Baryon fraction from the BAO amplitude: a consistent approach to parameterizing perturbation growth

TL;DR

The paper tackles obtaining the baryon fraction fb from galaxy clustering to enable H0 estimates based on energy densities, independent of recombination-era physics. It introduces a growth-based parameter γ_b that is embedded directly into the linear perturbation evolution in CAMB, ensuring coherent baryon and CDM growth across all epochs and preserving the thermal history. The approach is integrated into an EFT-based full-shape pipeline with HOD-informed priors, and validated against ΛCDM and EDE cosmologies, showing comparable precision to prior methods but with reduced systematic biases. This robust, self-consistent framework strengthens the use of baryon-fraction measurements to constrain H0 with upcoming DESI and Euclid data, offering a valuable cross-check for the standard cosmology and potential avenues to resolve the H0 tension.

Abstract

Galaxy clustering constrains the baryon fraction Omega_b/Omega_m through the amplitude of baryon acoustic oscillations and the suppression of perturbations entering the horizon before recombination. This produces a different pre-recombination distribution of baryons and dark matter. After recombination, the gravitational potential responds to both components in proportion to their mass, allowing robust measurement of the baryon fraction. This is independent of new-physics scenarios altering the recombination background (e.g. Early Dark Energy). The accuracy of such measurements does, however, depend on how baryons and CDM are modeled in the power spectrum. Previous template-based splitting relied on approximate transfer functions that neglected part of information. We present a new method that embeds an extra parameter controlling the balance between baryons and dark matter in the growth terms of the perturbation equations in the CAMB Boltzmann solver. This approach captures the baryonic suppression of CDM prior to recombination, avoids inconsistencies, and yields a clean parametrization of the baryon fraction in the linear power spectrum, separating out the simple physics of growth due to the combined matter potential. We implement this framework in an analysis pipeline using Effective Field Theory of Large-Scale Structure with HOD-informed priors and validate it against noiseless LCDM and EDE cosmologies with DESI-like errors. The new scheme achieves comparable precision to previous splitting while reducing systematic biases, providing a more robust way to baryon-fraction measurements. In combination with BBN constraints on the baryon density and Alcock-Paczynski estimates of the matter density, these results strengthen the use of baryon fraction measurements to derive a Hubble constant from energy densities, with future DESI and Euclid data expected to deliver competitive constraints.

Figures (5)

• Figure 1: LEFT Redshift evolution of the absolute density contrasts $|\Delta(z)|$ for baryons (dotted lines) and CDM (solid lines) at fixed comoving scale $k = 0.126\,h\,\mathrm{Mpc}^{-1}$. Three growth-baryon-fraction values are shown: $\gamma_b\approx0$, $\gamma_b=0.156$ (fiducial cosmological value), and $\gamma_b=1$. All lines share identical adiabatic initial conditions and the recombination redshift $z\simeq1100$. Before decoupling the baryon perturbations undergo acoustic oscillations that are mostly independent of $\gamma_b$. After decoupling the growth rate diverges: when $\gamma_b \approx 1$, perturbations evolve solely through baryons, showing delayed growth; when $\gamma_b \approx 0$, perturbations evolve solely through CDM, which grows slightly faster and baryons collapse immediately after recombination. RIGHT Same as on the left, but changing the global baryon fraction $f_b$ as well as the growth-baryon fraction $\gamma_b$. The figure shows the scenario where the global baryon fraction is varied for three values: $f_b=\gamma_b\approx0$, $f_b=\gamma_b=0.156$ (fiducial), and $f_b=\gamma_b=1$. While all lines share identical adiabatic initial conditions, they have distinct thermal and growth histories: changing the global baryon fraction not only alters the relative clustering of baryons and CDM, but also affects the recombination epoch and the subsequent evolution of perturbations, leading to significantly different BAO patterns. Since we wish to extract the growth information only while leaving the position of the peaks unchanged, we use the new parameter $\gamma_b$ to constrain the baryon fraction rather than $f_b$.
• Figure 2: Comparison between the linear power spectra obtained with our new method (solid lines) and the KP25 splitting scheme (dashed lines), for different values of $\gamma_b$ ranging from 0 to 1, including the fiducial cosmological value of 0.156. The two methods encapsulate different physical effects in the definition of the $\gamma_b$ parameter, leading to visible differences in amplitude, especially at the extremes. At $\gamma_b=0$, our method removes the baryon-induced suppression on the CDM transfer function prior to the drag epoch. At $\gamma_b=1$, it also eliminates the CDM-driven growth in baryon oscillations during drag epoch that is retained in the EH transfer functions used by KP25.
• Figure 3: Comparison of the impact of different values of $\gamma_b$ on the monopole and quadrupole of the power spectrum computed using EPT for both the KP25 splitting (dashed lines) and our new method (solid lines). The different values of $\gamma_b$ correspond to $\pm1\sigma$ and $\pm3\,\sigma$ around the fiducial value of 0.156.
• Figure 4: Validation test of the HOD-informed priors in scenarios where the growth and cosmological baryon fractions differ. The circles show the recovered values of $h_\mathrm{dens}$ against their true inputs, $h_\mathrm{dens, true}$, for both the KP25 splitting (blue) and the new method (red). The black squares show the value of the cosmological Hubble parameter $h$ on the y-axis, as a function of the true $h_\mathrm{dens}$ value. Their purpose is to illustrate the difference between the $h_\mathrm{dens}$ value used and the underlying cosmological $h$, showing that the pipeline successfully recovers the correct $h_\mathrm{dens}$ with an error smaller than the difference from the cosmological value. The small residual effect of the priors, which slightly push density-based values toward their cosmological counterparts, is negligible compared to the statistical uncertainty (only 10-15% of the error bar). The shaded gray band highlights the tension in $H_0$ between Planck 2018 and Pantheon+.
• Figure 5: Comparison between the true and inferred $\gamma_b$ and $h_\mathrm{dens}$ from noiseless data vectors, for both $\Lambda$CDM (blue) and EDE (orange) cosmologies. Circles represent the marginalized constraints using the HOD-informed prior, while squares represent the constraints using the default DESI priors. Crosses show the maximum of the posterior. Results are shown for the KP25 splitting method (left) and the new perturbation-evolution approach (right). The bottom panels show the residuals $\Delta$ with respect to the true value, with the shaded band marking the Planck–Pantheon+ tension, and the absolute deviation as number of $\sigma$.