Scalar-Induced Gravitational Waves in a $\Lambda$CDM Cosmology

TL;DR

This paper analyzes the spectrum of gravitational waves induced by scalar perturbations in a $\\Lambda$CDM universe, revealing overestimations in previous models and identifying gauge-dependent non-oscillating modes during cosmic transitions.

Contribution

It provides analytical corrections to the induced gravitational wave spectrum during matter and $\\Lambda$-dominated epochs in a flat FLRW universe, highlighting gauge effects and transition behaviors.

Findings

Overestimation of energy density spectrum during matter domination.

Identification of gauge-dependent non-oscillating tensor modes.

Numerical spectrum computation showing transition effects in $\\Lambda$CDM cosmology.

Abstract

We reconsider the gravitational wave spectrum induced by scalar perturbations in spatially flat Friedmann-Lema\^itre-Robertson-Walker spacetimes, focusing on the matter- and $\Lambda$-dominated epochs. During matter domination, sub-horizon modes are not free and a commonly applied approximation for the derivative of the tensor perturbation is flawed. We show analytically that this leads to a significant overestimation of the energy density spectrum. In addition, we demonstrate that gauge-dependent non-oscillating tensor perturbations appear in the presence of a cosmological constant. Complementing the analytical calculations, we compute the according present-day spectrum numerically for a Planck-like $\Lambda$CDM cosmology, finding that non-oscillating growing modes appear during the transition between matter and $\Lambda$ domination in conformal Newtonian gauge.