Simple expressions for second order density perturbations in standard cosmology

Abstract

In this paper we present four simple expressions for the relativistic first and second order fractional density perturbations for $\Lambda$CDM cosmologies in different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. A distinctive feature of our approach is the use of a canonical set of quadratic differential expressions involving an arbitrary spatial function, the so-called comoving curvature perturbation, to describe the spatial dependence, which enables us to unify, simplify and extend previous seemingly disparate results. The simple structure of the expressions makes the evolution of the density perturbations completely transparent and clearly displays the effect of the cosmological constant on the dynamics, namely that it stabilizes the perturbations. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the universe.

9 pages; some simplifications and notational changes

References in corpus (3)

• The cosmic microwave background bispectrum from the non-linear evolution of the cosmological perturbations
• Second order density perturbations for dust cosmologies
• Newtonian N-body simulations are compatible with cosmological perturbation theory

Cited by in corpus (9)

• The Intrinsic Matter Bispectrum in $\Lambda$CDM
• Galaxy bias and gauges at second order in General Relativity
• A relativistic signature in large-scale structure
• Growth of structure in interacting vacuum cosmologies
• Second order density perturbations for dust cosmologies
• Scalar field evolution at background and perturbation levels for a broad class of potentials
• Second order cosmological perturbations: new conserved quantities and the general solution at super-horizon scale
• Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019
• Relativistic perturbations in $\Lambda$CDM: Eulerian & Lagrangian approaches