Clustering with Light (but Massive) Relics

TL;DR

The paper investigates Light (but Massive) Relics (LiMRs) in the early Universe and their impact on matter clustering and CMB weak lensing. It develops a linearized analytic framework that models LiMRs as clustering or free-streaming components, using parameters $m_X$, $r$, and $f_X$ to track their influence on growth and the lensing power spectrum via the Limber approximation. The main finding is that LiMRs with masses around a few eV can constitute a non-negligible fraction of dark matter ($f_X \sim 0.1$) without severely suppressing CMB lensing, effectively allowing energy injected as dark radiation to redshift as matter before recombination and relax $\Delta N_{\mathrm{eff}}$ constraints. These results broaden viable beyond-Standard-Model scenarios and motivate future global cosmological analyses and potential detection methods for $\sim$eV-scale bosonic dark matter, bridging early-Universe physics with low-mass dark-matter phenomenology.

Abstract

We consider the effect of Light (but Massive) Relics (LiMRs) on the clustering of matter in the early Universe. We account for the fact that LiMRs which are massive enough may cluster on large length scales at early times, and may thus impact weak lensing of the cosmic microwave background (CMB) even on small angular scales. In particular, we find that LiMRs in the $\gtrsim$ eV mass range (and even $> 10$ eV), can constitute a non-negligible component of dark matter. This opens up a class of scenarios in which energy is injected as dark radiation, but begins to redshift as matter before recombination, thus avoiding constraints on $ΔN_{eff}$ while providing an eV-range dark matter component.

Figures (3)

• Figure 1: Plot of $\Delta C_{\ell}^{\kappa \kappa} / C_{\ell}^{\kappa \kappa}$ as a function of $\ell$, setting $f_\nu = 4 \times 10^{-3}$ and $\sum_\nu m_\nu = 0.058~\, {\rm eV}$ ($g = 3/2, n_s=1$).
• Figure 2: Plot of $\Delta C_{\ell}^{\kappa \kappa} / C_{\ell}^{\kappa \kappa}$ as a function of $\ell$, setting $r = (4/11)^{1/3}$ and $\sum_\nu m_\nu = 0.3~\, {\rm eV}$ ($g = 3/2, n_s=1$).
• Figure 3: Regions of the $(m_X, f_X)$ parameter space in which $|\Delta C_{\ell}^{\kappa \kappa} / C_{\ell}^{\kappa \kappa}| < 0.025~(0.017)$ for $\ell \leq 2000$ are plotted in blue (yellow). Also plotted are contours of constant $r \equiv T_X / T_\gamma$, as labelled.