Analytical growth functions for cosmic structures in a $\Lambda$CDM Universe

TL;DR

This paper develops high-order perturbative solutions for cosmic structure growth in a $\Lambda$CDM universe, revealing subtle effects of dark energy on matter clustering and providing refined tools for cosmological data analysis.

Contribution

It introduces a novel high-order perturbative approach incorporating the cosmological constant, improving the accuracy of matter power spectrum and bispectrum predictions.

Findings

Refined growth functions impact power and bispectra below 1% at late times.

Characteristic scale-dependent suppression similar to massive neutrino effects.

Provides a method to reduce theoretical uncertainties in cosmological analyses.

Abstract

The cosmological fluid equations describe the early gravitational dynamics of cold dark matter (CDM), exposed to a uniform component of dark energy, the cosmological constant $\Lambda$. Perturbative predictions for the fluid equations typically assume that the impact of $\Lambda$ on CDM can be encapsulated by a refined growing mode $D$ of linear density fluctuations. Here we solve, to arbitrary high perturbative orders, the nonlinear fluid equations with an {\it Ansatz} for the fluid variables in increasing powers of $D$. We show that $\Lambda$ begins to populate the solutions starting at the fifth order in this strict $D$-expansion. By applying suitable resummation techniques, we recast these solutions to a standard perturbative series where not $D$, but essentially the initial gravitational potential serves as the bookkeeping parameter within the expansion. Then, by using the refined growth functions at second and third order in standard perturbation theory, we determine the matter power spectrum to one-loop accuracy as well as the leading-order contribution to the matter bispectrum. We find that employing our refined growth functions impacts the total power- and bispectra at a precision that is below one percent at late times. However, for the power spectrum, we find a characteristic scale-dependent suppression that is fairly similar to what is observed in massive neutrino cosmologies. Therefore, we recommend employing our refined growth functions in order to reduce theoretical uncertainties for analysing data in related pipelines.