift surveys. Without formulating an optimal estimator, we find that the full BOSS survey should be able to detect gravitational redshifts from large-scale structure at the ~4 sigma level. Upcoming redshift surveys will greatly increase the number of galaxies useable in such studies and the BigBOSS and Euclid experiments should be capable of measurements with precision at the few percent level. As has been recently pointed out by McDonald, Kaiser and Zhao et al, other interesting effects including relativistic beaming and transverse Doppler shift can add additional asymmetric distortions to the correlation function. While these contributions are subdominant to the gravitational redshift on large scales, they represent additional opportunities to probe gravitational physics and indicate that many qualitatively new measurements should soon be possible using large redshift surveys.
A relativistic theory of modified gravity has been recently proposed by Bekenstein. The tensor field in Einsteins theory of gravity is replaced by a scalar, a vector, and a tensor field which interact in such a way to give Modified Newtonian Dynamics (MOND) in the weak-field non-relativistic limit. We study the evolution of the universe in such a theory, identifying its key properties and comparing it with the standard cosmology obtained in Einstein gravity. The evolution of the scalar field is akin to that of tracker quintessence fields. We expand the theory to linear order to find the evolution of perturbations on large scales. The impact on galaxy distributions and the cosmic microwave background is calculated in detail. We show that it may be possible to reproduce observations of the cosmic microwave background and galaxy distributions with Bekensteins theory of MOND.
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