Cosmological Dark sector from a Mimetic-Metric-Torsion perspective

We generalize the basic theory of mimetic gravity by extending its purview to the general metric-compatible geometries that admit torsion, in addition to curvature. This essentially implies reinstating the mimetic principle of isolating the conformal degree of freedom of gravity in presence of torsion, by parametrizing both the physical metric and torsion in terms of the scalar `mimetic' field and the metric and torsion of a fiducial space. We assert the requisite torsion parametrization from an inspection of the fiducial space Cartan transformation which, together with the conformal transformation of the fiducial metric, preserve the physical metric and torsion. In formulating the scalar-tensor equivalent Lagrangian, we consider an explicit contact coupling of the mimetic field with torsion, so that the former can manifest itself geometrically as the source of a torsion mode, and most importantly, give rise to a viable `dark universe' picture from a mimicry of an evolving dust-like cosmological fluid with a non-zero pressure. A further consideration of higher derivatives of the mimetic field in the Lagrangian leads to physical bounds on the mimetic-torsion coupling strength, which we determine explicitly.