Detectability of Torsion Gravity via Galaxy Clustering and Cosmic Shear Measurements

Alterations of the gravity Lagrangian introduced in modified torsion gravity theories---also referred to as $f(T)$ gravity---allows for an accelerated expansion in a matter dominated Universe. In this framework, the cosmic speed up is driven by an effective `torsion fluid'. Besides the background evolution of the Universe, structure formation is also modified because of a time dependent effective gravitational constant. Here, we investigate the imprints of $f(T)$ gravity on galaxy clustering and weak gravitational lensing to the aim of understanding whether future galaxy surveys could constrain torsion gravity and discriminate amongst it and standard general relativity. Specifically, we compute Fisher matrix forecasts for two viable $f(T)$ models to both infer the accuracy on the measurement of the model parameters and evaluate the power that a combined clustering and shear analysis will have as a tool for model selection. We find that with such a combination of probes it will indeed be possible to tightly constrain $f(T)$ model parameters. Moreover, the Occam's razor provided by the Bayes factor will allow us to confirm an $f(T)$ power-law extension of the concordance $\Lambda{\rm CDM}$ model, were a value larger than 0.02 of its power-law slope measured, whereas in $\Lambda{\rm CDM}$ it is exactly 0.