Second-order Cosmological Perturbation Research Articles

Second-order dust perturbations of the non-flat FLRW model with the positive cosmological constant

In this paper, a specific solution to the second-order cosmological perturbation theory is given. Perturbations are performed around any Friedmann–Lemaître–Robertson–Walker spacetime filled with dust and with a positive cosmological constant. In particular, with a possibly non-vanishing spatial curvature. The adopted symmetry condition allows us to simplify the equations, leaving us with a great deal of freedom to choose the density distribution. In the result, we get a relatively simple metric of an inhomogeneous cosmological model, which will give a perfect tool for studying the influence of the local inhomogeneities onto the cosmological observables.

Cosmic microwave background spectral distortions from Rayleigh scattering at second order

Cosmic microwave background (CMB) spectral distortion from Rayleigh scattering is calculated for the first time in rigorous second-order cosmological perturbation theory. The new spectral distortion is sensitive to acoustic dissipation at $10^{-2}<k{\rm Mpc}/h<1$, which slightly extends the scale constrained by the CMB anisotropies. The spectral shape is different from either temperature perturbations or any other traditional spectral distortions from Compton scattering, such as $y$ and $\mu$. The new spectral distortion is not formed in the late Universe, unlike the thermal Sunyaev-Zel'dovich effect degenerated with the primordial $y$ distortions since photons must be hot for Rayleigh scattering. Therefore, ideal measurements can distinguish the signal from the other effects and extract new information during recombination. Assuming cosmological parameters consistent with the recent CMB anisotropy measurements, we find the new spectral distortion is $6.5\times 10^{-3}$Jy/str, which is one order of magnitude smaller than the currently proposed target sensitivity range of voyage 2050.

Multi-scale perturbation theory II: Solutions and leading-order bispectrum in the ΛCDM universe

Two-parameter perturbation theory (2PPT) is a framework designed to include the relativistic gravitational effects of small-scale nonlinear structures on the large-scale properties of the Universe. In this paper we use the 2PPT framework to calculate and study the bispectrum of matter in a spatially-flat ΛCDM cosmology. This is achieved by deploying Newtonian perturbation theory to model the gravitational fields of quasi-nonlinear structures, and then subsequently using them as source terms for the large-scale cosmological perturbations. We find that our approach reproduces some of the expected relativistic effects from second-order cosmological perturbation theory, but not all. This work therefore provides a first step in deploying a formalism that can simultaneously model the weak gravitational fields of both linear and nonlinear structures in a realistic model of the Universe.

The observed galaxy bispectrum from single-field inflation in the squeezed limit

Using the consistency relation in Fourier space, we derive the observed galaxy bispectrum from single-field inflation in the squeezed limit, in which one of the three modes has a wavelength much longer than the other two. This provides a non-trivial check of the full computation of the bispectrum based on second-order cosmological perturbation theory in this limit. We show that gauge modes need to be carefully removed in the second-order cosmological perturbations in order to calculate the observed galaxy bispectrum in the squeezed limit. We then give an estimate of the effective non-Gaussianity due to general-relativistic lightcone effects that could mimic a primordial non-Gaussian signal.

Second-order cosmological perturbation theory and initial conditions forN-body simulations

We use gauge-invariant cosmological perturbation theory to calculate the displacement field that sets the initial conditions for $N$-body simulations. Using first and second-order fully relativistic perturbation theory in the synchronous-comoving gauge, allows us to go beyond the Newtonian predictions and to calculate relativistic corrections to it. We use an Einstein--de Sitter model, including both growing and decaying modes in our solutions. The impact of our results should be assessed through the implementation of the featured displacement in cosmological $N$-body simulations.

Non-Gaussianity from the second-order cosmological perturbation

Several conserved and/or gauge invariant quantities described as the second-order curvature perturbation have been given in the literature. We revisit various scenarios for the generation of second-order non-gaussianity in the primordial curvature perturbation \zeta, employing for the first time a unified notation and focusing on the normalisation f_{NL} of the bispectrum. When the classical curvature perturbation first appears a few Hubble times after horizon exit, |f_{NL}| is much less than 1 and is, therefore, negligible. Thereafter \zeta (and hence f_{NL}) is conserved as long as the pressure is a unique function of energy density (adiabatic pressure). Non-adiabatic pressure comes presumably only from the effect of fields, other than the one pointing along the inflationary trajectory, which are light during inflation (`light non-inflaton fields'). During single-component inflation f_{NL} is constant, but multi-component inflation might generate |f_{NL}| \sim 1 or bigger. Preheating can affect f_{NL} only in atypical scenarios where it involves light non-inflaton fields. The curvaton scenario typically gives f_{NL} \ll -1 or f_{NL} = +5/4. The inhomogeneous reheating scenario can give a wide range of values for f_{NL}. Unless there is a detection, observation can eventually provide a limit |f_{NL}| \lsim 1, at which level it will be crucial to calculate the precise observational limit using second order theory.

Non-Gaussianity in the curvaton scenario

Since a positive future detection of non-linearity in the cosmic microwave background anisotropy pattern might allow to descriminate among different mechanisms giving rise to cosmological adiabatic perturbations, we study the evolution of the second-order cosmological curvature perturbation on super-horizon scales in the curvaton scenario. We provide the exact expression for the non-Gaussianity in the primordial perturbations including gravitational second-order corrections which are particularly relevant in the case in which the curvaton dominates the energy density before it decays. As a byproduct, we show that in the standard scenario where cosmological curvature perturbations are induced by the inflaton field, the second-order curvature perturbation is conserved even during the reheating stage after inflation.