Constraining Dark Acoustic Oscillations with the High-Redshift UV Luminosity Function

Technical Summary: Constraining Dark Acoustic Oscillations with the high-redshift UV Luminosity Function

Problem Statement
While the standard $\Lambda$CDM model posits that dark matter (DM) is cold and collisionless, various well-motivated extensions to the dark sector predict "Dark Acoustic Oscillations" (DAOs). These arise when a fraction of DM interacts with a dark radiation (DR) species in the early universe, leading to suppression and damped oscillations in the matter power spectrum $P(k)$ at small scales. Existing constraints from the Cosmic Microwave Background (CMB) are stringent on large scales but limit the fraction of interacting DM to $\lesssim 5\%$ for strong DAOs. Conversely, constraints from the Lyman-$\alpha$ forest are effective for weak DAOs or fully interacting models but face challenges in distinguishing strong DAO signatures from Warm Dark Matter (WDM) effects. There is a need for model-agnostic constraints on the small-scale structure of the universe, particularly at high redshifts ($z \sim 3-9$), where the non-linear evolution of structure and the specific imprint of DAOs on the halo mass function (HMF) can be probed.

Methodology
The authors develop a pipeline to constrain DAO parameters using the high-redshift Ultraviolet Luminosity Function (UVLF) of galaxies. The methodology consists of four main components:

1. Phenomenological Transfer Function Model:
   To avoid the computational expense of solving Boltzmann equations for every point in a Markov Chain Monte Carlo (MCMC) scan, the authors introduce a new four-parameter phenomenological transfer function $T(k)$ relative to $\Lambda$CDM. This model captures the suppression and damped oscillations of DAOs and allows for a sub-unity fraction of interacting DM ($f$). The parameters are:

   • $f$: The fraction of DM undergoing DAOs.
   • $k_{\text{peak}}$: The wave number of the first DAO peak.
   • $k_{\text{damp}}$: The damping scale of the oscillations.
   • $A$: The amplitude of the oscillations.
     The model is calibrated against power spectra generated by the modified Boltzmann code CLASS-aDM (for Atomic Dark Matter) and CLASS (for Interacting Dark Matter), demonstrating that the parameters map directly to physical quantities like the dark sound horizon and diffusion damping scale.

2. Extended Press-Schechter (EPS) Formalism and N-body Calibration:
   To predict the HMF from the linear power spectrum, the authors employ the Extended Press-Schechter formalism. Recognizing that standard window functions (e.g., real-space top-hat) fail for truncated power spectra, they utilize a "smooth-k" window function. Crucially, they perform a suite of 13 DM-only N-body simulations using the GIZMO code with MUSIC initial conditions. These simulations cover various fractions of interacting DM ($f=0.1, 0.5, 1$) and DAO scales ($k_{\text{DAO}} = 5, 20, 66, 190 \, h/\text{Mpc}$). The simulations are used to calibrate the EPS parameters ($q, \beta, c$) to ensure the semi-analytic HMF accurately reproduces the simulation results across redshifts $z=4$ to $12$.

3. Halo-Galaxy Connection:
   The connection between the HMF and the observable UVLF is modeled using the GALLUMI code. This pipeline assumes that UV luminosity is driven by star formation rates (SFR) which, on average, follow a double-power law relation with the halo accretion rate. The model includes eight astrophysical nuisance parameters (describing the normalization, pivot scale, and evolution of the SFR-halo mass relation, as well as stochasticity in the magnitude). These parameters are marginalized over to account for uncertainties in high-redshift galaxy formation physics.

4. Data Analysis:
   The authors combine UVLF measurements from the Hubble Space Telescope (HST, both blank and lensed fields), James Webb Space Telescope (JWST), Subaru Telescope, and Canada-France-Hawaii Telescope (CFHT) covering redshifts $z=3$ to $9$. They perform Bayesian MCMC scans and frequentist profile likelihood analyses to constrain the DAO parameters, fixing $\Lambda$CDM parameters to Planck 2018 best-fit values.

Key Contributions

• New Phenomenological Model: Introduction of a flexible transfer function model that accommodates sub-dominant interacting DM fractions, bridging the gap between specific particle physics models (like Atomic DM) and general constraints.
• Simulation Calibration: The first calibration of the EPS formalism for DAO models using a dedicated set of N-body simulations, validating the semi-analytic approach for predicting the HMF in the presence of damped oscillations.
• Model-Agnostic Constraints: The derivation of constraints on the DAO parameter space ($f$ vs. $k_{\text{peak}}$) that are independent of specific dark sector particle physics, allowing for easy reinterpretation in various models (e.g., IDM, Atomic DM).

Results

• Constraints on $f$ and $k_{\text{peak}}$: The analysis yields a strong correlation between the fraction of interacting DM and the scale of the DAOs.
  • If the fraction of interacting DM is significant ($f \gtrsim 0.07$), the wave number of the first DAO peak must be $k_{\text{peak}} \gtrsim 50 \, h/\text{Mpc}$ to remain consistent with UVLF data.
  • Conversely, if $k_{\text{peak}}$ is small (indicating earlier decoupling or stronger interactions), the fraction of interacting DM is constrained to be $f \lesssim 0.07$.
• Comparison with Other Probes:
  • For high fractions of interacting DM ($f \sim 1$), the UVLF constraints improve upon CMB-derived bounds by approximately an order of magnitude in $k_{\text{peak}}$.
  • For very small scales ($k_{\text{peak}} \lesssim 1 \, h/\text{Mpc}$), CMB constraints remain tighter on the abundance of interacting DM ($f \lesssim 5\%$).
  • The constraints on the DM-baryon scattering cross-section in Interacting Dark Matter (IDM) models are found to be over five orders of magnitude stronger than CMB constraints and competitive with bounds derived from Milky Way satellite abundances.
• Unconstrained Parameters: The analysis finds no significant constraints on the DAO amplitude ($A$) or the damping scale ratio ($k_{\text{damp}}/k_{\text{peak}}$) when marginalizing over other parameters, as the UVLF sensitivity is primarily driven by the initial suppression of the power spectrum rather than the oscillatory features.

Significance
The paper demonstrates that high-redshift UV luminosity function measurements provide a powerful, complementary probe to CMB and Lyman-$\alpha$ forest data for constraining small-scale dark matter physics. By successfully calibrating the EPS formalism against N-body simulations and employing a flexible halo-galaxy connection model, the authors establish robust limits on the fraction of dark matter that can undergo acoustic oscillations. These results push the decoupling epoch of interacting dark matter to earlier times (higher $k_{\text{peak}}$) or require the interacting fraction to be sub-dominant ($f < 7\%$) for specific interaction scales. The work highlights the utility of high-redshift observables in distinguishing between different dark sector paradigms and sets a foundation for future constraints using upcoming data from the Vera Rubin Observatory, Nancy Grace Roman Space Telescope, and Square Kilometer Array.