Reconstructing Primordial Curvature Perturbations via Scalar-Induced Gravitational Waves with LISA

TL;DR

This paper explores how LISA can detect and analyze scalar-induced gravitational waves to reconstruct primordial curvature perturbations, offering new insights into early universe physics through different modeling approaches.

Contribution

It introduces a comprehensive forecasting framework for LISA to constrain primordial curvature perturbations via SIGWs using agnostic, template-based, and first-principles models.

Findings

LISA can probe curvature perturbations at scales $k in [10^{10}, 10^{14}]$ Mpc$^{-1}$.

Different modeling approaches have unique advantages and limitations.

The study discusses the effects of non-standard thermal histories and non-Gaussianity on SIGW signals.

Abstract

Many early universe scenarios predict an enhancement of scalar perturbations at scales currently unconstrained by cosmological probes. These perturbations source gravitational waves (GWs) at second order in perturbation theory, leading to a scalar-induced gravitational wave (SIGW) background. The LISA detector, sensitive to mHz GWs, will be able to constrain curvature perturbations in a new window corresponding to scales $k \in [10^{10}, 10^{14}] \,{\rm Mpc}^{-1}$, difficult to probe otherwise. In this work, we forecast the capabilities of LISA to constrain the source of SIGWs using different approaches: i) agnostic, where the spectrum of curvature perturbations is binned in frequency space; ii) template-based, modeling the curvature power spectrum based on motivated classes of models; iii) ab initio, starting from first-principles model of inflation featuring an ultra-slow roll phase. We compare the strengths and weaknesses of each approach. We also discuss the impact on the SIGW spectrum of non-standard thermal histories affecting the kernels of SIGW emission and non-Gaussianity in the statistics of the curvature perturbations. Finally, we propose simple tests to assess whether the signal is compatible with the SIGW hypothesis. The pipeline used is built into the SIGWAY code.