Yano-Schr\"odinger Hyperfluid: Cosmological Implications

Perfect cosmological hyperfluids generalize the concept of a perfect fluid within the framework of metric affine gravity. These hyperfluids encode the microstructure of matter including shear, dilation, and spin via the hypermomentum tensor. In this paper, we focus on the observational constraints of the recently introduced Yano-Schr\"odinger hyperfluid, which sources a special type of nonmetricity, that preserves the lengths of vectors under autoparallel transport. We propose a model in which the effective nonmetricity contributions to pressure and matter density are related linearly as $p_{\text{eff}} = \omega \rho_{\text{eff}}$. This assumption allows for a straightforward parameterization of deviations from standard cosmological behavior while maintaining analytical tractability. To constrain the effective equation of state parameter $\omega$, we perform a Bayesian parameter estimation using Nested Sampling, implemented via the \texttt{PyPolyChord} library. We use Baryon Acoustic Oscillation measurements from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2), along with Type Ia supernova and Cosmic Chronometer data. In our analysis, we treat $r_d$ as a free parameter, enabling late-time data to extract posterior distributions for the Hubble constant ($H_0$) and the sound horizon ($r_d$), along with the corresponding model parameters. Our results yield $H_0 = 67.4 \pm 4.0 km s ^{-1} Mpc ^{-1}$ and $r_d = 148.8 \pm 7.4$ Mpc, with $\omega = -0.488$ . Finally, we use the logarithm of the Bayes factor to compare different Yano-Schr\"odinger model against the $\Lambda$CDM model. We find that the LESC model provides a better fit to the data, suggesting that modifications to metric-affine gravity could offer viable alternatives to the standard cosmological paradigm.