Can small-scale baryon inhomogeneities resolve the Hubble tension? An investigation with ACT DR4

Small-scale inhomogeneities in the baryon density around recombination have been proposed as a solution to the tension between local and global determinations of the Hubble constant. These baryon clumping models make distinct predictions for the cosmic microwave background anisotropy power spectra on small angular scales. We use recent data from the Atacama Cosmology Telescope to test these predictions. No evidence for baryon clumping is found, assuming a range of parametrizations for time-independent baryon density probability distribution functions. The inferred Hubble constant remains in significant tension with the SH0ES measurement.

Figure 1

Posteriors in the same parametrizations and with the same likelihod as the one used in JP20. The solid lines are our results, while the dashed lines are JP20. Here and in all subsequent posterior plots, the gray shaded region is the $1\sigma$ confidence interval from the latest SH0ES measurement [1]. We have also indicated the $1\sigma$ confidence interval of the SMH $H_0$ likelihood used in this plot and in Sec. 4.

Figure 2

Posteriors in the same parametrizations as in JP20, comparing Planck alone with ACT added. Here and in the following posteriors, the line color indicates the model while the line style differentiates between different likelihoods.

Figure 3

Posteriors in the parametrizations with one more degree of freedom, ${\mathrm{\Delta }}_1$.

Figure 4

Posteriors in the extended parametrization, illustrating the effect of adding a BAO likelihood.

Figure 5

The ionization fraction as a function of redshift for the best-fit models listed in Table 3.

Figure 6

Fractional changes in CMB power spectra for the best-fit models listed in Table 3, with respect to the Planck$+\mathrm{ACT}$ $\mathrm{\Lambda }\mathrm{CDM}$ baseline. In the second panel (TE), because the data have zero crossings, we computed the normalizing factor $\overline{|C_{\ell }^{\mathrm{ref}}|}$ as a convolution of the absolute value of the reference TE power spectrum with a Gaussian filter of width $\sigma =100$ (in $\ell$). This gives a useful normalization without artifacts from the roots. Note that for clarity the experimental data curves for ACT and Planck have been rescaled by the given factors. While the Planck data points are relatively close to what we use in our likelihood (except for binning and $\ell$-cuts to improve clarity, in particular for TE and EE), the ACT data points are for illustration purposes only and were generated as explained (The ACT DR4 data only contain band powers, which are related to the underlying CMB power spectra by $C_b=W_{b\ell }{C}_{\ell }$, where $W_{b\ell }$ is an $m\times n$ matrix with $m<n$. Thus, it is not possible to uniquely infer the $C_{\ell }$ from the band powers. In order to generate power spectra that can be directly compared to Planck and the theory models, we first find some solution $C_{\ell }^0$ of the above equation (which is, of course, completely unphysical). Then, writing $K_{\ell \alpha }$ for the $n\times (n-m)$ matrix whose columns are a basis for the kernel of $W_{b\ell }$, we can generate additional solutions $C_{\ell }(a_{\alpha })=C_{\ell }^0+K_{\ell \alpha }{a}_{\alpha }$, where $a_{\alpha }$ is an arbitrary vector. We now find the $a_{\alpha }$ that minimizes $||{\mathrm{\Lambda }}_{{\ell }^{\prime }\ell }{C}_{\ell }(a_{\alpha })||$, where ${\mathrm{\Lambda }}_{{\ell }^{\prime }\ell }$ implements a discrete second derivative. We perform this procedure for both the ‘deep’ and ‘wide’ parts of the ACT data set, associating approximate error bars with the resulting $C_{\ell }$ according to the normalized diagonal elements of the covariance matrix of the $C_b$. Finally, we take the weighted average of the ‘deep’ and ‘wide’ $C_{\ell }$).

Figure 7

Comparison between the posterior in the unconstrained $f_2=1/2$ model, same as in Fig. 3, and the one with the constraint $f_1>0.1$. The latter should substantially reduce the prior volume effect arising from the degeneracy with $\mathrm{\Lambda }\mathrm{CDM}$ at $f_1=0$. In the dashed posterior, the nonvanishing support at $b=0$ is an artifact of montepython’s posterior smoothing routine.

Figure 8

Likelihood profiles as a function of $b$ for the $f_2=1/2$ Markov chain. The ‘mean’ and ‘best-fit’ lines are computed as described in the text. The orange line is the same marginalized likelihood that was shown in Fig. 3. The blue dashed line is a Gaussian fit with only the standard deviation varied, while the green dashed line is a thee-parameter Gaussian fit. The green solid line was rescaled so that the Gaussian fit attains its maximum at one. These fits should only be treated as visual guides.