Testing Schouten--Codazzi Gravity: Cosmological Constraints and Deviations from $\Lambda$CDM

Abstract

Schouten--Codazzi gravity (SCG) admits a cosmological background that extends flat $\Lambda$CDM by one integration constant, ${\gamma }_0$. Its contribution to the Friedmann equation scales as $(1+z)$ and corresponds to an effective component with equation of state $w_{{\gamma }_0}=-2/3$. We constrain this extension using 15 combinations of Type~Ia supernovae, DESI~DR2 baryon acoustic oscillations, and compressed cosmic microwave background information, supplemented by a big-bang nucleosynthesis prior as specified in the analysis. Supernovae paired with either BAO or CMB favor positive ${\Omega }_{{\gamma }_0}\equiv {\gamma }_0/H_0^2$, with approximate marginal departures from zero of $1.7$--$3.2\sigma$. In contrast, all three supernovae$+$BAO$+$CMB combinations are consistent with ${\Omega }_{{\gamma }_0}=0$ within their 68\% credible intervals. Their central log Bayes factors favor $\Lambda$CDM, with $\Delta \ln \mathcal{Z}$ between $-2.54$ and $-1.13$, and the inferred Hubble constants remain close to those of the corresponding $\Lambda$CDM fits. These results provide a background-level test of SCG conditional on the adopted priors and likelihood approximations, particularly the model assumptions entering the CMB compression.

arXiv comment15 pages, 4 figures