Second Order Perturbations of Flat Dust FLRW Universes with a Cosmological Constant

TL;DR

This paper investigates the evolution of second order perturbations in flat dust FLRW universes with a cosmological constant, showing they tend to constants over time, supporting the cosmic no-hair conjecture, with numerical solutions and implications for structure formation.

Contribution

It provides a numerical analysis of second order perturbations in flat dust FLRW models with a cosmological constant, confirming their asymptotic behavior and discussing implications for structure formation.

Findings

Perturbations tend to constants asymptotically.

Numerical solutions illustrate the behavior of scalar perturbations.

Results support the cosmic no-hair conjecture.

Abstract

We summarize recent results concerning the evolution of second order perturbations in flat dust irrotational FLRW models with $\Lambda\ne 0$. We show that asymptotically these perturbations tend to constants in time, in agreement with the cosmic no-hair conjecture. We solve numerically the second order scalar perturbation equation, and very briefly discuss its all time behaviour and some possible implications for the structure formation.