Large-Scale Structure Probes of the Post-Inflationary Axiverse

TL;DR

The paper addresses how post-inflationary axions generate isocurvature perturbations from string and domain-wall networks and how these perturbations influence high-redshift structure. It develops a two-pronged approach: (i) modeling the axion-induced matter power spectrum, including a white-noise isocurvature tail peaking at $k_ ext{wn}=C k_ ext{*}$ with $k_ ext{*} eq 0$ and $C= ext{O}(10)$, and (ii) constraining this tail using UV luminosity functions from HST (via the GALLUMI framework) in combination with Lyman-$ abla$ forest and CMB data. The work provides the strongest cosmological limits on subdominant post-inflationary axion dark matter for $m_a \\lesssim 10^{-21}$ eV and translates UVLF bounds into generic limits on white-noise power spectra. By connecting early-universe AXION dynamics to observable high-redshift galaxy statistics, the paper offers a robust framework to test the axiverse with upcoming JWST, 21 cm, and GW observations, and highlights remaining uncertainties in the relic abundance and spectrum from strings and domain walls.

Abstract

We study the cosmology of axions in the post-inflationary scenario, where random initial conditions and the ensuing string-domain-wall network generate an isocurvature power spectrum. Axions radiated from strings behave as warm, wave-like dark matter: when they constitute the full dark matter abundance, free streaming sets the strongest bounds on their mass. For subdominant fractions, despite being warm, they still lead to an overall enhancement of structure growth in the dominant component, seeded by the axion white-noise fluctuations. We search for this effect using the ultraviolet luminosity function (UVLF) of galaxies at $z=4$-$10$, probing $k\simeq0.5$-$10\,\mathrm{Mpc}^{-1}$. Combining the UVLF analysis with Lyman-$α$ and CMB data yields the leading cosmological limits on post-inflationary axion dark matter, sensitive to tiny fractions for $m_a\lesssim10^{-21}\,\mathrm{eV}$. As a byproduct, we obtain new constraints on generic white-noise power spectra from the UVLF. These results apply broadly to scenarios that generate similar isocurvature perturbations, linking early-universe field dynamics to high-redshift structure formation.

Figures (10)

• Figure 1: The dimensionless power spectrum of the axion dark matter overdensity field as it is expected to be produced by axion strings at $\log(m_r/H)\gg1$, as a function of the comoving momentum $k$ normalized to $k_\star = m_a a_\star$. The blue lines show the nontrivial (yet small) evolution of the spectrum around $H = H_\ell \simeq H_\star/200$, when the axions emitted from strings experience a nonlinear transient as the axion potential becomes relevant. This increases mildly the typical momentum with respect to a purely linear evolution (orange line). At the end of the nonlinear transient (black line), the spectrum is of order one at $k_{\rm wn}=Ck_\star$ with $C=\mathcal{O}(10)$ or slightly larger. At $k\ll k_{\rm wn}$, the spectrum acquires the white-noise form $(k/k_{\rm wn})^3$.
• Figure 2: A sketch of the dimensionless power spectrum $\mathcal{P}=\mathcal{P}_{\rm ad}+\mathcal{P}_{\rm iso}$ around matter-radiation equality, shown as a function of comoving momentum $k$ in units of $k_\star=m_a a_\star\simeq 54 (m_a/10^{-20}\,\mathrm{eV})^{1/2}\,\mathrm{Mpc}^{-1}$. The isocurvature contribution $\mathcal{P}_{\rm iso}$ peaks at $k_{\rm wn}=Ck_\star$ with $C=\mathcal{O}(10)$. For $f_{\rm DM}=1$, axion free streaming suppresses the adiabatic component $\mathcal{P}_{\rm ad}$ at $k \gtrsim k_{\rm fs}$, visible as the dip in the dark blue curve, while leaving the white-noise tail of $\mathcal{P}_{\rm iso}$ unaffected. This suppression becomes increasingly smaller for subdominant axion fractions $f_{\rm DM}=0,0.1,0.5$ (orange, light blue, and purple curves, respectively). In addition, the axion velocity dispersion (classical pressure) and quantum pressure inhibit the growth of the axion fluctuations at $k \gtrsim k_J \propto (a/a_{\rm eq})^{1/2}\equiv y^{1/2}$ and $k \gtrsim k_j \propto y^{1/4}$ (light and dark gray regions).
• Figure 3: Left: The free-streaming transfer function $T^2_{\rm fs}$ for the adiabatic power spectrum $\mathcal{P}_{\rm ad}$ for different values of the fraction $f_{\rm DM}$ of dark matter in axions. For $f_{\rm DM}\ll1$, only the adiabatic perturbations in the (warm) axion dark matter component are affected by free streaming and $T^2_{\rm fs}\simeq 1-2f_{\rm DM}$ for $k\gtrsim k_{\rm fs}(a_{\rm eq})$; free-streaming effect is increasingly negligible. Right: Sketch of the isocurvature transfer function for $f_{\rm DM}\ll1$ and at $a\gg a_{\rm eq}$, normalized that expected in pure CDM. For $k\gtrsim k_J^{\rm eq}$ the axion velocity dispersion mildly suppresses the growth of the axion+CDM fluctuations, leading to $T_{\rm iso}^2\propto 1/k$.
• Figure 4: 95% C.L. exclusion limits on the primordial amplitude $A_{\rm iso}$ of the isocurvature component of the power spectrum $\mathcal{P}_{\rm iso}(k)=A_{\rm iso}(k/k_{\rm cut})^3$ as a function of its UV cutoff $k_{\rm cut}$. The bounds originate from CMB+BAO measurements Buckley:2025zgh (orange), Lyman-$\alpha$ MIKE/HIRES data with EFT-based Ivanov:2025pbu (blue) and hydrodynamic simulations Murgia:2019duy (red), as well as the UVLF of HST galaxies (green) used in this work. The bounds assume all dark matter fluctuations evolve as CDM, i.e. with negligible velocity dispersion and quantum pressure.
• Figure 5: Linear matter power spectrum $P(k)=(2\pi^2/k^3)\mathcal{P}(k)$ at $z=0$ as a function of the comoving momentum $k$. The $\Lambda$CDM prediction (black) is compared to two benchmark models with additional isocurvature white-noise components (gray, dashed and dotted). Black points with error bars show the 95% C.L. constraints on excess power inferred in this work from Hubble Space Telescope UVLF data. Blue points denote Lyman-$\alpha$ measurements from eBOSS DR14 eBOSS:2018qyjChabanier:2019eai, and gray points the Lyman-$\alpha$ EFT analysis Ivanov:2025pbu (which constrains an isocurvature enhancement as well). The remaining error bars correspond to SDSS DR7 luminous red galaxies (purple) 2010MNRAS.404...60R and the Planck 2018 CMB power spectra—temperature (red), polarization (orange), and lensing (green) Planck:2018vyg.