Cosmological test of a length-preserving biconnection gravity

TL;DR

This paper explores a biconnection gravity framework's cosmological implications, deriving modified Friedmann equations, and tests its effective dark energy models against observational data, finding some parametrizations competitive with Lambda-CDM.

Contribution

It introduces a biconnection gravity model with non-Riemannian degrees of freedom, deriving generalized cosmological equations and testing dark energy parametrizations against data.

Findings

Barboza-Alcaniz and logarithmic parametrizations are strongly supported by data.

The model's equations reproduce standard cosmology at the background level.

Certain parametrizations are competitive with Lambda-CDM in explaining cosmic acceleration.

Abstract

We investigate the cosmological implications of an extended gravitational framework based on biconnection gravity, constructed from the Schr$\ddot{o}$dinger connection and its dual. In this approach, the difference between the two connections defines the mutual curvature, which encodes the non-Riemannian geometric degrees of freedom, while their symmetric combination reduces to the Levi-Civita connection and hence reproduces general relativity at the background level. Within this setting, we derive the generalized Friedmann equations for a spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker Universe. The resulting equations contain additional geometric contributions that may naturally encode an effective dark energy sector induced by the biconnection degrees of freedom. We explore this extra dark energy by adopting five commonly used parametrizations, namely B$\Lambda$CDM, $\omega$CDM, Chevallier-Polarski-Linder, Barboza-Alcaniz, and a logarithmic equations of state. These considerations are confronted with recent observational data, including DESI DR2, Pantheon$^+$, and CC observations. Our analysis shows that the four parameterizations enter the acceleration phase at almost the same redshifts and share the same current value of the Hubble rate. Furthermore, the statistical comparison based on the Akaike, Bayesian, and Deviance Information Criterion shows that Barboza-Alcaniz, and logarithmic parameterizations have strong evidence and are competitive with $\Lambda$CDM. To classify this biconnection gravity in the plethora theoretical models describing the current cosmic acceleration, we examine its implications through cosmographic tools, including the deceleration, jerk, and snap parameters, as well as through the Statefinder analysis and $Om(z)$ diagnostic.