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.
The observed galaxy power spectrum acquires relativistic corrections from lightcone effects, and these corrections grow on very large scales. Future galaxy surveys in optical, infrared and radio bands will probe increasingly large wavelength modes an
d reach higher redshifts. In order to exploit the new data on large scales, an accurate analysis requires inclusion of the relativistic effects. This is especially the case for primordial non-Gaussianity and for extending tests of dark energy models to horizon scales. Here we investigate the latter, focusing on models where the dark energy interacts non-gravitationally with dark matter. Interaction in the dark sector can also lead to large-scale deviations in the power spectrum. If the relativistic effects are ignored, the imprint of interacting dark energy will be incorrectly identified and thus lead to a bias in constraints on interacting dark energy on very large scales.
We discuss the question of gauge choice when analysing relativistic density perturbations at second order. We compare Newtonian and General Relativistic approaches. Some misconceptions in the recent literature are addressed. We show that the comoving
-synchronous gauge is the unique gauge in General Relativity that corresponds to the Lagrangian frame and is entirely appropriate to describe the matter overdensity at second order. The comoving-synchronous gauge is the simplest gauge in which to describe Lagrangian bias at second order.
If dark energy and dark matter interact via exchange of energy and momentum, then this may affect the galaxy power spectrum on large scales. When this happens, it may be degenerate with the signal from primordial non-Gaussianity via scale-dependent b
ias. We consider a class of interacting dark energy models and show that the matter overdensity is scale-dependent on large scales. We estimate the effective non-Gaussianity arising from the large-scale effects of interaction in the dark sector. The signal of dark sector interaction can be disentangled from a primordial non-Gaussian signal by measuring the power at two redshifts.
We study up to second order the galaxy number over-density that depends on magnification in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order which arise from observ
ing on the past light cone, including all redshift and lensing distortions, contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. We find several new terms and contributions that could be potentially important for an accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates.
We present a detailed derivation of the observed galaxy number over-density on cosmological scales up to second order in perturbation theory. We include all relativistic effects that arise from observing on the past lightcone. The derivation is in a
general gauge, and applies to all dark energy models (including interacting dark energy) and many modified gravity models. The result will be important for accurate cosmological parameter estimation, including non-Gaussianity, since all projection effects need to be taken into account. It also offers the potential for new probes of General Relativity, dark energy and modified gravity. This paper accompanies Paper I which presents the key results for the concordance model in Poisson gauge.
We present the galaxy number overdensity up to second order in redshift space on cosmological scales for a concordance model. The result contains all general relativistic effects up to second order that arise from observing on the past light cone, in
cluding all redshift effects, lensing distortions from convergence and shear, and contributions from velocities, Sachs-Wolfe, integrated SW and time-delay terms. This result will be important for accurate calculation of the bias on estimates of non-Gaussianity and on precision parameter estimates, introduced by nonlinear projection effects.
Galaxy clustering on very large scales can be probed via the 2-point correlation function in the general case of wide and deep separations, including all the lightcone and relativistic effects. Using our recently developed formalism, we analyze the b
ehavior of the local and integrated contributions and how these depend on redshift range, linear and angular separations and luminosity function. Relativistic corrections to the local part of the correlation can be non-negligible but they remain generally sub-dominant. On the other hand, the additional correlations arising from lensing convergence and time-delay effects can become very important and even dominate the observed total correlation function. We investigate different configurations formed by the observer and the pair of galaxies, and we find that the case of near-radial large-scale separations is where these effects will be the most important.
We investigate the properties of the 2-point galaxy correlation function at very large scales, including all geometric and local relativistic effects -- wide-angle effects, redshift space distortions, Doppler terms and Sachs-Wolfe type terms in the g
ravitational potentials. The general three-dimensional correlation function has a nonzero dipole and octupole, in addition to the even multipoles of the flat-sky limit. We study how corrections due to primordial non-Gaussianity and General Relativity affect the multipolar expansion, and we show that they are of similar magnitude (when f_NL is small), so that a relativistic approach is needed. Furthermore, we look at how large-scale corrections depend on the model for the growth rate in the context of modified gravity, and we discuss how a modified growth can affect the non-Gaussian signal in the multipoles.
Quintessence can cluster only on horizon scales. What is the effect on the observed matter distribution? To answer this, we need a relativistic approach that goes beyond the standard Newtonian calculation and deals properly with large scales. Such an
approach has recently been developed for the case when dark energy is vacuum energy, which does not cluster at all. We extend this relativistic analysis to deal with dynamical dark energy. Using three quintessence potentials as examples, we compute the angular power spectrum for the case of an HI intensity map survey. Compared to the concordance model with the same small-scale power at z=0, quintessence boosts the angular power by up to ~15% at high redshifts, while power in the two models converges at low redshifts. The difference is mainly due to the background evolution, driven mostly by the normalization of the power spectrum today. The dark energy perturbations make only a small contribution on the largest scales, and a negligible contribution on smaller scales. Ironically, the dark energy perturbations remove the false boost of large-scale power that arises if we impose the (unphysical) assumption that the dark energy is smooth.
