Cosmological signatures of torsion and how to distinguish torsion from the dark sector.

Torsion is a non-Riemannian geometrical extension of general relativity that allows including the spin of matter and the twisting of spacetime. Cosmological models with torsion have been considered in the literature to solve problems of either the very early (high redshift $z$) or the present-day Universe. This paper focuses on distinguishable observational signatures of torsion that could not be otherwise explained with a scalar field in pseudo-Riemannian geometry. We show that when torsion is present, the cosmic duality relation between the angular diameter distance, $D_{\mathrm A}$, and the luminosity distance, $D_{\mathrm L}$, is broken. We show how the deviation described by the parameter $\eta = D_{\mathrm L}/[ D_{\mathrm A}(1+z)^2] -1 $ is linked to torsion and how different forms of torsion lead to special-case parametrisations of $\eta$, including $\eta_0 z$, $\eta_0 z/(1+z)$, and $\eta_0 \ln (1+z)$. We also show that the effects of torsion could be visible in low-redshift data, inducing biases in supernovae-based $H_0$ measurements. We also show that torsion can impact the Clarkson-Bassett-Lu (CBL) function ${\cal C}(z) = 1 + H^2 (D D'' - D'^2) + H H' D D'$, where $D$ is the transverse comoving distance. If $D$ is inferred from the luminosity distance, then, in general non-zero torsion models, ${\cal C}(z) \ne 0$. For pseudo-Riemannian geometry, the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric has ${\cal C}(z) \equiv 0$; thus, measurement of the CBL function could provide another diagnostic of torsion.