Weakly dynamic dark energy via metric-scalar couplings with torsion

Abstract

Abstract. We study the dynamical aspects of dark energy in the context of a non-minimally coupled scalar field with curvature and torsion. Whereas the scalar field acts as the source of the trace mode of torsion, a suitable constraint on the torsion pseudo-trace provides a mass term for the scalar field in the effective action. In the equivalent scalar-tensor framework, we find explicit cosmological solutions representing dark energy in both Einstein and Jordan frames. We demand the dynamical evolution of the dark energy to be weak enough, so that the present-day values of the cosmological parameters could be estimated keeping them within the confidence limits set for the standard ΛCDM model from recent observations. For such estimates, we examine the variations of the effective matter density and the dark energy equation of state parameters over different redshift ranges. In spite of being weakly dynamic, the dark energy component differs significantly from the cosmological constant, both in characteristics and features, for e.g. it interacts with the cosmological (dust) fluid in the Einstein frame, and crosses the phantom barrier in the Jordan frame. We also obtain the upper bounds on the torsion mode parameters and the lower bound on the effective BransDicke parameter. The latter turns out to be fairly large, and in agreement with the local gravity constraints, which therefore come in support of our analysis.

Dynamical system analysis of dark energy models in scalar coupled Metric-Torsion theories

“…that of scalar field couplings to the four-dimensional Riemann-Cartan (U 4 ) Lagrangian. 50 The U 4 space-time is characterized by an asymmetric affine connection: Γ λ µν ( = Γ λ νµ ), which incorporates the third-rank torsion tensor defined as:…”

“…28,50,51 Now, in the standard cosmological framework, the torsion degrees of freedom get restricted by the FRW metric structure. 30 Also since φ acts as the source of the trace mode of torsion (via the corresponding equation of motion), we effectively have a scalar-tensor equivalent MST setup.…”

“…The pseudo-trace mode of torsion can give rise to a mass term for φ, via suitable augmentation of the effective action with say, some higher order torsion terms. 50 Considering further a pressureless dust-like cosmological matter, viable DE solutions in Einstein and Jordan frames have been worked out analytically in paper I, 50 keeping the cosmological parameters within the corresponding error estimates for the ΛCDM model from recent observations. However, there remains the important question:…”

“…the dust-like matter and a left-over, supposedly the DE. 50 In such a scenario, the physical relevance of the existent CPs in the phase plane is implicated by the eventual extinction of the matter sector, irrespective of the initial conditions. Secondly, it is not desirable to have the chosen phase space variables depending explicitly on the system parameter β.…”

“…The limiting values set on w from extensive studies, 56,57 provide an independent credibility check of the cosmological solutions. 50 the Jordan frame. Some characteristic differences are there of course, compared to the Einstein frame analysis.…”