Abstract
We extend the basic formalism of mimetic-metric-torsion gravity theory, in a way that the mimetic scalar field can manifest itself geometrically as the source of not just the trace mode of torsion, but its axial (or, pseudo-trace) mode as well. Specifically, we consider the mimetic field to be (i) coupled explicitly to the well-known Holst extension of the Riemann–Cartan action, and (ii) identified with the square of the associated Barbero–Immirzi field, presumably a pseudo-scalar. The conformal symmetry originally prevaling in the theory would still hold, as the associated Cartan transformations do not affect the torsion pseudo-trace, and hence the Holst term. Demanding the theory to preserve the spatial parity symmetry as well, we show a geometric unification of the cosmological dark sector, and the feasibility of a super-accelerating regime in the course of evolution of the universe. From the observational perspective, assuming the cosmological evolution profile to be very close to that for varLambda CDM, we further illustrate a smooth crossing of the so-called phantom barrier at a low red-shift, albeit with a restricted parametric domain. Subsequently, we determine the extent of the super-acceleration by examining the evolution of the relevant torsion parameters.
Highlights
The basic CM theory amounts to a scalartensor reformulation of General Relativity (GR), of a specific sort which exploits the diffeomorphism invariance to reparametrize the physical metric gμν by a fiducial metric gμν and a scalar field φ, in a way that gμν remains invariant under a conformal transformation of gμν
The gravitational conformal degree of freedom gets encoded by the field φ, known as the ‘mimetic field’ [1], which ostensibly has no prior relevance to geometry
A viable phantom crossing evolution of a unified cosmological dark sector is demonstrated by extending the basic mimetic-metric-torsion (MMT) formalism with an explicit coupling of the mimetic field φ and the Holst term, motivated from the following: Firstly, its compliance with the basic precept of MMT gravity, viz. the preservation of conformal symmetry while letting φ to manifest geometrically as the source of torsion (or certain mode(s) thereof)
Summary
The basic CM theory amounts to a scalartensor reformulation of General Relativity (GR), of a specific sort which exploits the diffeomorphism invariance to reparametrize the physical metric gμν by a fiducial metric gμν and a scalar field φ, in a way that gμν remains invariant under a conformal transformation of gμν. An appropriate methodology, which has been motivated from various standpoints (such as the chiral anomaly cancellation), is to promote the associated coupling parameter γ , known as the Berbero–Immirzi (BI) parameter, to the status of a scalar or a pseudo-scalar field [211,217– 222] The latter is the most suitable option if the theory is to preserve spatial parity symmetry – a consideration amenable to our endeavour on extending the basic MMT formalism by incorporating the Holst term, coupled to the mimetic field φ, in this paper. Commonly known scalar field DE models (quintessence, k-essence, etc.) cannot usually account for this without the involvement of ghost (or phantom) degree(s) of freedom There is no such concern though, with our MMT extension scheme outlined above, as the corresponding Lagrangian we propose does not ostensibly consist of any ghost-like term, and in a reduced form looks precisely the same as that in the existing literature on mimetic gravity [2,3].
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