Amplification of Cosmological Inhomogeneities by the QCD Transition
Christoph Schmid, Dominik J. Schwarz, Peter Widerin
TL;DR
This work demonstrates that a first-order cosmological QCD transition can dramatically modify subhorizon density perturbations by driving the radiation fluid into free fall (c_s^2 → 0) and generating peaks in the density spectrum. Using bag-model, lattice QCD fits, and a crossover scenario, the authors derive both numerical transfer functions and analytic solutions for the radiation fluid and CDM, showing subhorizon amplification that scales with wave number (e.g., ∝ $k$ in the bag model or ∝ $k^{3/4}$ for lattice EOS). For CDM decoupled at the QCD transition, these perturbations seed CDM clumps with masses between $10^{-20} M_igodot$ and $10^{-10} M_igodot$, while neutrino diffusion damps radiation-fluid peaks before BBN, and PBH formation remains non-dominant without fine-tuning. The results imply a potentially rich microstructure in kinetically decoupled CDM (notably axions) with observable implications for axion searches and microlensing, though they do not require dramatic revision of large-scale structure histories. Overall, the paper links QCD-scale thermodynamics to small-scale dark matter clustering, highlighting a concrete mechanism for primordial microstructure formation within certain DM paradigms.
Abstract
The cosmological QCD transition affects primordial density perturbations. If the QCD transition is first order, the sound speed vanishes during the transition and density perturbations fall freely. For scales below the Hubble radius at the transition the primordial Harrison-Zel'dovich spectrum of density fluctuations develops large peaks and dips. These peaks grow with wave number for both the hadron-photon-lepton fluid and for cold dark matter. At the horizon scale the enhancement is small. This by itself does not lead to the formation of black holes at the QCD transition. The peaks in the hadron-photon-lepton fluid are wiped out during neutrino decoupling. For cold dark matter that is kinetically decoupled at the QCD transition (e.g., axions or primordial black holes) these peaks lead to the formation of CDM clumps of masses $10^{-20} M_\odot< M_{\rm clump} < 10^{-10} M_\odot$.