Effective Field Theory Constraints on Primordial Black Holes from the High-Redshift Lyman-$α$ Forest

TL;DR

This work develops and applies an effective field theory (EFT) description of the Lyman-$\alpha$ forest to high-redshift data (MIKE/HIRES) in order to constrain primordial black holes (PBHs) as dark matter. By modeling the 1D flux power spectrum with a perturbative EFT that includes tree-level and one-loop contributions and a set of nuisance parameters calibrated by state-of-the-art simulations, the authors extract robust bounds on scale-dependent isocurvature power induced by PBHs, including the Poisson shot-noise contribution. The analysis translates limits on the PBH-induced power into bounds on the PBH fraction $f_{PBH}$ across a wide mass range $M_{PBH} \sim 10^{4}-10^{16} M_\odot$, excluding $f_{PBH} \gtrsim 10^{-3}$ and providing the leading constraints for PBHs heavier than $10^{9} M_\odot$. The results demonstrate the Lyman-$\alpha$ forest as a powerful probe of small-scale cosmological physics and illustrate the EFT framework's ability to explore parameter spaces inaccessible to hydrodynamic simulations. Looking ahead, upcoming spectroscopic surveys and complementary probes (galaxy clustering with EFT, 21-cm, JWST) will further tighten constraints on PBHs and related new-physics scenarios.

Abstract

We present updated constraints on the abundance of primordial black holes (PBHs) dark matter from the high-redshift Lyman-$α$ forest data from MIKE/HIRES experiments. Our analysis leverages an effective field theory (EFT) description of the 1D flux power spectrum, allowing us to analytically predict the Lyman-$α$ fluctuations on quasi-linear scales from first principles. Our EFT-based likelihood enables robust inference across redshifts $z = 4.2-5.4$ and down to scales of 100 kpc, within previously unexplored regions of parameter space for this dataset. We derive new bounds on the PBH fraction with respect to the total dark matter $f_{\text{PBH}}$, excluding populations with $f_{\text{PBH}} \gtrsim 10^{-3}$ for masses $M_{\text{PBH}} \sim 10^{4}-10^{16} M_{\odot}$. This offers the leading constraint for PBHs heavier than $10^{9} M_{\odot}$ and highlights the Lyman-$α$ forest as a uniquely sensitive probe of new physics models that modify the structure formation history of our universe.

Figures (3)

• Figure 1: The linear matter power spectrum at $z=0$ is shown for $\Lambda$CDM (black), and for a PBH model with $f_{\rm PBH}=10^{-2}$ and $M_{\rm PBH}=10^{7} M_{\odot}$ (gray dashed). The black dots (and corresponding errorbars) denote the 95% C.L. constrains on overfluctuations from the high-redshift Lyman-$\alpha$ data from MIKE/HIRES, that are derived in this work. The blue dots denote the Lyman-$\alpha$ from eBOSS DR14 eBOSS:2018qyjChabanier:2019eai. The rest of the errorbars correspond to observations of Luminous Red Galaxies (purple) by SDSS DR7 2010MNRAS.404...60R (purple) and the Planck 2018 Planck:2018vyg CMB temperature (red), polarization (orange) and lensing (green) power spectra.
• Figure 2: Constraints on the parameter space of supermassive and stupendously large primordial black holes at 95% C.L. The red shaded region denotes the region excluded due to Lyman-$\alpha$ MIKES/HIRES data derived in this work. We also show the Lyman-$\alpha$ constraints from the simulation-based study of Ref. Murgia:2019duy (dashed red). Limits arise also due to CMB anisotropies produced by accreting PBHs measured by Planck Serpico:2020ehh (PLANCK, yellow), X-ray flux induced by accretion Inoue:2017csr (XB, cyan), millilensing of radio sources Wilkinson:2001vv (magenta), dynamical friction causing halo objects to fall in the nucleus of the Milky Way Carr:1997cn (DF, grey), overheating of stars in the galactic disk Carr:1997cn (DH, purple), high-redshift formation of large-scale structures Carr:2018rid (LSS, brown),the Hubble Space Telescope Ultraviolet Luminosity Function Gouttenoire:2023nzrSabti:2023xwo (UVLF, blue), and the CMB dipole anisotropy Carr:2020gox (CMB, green). The region on the left side of the yellow dashed line is constrained by CMB spectral $\mu$-distortion measured by COBE/FIRAS surveys Kohri:2014lza in the Gaussian limit.ftn:CMB_spectral The right side of the light green line denotes the incredulity limit (IL), which corresponds to one black hole per Hubble volume.
• Figure S1: Combined MIKE/HIRES 1D flux power spectrum data and the best-fitting EFT theory curves. The data points are offset along the x axis for clarity. The error bars shown are diagonal elements of the covariance matrix. Note that they account for both statistical and systematic uncertainties.