Robustness of baryon acoustic oscillation constraints for early-Universe modifications of $\mathrm{\Lambda }\mathrm{CDM}$ cosmology

Baryon acoustic oscillations (BAO) provide a robust standard ruler and can be used to constrain the expansion history of the Universe at low redshift. Standard BAO analyses return a model-independent measurement of the expansion rate and the comoving angular diameter distance as a function of redshift, normalized by the sound horizon at radiation drag. However, this methodology relies on anisotropic distance distortions of a fixed, precomputed template (obtained in a given fiducial cosmology) in order to fit the observations. Therefore, it may be possible that extensions to the consensus $\mathrm{\Lambda }\mathrm{CDM}$ add contributions to the BAO feature that cannot be captured by the template fitting. We perform mock BAO fits to power spectra computed assuming cosmological models that modify the growth of perturbations prior to recombination in order to test the robustness of the standard BAO analysis. We find no significant bias in the BAO analysis for the models under study ($\mathrm{\Lambda }\mathrm{CDM}$ with a free effective number of relativistic species, early dark energy, and a model with interactions between neutrinos and a fraction of the dark matter), even for cases that do not provide a good fit to Planck measurements of the cosmic microwave background power spectra. This result supports the use of the standard BAO analysis and its measurements to perform cosmological parameter inference and to constrain exotic models. In addition, we provide a methodology to reproduce our study for different models and surveys, as well as discuss different options to handle eventual biases in the BAO measurements.

Figure 1

BAO feature $O_{\mathrm{lin}}$ in the matter power spectrum for varying cosmological parameters (with $k$ rescaled by $r_{\mathrm{d}}/r_{\mathrm{d}}^{\mathrm{fid}}$), compared with the fiducial prediction (red dashed lines), and the corresponding ratio (i.e., modified over fiducial cosmology) in the lower panels. The insets show $r_{\mathrm{d}}/r_{\mathrm{d}}^{\mathrm{fid}}$ for each case, and the model under consideration is given in the upper left corner of each panel. We keep all $\mathrm{\Lambda }\mathrm{CDM}$ parameters to their fiducial values except for when each of them is varied, as indicated in the corresponding color bars. The intervals limited by white lines in the color bars correspond to the 68% confidence level constraints of each parameter from Planck observations, and additional datasets for EDE and DNI. For the panels corresponding to EDE, we use $f_{\mathrm{EDE}}=0.2$, ${\log }_{10}{z}_{\mathrm{EDE}}^c=3.5$, ${\mathrm{\Theta }}_{\mathrm{EDE}}=2.8$, and $n_{\text{axion}}=3$, unless otherwise indicated. For the DNI model, we use $f_{\mathrm{DNI}}=0.02$ and $u_{\mathrm{DNI}}=5$, unless otherwise indicated. DNI constraints are reported in terms of $f_{\mathrm{DNI}}{u}_{\mathrm{DNI}}$; hence they are adapted to the fixed values of $u_{\mathrm{DNI}}$ and $f_{\mathrm{DNI}}$ assumed in this figure. Note the change in scale of the $y$ axis for the lower sections of each panel.

Figure 2

The 68% and 95% confidence level marginalized constraints in the ${\alpha }_{\perp }-{\alpha }_{\parallel }$ plane, shown with their maximum-posterior and true values (represented as circles and stars, respectively), for different mock galaxy power spectra computed in $\mathrm{\Lambda }\mathrm{CDM}$, $\mathrm{\Lambda }\mathrm{CDM}+N_{\mathrm{eff}}$, EDE, and DNI, as indicated in the legend (rows), and for BOSS LOWZ and CMASS, as well as DESI at $z=0.8$ and $z=1.0$ (columns; note the different scales in the columns in the left and in the right). For all analyses, we use a template computed under a fiducial that matches the mean values of the $\mathrm{\Lambda }\mathrm{CDM}$ parameters from Planck’s analysis. Blue contours refer to the cosmologies numbered as 1 (best fit from Planck, as well as external datasets for EDE and DNI) and red contours to cosmologies numbered as 2. Cosmological parameters and survey specifications are listed in Tables 1 and 2, respectively.

Figure 3

Hubble expansion rate over $(1+z{)}^{3/2}$ (top) and comoving angular diameter distance over $(1+z{)}^{3/2}$ (bottom) as a function of redshift, weighted by the ratio between the actual sound horizon at radiation drag and its fiducial value ($\mathrm{\Lambda }\mathrm{CDM}$ best fit to Planck). We show predictions for $\mathrm{\Lambda }\mathrm{CDM}$ (blue lines) and DNI (green lines), as well as existing measurements from BOSS [6] and eBOSS [7, 8, 9]. Note that the error bars shown here do not include the covariance between measurements.

Figure 4

Top: Total linear matter power spectrum before (solid lines) and after (dashed lines) the removal of the BAO contribution ($P_{\mathrm{m}}$ and $P_{\mathrm{m},\mathrm{sm}}$, respectively). Bottom: Same as top but in configuration space. Factors of $k$ and $r^2$ are added, respectively, for clarity. Blue lines correspond to $\mathrm{\Lambda }\mathrm{CDM}$ predictions and red lines to EDE predictions (with $f_{\mathrm{EDE}}=0.3$).