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Register a new userDynamical system analysis of dark energy models in scalar coupled metric-torsion theories
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Added by
Arshdeep Singh Bhatia
Publication date
2017
fields
Physics
and research's language is
English
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We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting cosmic acceleration driven by the {em dark energy}. The latter is defined in a way that it effectively has no direct interaction with the cosmological fluid, although in an equivalent scalar-tensor cosmological setup the scalar field interacts with the fluid (which we consider to be the pressureless dust). Determining the conditions for the existence of the stable critical points we check their physical viability, in both Einstein and Jordan frames. We also verify that in either of these frames, the evolution of the universe at the corresponding stable points matches with that given by the respective exact solutions we have found in an earlier work (arXiv: 1611.00654 [gr-qc]). We not only examine the regions of physical relevance for the trajectories in the phase space when the coupling parameter is varied, but also demonstrate the evolution profiles of the cosmological parameters of interest along fiducial trajectories in the effectively non-interacting scenarios, in both Einstein and Jordan frames.
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We study the phase space dynamics of the non-minimally coupled Metric-Scalar-Torsion model in both Jordan and Einstein frames. We specifically check for the existence of critical points which yield stable solutions representing the current state of accelerated expansion of the universe fuelled by the Dark Energy. It is found that such solutions do indeed exist, subject to constraints on the free model parameter. In fact the evolution of the universe at these stable critical points exactly matches the evolution given by the cosmological solutions we found analytically in our previous work on the subject.
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 $L$CDM 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 Brans-Dicke 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.
We investigate the cosmological dynamics in teleparallel gravity with nonminimal coupling. We analytically extract several asymptotic solutions and we numerically study the exact phase-space behavior. Comparing the obtained results with the corresponding behavior of nonminimal scalar-curvature theory, we find significant differences, such is the rare stability and the frequent presence of oscillatory behavior.
We study the viability conditions for the absence of ghost, gradient and tachyonic instabilities, in scalar-torsion $f(T,phi)$ gravity theories in the presence of a general barotropic perfect fluid. To describe the matter sector, we use the Sorkin-Schutz action and then calculate the second order action for scalar perturbations. For the study of ghost and gradient instabilities, we found that the gravity sector keeps decoupled from the matter sector and then applied the viability conditions for each one separately. Particularly, we verified that this theory is free from ghost and gradient instabilities, obtaining the standard results for matter, and for the gravity sector we checked that the corresponding speed of propagation satisfies $c_{s,g}^2=1$. On the other hand, in the case of tachyonic instability, we obtained the general expressions for the mass eigenvalues and then evaluated them in the scaling matter fixed points of a concrete model of dark energy. Thus, we found a space of parameters where it is possible to have a stable configuration respecting the constraints from the CMB measurements and the BBN constraints for early dark energy. Finally, we have numerically corroborated these results by solving the cosmological equations for a realistic cosmological evolution with phase space trajectories undergoing scaling matter regimes, and then showing that the system presents a stable configuration throughout cosmic evolution.
With a scalar field non-minimally coupled to curvature, the underlying geometry and variational principle of gravity - metric or Palatini - becomes important and makes a difference, as the field dynamics and observational predictions generally depend on this choice. In the present paper we describe a classification principle which encompasses both metric and Palatini models of inflation, employing the fact that inflationary observables can be neatly expressed in terms of certain quantities which remain invariant under conformal transformations and scalar field redefinitions. This allows us to elucidate the specific conditions when a model yields equivalent phenomenology in the metric and Palatini formalisms, and also to outline a method how to systematically construct different models in both formulations that produce the same observables.
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