$S_8-H_0$ tension in a SI-ULDM scenario

TL;DR

This paper investigates how a transient self-interaction phase in Ultra-Light Dark Matter can simultaneously affect early universe expansion and late-time structure growth, offering a unified analytical framework for the $S_8$-$H_0$ tension.

Contribution

It introduces a model-independent, perturbative approach to analyze the impact of a short-lived self-interaction phase in ULDM on cosmological observables, linking early and late-time effects.

Findings

A localized early-time modification can shift $H_0$ and $S_8$ in correlated ways.

The response of observables can be expressed as weighted integrals over cosmic history.

Analytic relations predict the sign and magnitude of shifts based on the timing of the self-interaction.

Abstract

We study the cosmological impact of a transient self-interaction phase in Ultra-Light Dark Matter (ULDM), focusing on its simultaneous effects on the sound horizon and the late-time growth of structure. In the presence of a quartic self-interaction, the scalar field undergoes a short-lived radiation-like phase before evolving into matter-like behaviour, inducing a localized modification of the expansion history at early times. We develop a perturbative and model-independent framework in which the self-interaction energy density is parametrized as a localized contribution to the total energy budget. Within this approach, the responses of the sound horizon and the linear growth factor can be expressed as weighted integrals over cosmic time, with distinct kernels encoding the temporal sensitivity of each observable. This structure leads to a simple analytic relation linking the corresponding early- and late-time responses, and naturally predicts correlated shifts in $H_0$ and $S_8$ whose sign and magnitude depend on the timing of the self-interaction episode. Our results show that a single transient modification of the expansion history can interpolate between early-time effects on the sound horizon and late-time suppression of structure growth within a unified physical framework, providing an analytical understanding of their joint response.