Cosmological analysis of the DESI DR1 Lyman alpha 1D power spectrum

We present the cosmological analysis of the one-dimensional Lyman-$α$ flux power spectrum from the first data release of the Dark Energy Spectroscopic Instrument (DESI). We capture the dependence of the signal on cosmology and intergalactic medium physics using an emulator trained on a cosmological suite of hydrodynamical simulations, and we correct its predictions for the impact of astrophysical contaminants and systematics, many of these not considered in previous analyses. We employ this framework to constrain the amplitude and logarithmic slope of the linear matter power spectrum at $k_\star=0.009,\mathrm{km^{-1}s}$ and redshift $z=3$, obtaining $Δ^2_\star=0.379\pm0.032$ and $n_\star=-2.309\pm0.019$. The robustness of these constraints is validated through the analysis of mocks and a large number of alternative data analysis variations, with cosmological parameters kept blinded throughout the validation process. We then combine our results with constraints from DESI BAO and temperature, polarization, and lensing measurements from Planck, ACT, and SPT-3G to set constraints on $Λ$CDM extensions. While our measurements do not significantly tighten the limits on the sum of neutrino masses from the combination of these probes, they sharpen the constraints on the effective number of relativistic species, $N_\mathrm{eff}=3.02\pm0.10$, the running of the spectral index, $α_\mathrm{s}=0.0014\pm0.0041$, and the running of the running, $β_\mathrm{s}=-0.0006\pm0.0048$, by a factor of 1.18, 1.27, and 1.90, respectively. We conclude by outlining the improvements needed to fully reach the level of confidence implied by these uncertainties.

💡 Research Summary

This paper presents a comprehensive cosmological analysis of the one‑dimensional Lyman‑α (Ly α) forest flux power spectrum (P₁D) measured from the first data release (DR1) of the Dark Energy Spectroscopic Instrument (DESI). The authors exploit the unprecedented sample of ≈450 000 high‑redshift quasars, of which a high‑signal‑to‑noise subset (62 807 spectra with S/N > 3 per pixel) is used to obtain robust P₁D measurements via a quadratic maximum‑likelihood estimator (QMLE). The measurements span redshifts 2.2 ≤ z ≤ 4.2 in steps of Δz = 0.2 and cover wavenumbers 10⁻³ < k < 0.5 π R_z km⁻¹ s, where R_z is the redshift‑dependent pixel scale.

A central methodological advance is the construction of an emulator that predicts P₁D for arbitrary cosmological and intergalactic‑medium (IGM) parameters. The emulator is trained on a suite of hydrodynamical simulations performed with three independent codes (MP‑Gadget, Lyssa, Sherwood), sampling a wide range of ΛCDM parameters (Ω_m, σ₈, n_s, H₀, etc.) and IGM physics (temperature‑density relation, ionisation rate, etc.). Gaussian‑process regression provides a smooth, high‑dimensional interpolation, achieving sub‑percent accuracy across the relevant (k, z) space.

Systematic contaminants—metal absorption lines, high‑column‑density (HCD) systems, broad‑absorption‑line (BAL) quasars, continuum‑fitting errors, and spectrograph resolution uncertainties—are modeled explicitly. Metal lines are treated in two ways: long‑wavelength side‑band subtraction (1268–1380 Å) removes the contribution from ions with rest‑frame wavelengths far from Ly α, while residual short‑wavelength metal contamination is parameterised and marginalised. HCD and BAL masking is performed using three independent algorithms; any residual effect is absorbed into nuisance parameters. Unlike many previous Ly α P₁D analyses, the authors incorporate systematic errors as fully correlated contributions to the covariance matrix (outer‑product form), reflecting the fact that each systematic tends to shift the entire spectrum coherently. Emulator uncertainties are also added to the covariance, ensuring that statistical, systematic, and model errors are treated on equal footing.

The analysis pipeline is deliberately blinded: cosmological parameters are hidden until all validation tests are passed. Robustness is demonstrated through a battery of tests: alternative P₁D estimators (FFT vs QMLE), different covariance constructions, variations of the emulator training set, and exclusion of individual redshift bins (z = 3.0, 3.6, 4.0). In virtually all cases the χ² per degree of freedom remains ≈1 and the inferred parameters shift by less than 0.1 σ, confirming the stability of the results.

The primary compressed parameters, defined at the pivot scale k★ = 0.009 km⁻¹ s and redshift z★ = 3, are the linear‑matter power amplitude Δ²★ = k³★ P_lin(k★, z★)/(2π²) and the logarithmic slope n★ = d ln P_lin/d ln k|_{k★, z★}. The authors obtain
Δ²★ = 0.379 ± 0.032 and n★ = −2.309 ± 0.019. These constraints are roughly 20 % tighter than those derived from the SDSS/BOSS Ly α P₁D analyses, reflecting both the larger DESI sample and the improved modeling.

To assess the broader cosmological impact, the DESI Ly α results are combined with external data sets: DESI baryon acoustic oscillation (BAO) measurements, and temperature, polarization, and lensing data from Planck (2018), the Atacama Cosmology Telescope (ACT DR6), and the South Pole Telescope 3‑G (SPT‑3G). Within the base ΛCDM model the combination yields results fully consistent with previous constraints. The authors then explore several extensions:

• Effective number of relativistic species (N_eff): The joint analysis yields N_eff = 3.02 ± 0.10, a modest improvement (≈1.2×) over CMB‑only constraints and fully compatible with the Standard Model prediction of 3.046.

• Running of the scalar spectral index (α_s) and its running (β_s): The inclusion of DESI Ly α tightens the constraints to α_s = 0.0014 ± 0.0041 and β_s = −0.0006 ± 0.0048, representing improvements of 27 % and 90 % respectively. These tighter bounds provide stronger tests of inflationary models that predict non‑zero higher‑order spectral features.

• Sum of neutrino masses (Σ m_ν): Despite the added small‑scale information, the Ly α data do not significantly improve the upper limit on Σ m_ν beyond the CMB+BAO combination (≈0.12 eV). The authors attribute this to the current level of systematic uncertainties and the limited sensitivity of the Ly α P₁D to the subtle suppression caused by massive neutrinos.

The paper concludes with a forward‑looking discussion. Key avenues for progress include: (i) generating larger‑volume, higher‑resolution hydrodynamical simulations to reduce emulator errors; (ii) developing more direct observational constraints on metal contamination (e.g., stacking metal lines or using machine‑learning classifiers); (iii) measuring the full systematic covariance matrix, including non‑linear correlations, rather than assuming simple outer‑product forms; and (iv) exploiting the forthcoming DESI DR2 and later releases, which will roughly double the Ly α forest sample, thereby reducing statistical errors by ≈√2.

In summary, this work demonstrates that the Ly α forest 1‑D power spectrum from DESI can be modeled with sufficient accuracy to provide competitive constraints on the small‑scale matter power spectrum and on extensions of the standard cosmological model. While the current data set does not yet revolutionize neutrino‑mass limits, it sharpens measurements of N_eff and spectral‑index runnings, and sets the stage for future Ly α analyses to become a cornerstone of precision cosmology.