Several recent studies have shown how to properly calculate the observed clustering of galaxies in a relativistic context, and uncovered corrections to the Newtonian calculation that become significant on scales near the horizon. Here, we retrace these calculations and show that, on scales approaching the horizon, the observed galaxy power spectrum depends strongly on which gauge is assumed to relate the intrinsic fluctuations in galaxy density to matter perturbations through a linear bias relation. Starting from simple physical assumptions, we derive a gauge-invariant expression relating galaxy density perturbations to matter density perturbations on large scales, and show that it reduces to a linear bias relation in a synchronous-comoving gauge, corroborating an assumption made in several recent papers. We evaluate the resulting observed galaxy power spectrum, and show that it leads to corrections similar to an effective non-Gaussian bias corresponding to a local $f_{\mathrm{NL},\mathrm{eff}}\lesssim 0.5$. This number can serve as a guideline as to which surveys need to take into account relativistic effects. We also discuss the scale-dependent bias induced by primordial non-Gaussianity in the relativistic context, which again is simplest in a synchronous-comoving gauge.

We compare the non-linear matter power spectrum in real space calculated analytically from 3rd-order perturbation theory with N-body simulations at 11, the shape of oscillations is distorted from the linear theory prediction. Nevertheless, our results suggest that one can correct the distortion caused by non-linearity almost exactly. We also find that perturbation theory, which does not contain any free parameters, provides a significantly better fit to the simulations than the conventional approaches based on empirical fitting functions to simulations. The future work would include perturbation theory calculations of non-linearity in redshift space distortion and halo biasing in the weakly non-linear regime.Comment: 6 pages, 7 figures, submitted to ApJ. (v2) Four figures have been added to show the residual between theory and N-body simulations for clarity, the dependence of non-linearity on sigma8, and convergence tests of the results. An artificial numerical smoothing of baryonic oscillations from COSMICS has been fixed in Fig.

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 study the dissipation of small-scale adiabatic perturbations at early times when the Universe is hotter than $T\simeq 0.5\mathrm{keV}$. When the wavelength falls below the damping scale $k_D^{-1}$, the acoustic modes diffuse and thermalize, causing entropy production. Before neutrino decoupling, $k_D$ is primarily set by the neutrino shear viscosity, and we study the effect of acoustic damping on the relic neutrino number, primordial nucleosynthesis, dark-matter freeze-out, and baryogenesis. This sets a new limit on the amplitude of primordial fluctuations of ${\mathrm{\Delta }}_{\mathcal{R}}^2<0.007$ at $10^4{\mathrm{Mpc}}^{-1}\lesssim k\lesssim 10^5{\mathrm{Mpc}}^{-1}$ and a model-dependent limit of ${\mathrm{\Delta }}_{\mathcal{R}}^2\lesssim 0.3$ at $k\lesssim 10^{20–25}{\mathrm{Mpc}}^{-1}$.