Quintessential and Phantom Power-Law Solutions in Scalar Tensor Model of Dark Energy

Abstract

We consider a scalar-tensor model of dark energy with kinetic and Gauss Bonnet couplings. We study the conditions for the existence of quintessential and phantom power-law expansion, and also analyze these conditions in absence of potential (closely related to string theory). A mechanism to avoid the Big Rip singularity in various asymptotic limits of the model has been studied. It was found that the kinetic and Gauss-Bonnet couplings might prevent the Big Rip singularity in a phantom scenario. The autonomous system for the model has been used to study the stability properties of the power-law solution, and the centre manifold analysis was used to treat zero eigenvalues.PACS 98.80.-k, 95.36+x, 04.50.kd

Higgs potential from extended Brans–Dicke theory and the time-evolution of the fundamental constants

“…Combining this outcome with the previously noted η < 0, it follows that γ must be a negative quantity and hence the reason for the minus sign in Eq. (33). Thus, the signs η < 0 and γ < 0 become uniquely fixed.…”

“…This equation is remarkable since it links in a specific way the expected large value of ω in BD-gravity with a possible mild "running" of the gravitational "constant", G, which is controlled by the coefficient γ in the third scaling relation (17). In particular, we can see from (33) that ω → ∞, if and only if γ → 0, which is the limit of GR in which G =const. We will come back to this point in the next section.…”

“…Specifically, in this work we explore an extend Jordan-Fierz-Brans-Dicke ("BD" for short) type of gravitational theory [25,26], in which apart from including the usual non-minimal scalar-tensor interaction [27] for the BD-field, ψ, we introduce an interaction term between ψ and a second scalar, φ, which will play the role of Higgs boson after we determine self-consistently the form of its effective potential.Remarkably, this is possible if φ interacts non-minimally with curvature and if its kinetic term interacts with the Ricci tensor, thereby through a derivative interaction with gravity [28,29]. We do not address here higher order gravitational theories, as in our case we limit ourselves to generalized forms of Einstein's gravity involving only the first power of the Ricci tensor and scalar, but we extend our study to the case of Grand Unified Theories (GUT's), where more than one type of Higgs field is involved.The kind of cosmological solutions that we search for in order to fix self-consistently the Higgs potential are the simplest possible ones, namely the power-law solutions of the cosmological equations in a Friedmann-Lemaître-Robertson-Walker (FLRW) background.These scaling solutions are interpreted as representing asymptotic states of the different phases of the cosmic evolution [30][31][32][33][34][35][36][37][38][39]. The interpolation between the asymptotic states can only be described in terms of more general solutions, but in cosmology we are mostly interested in phases characterized by a stationary equation of state (EoS), such as e.g.…”

Slow-roll inflation with exponential potential in scalar-tensor models

“…So this model could describe an inflationary de Sitter solution that can evolve towards scaling solutions with saddle character or to stable attractor dominated by the scalar field, describing accelerated expansion [89]. Thus, the present model can provide a connection between early time inflation and late time accelerated expansion (in [90] special cases of quintessence and phantom solutions have been studied with exponential couplings). For unified description of early time inflation and late time accelerated expansion in the framework of scalar tensor theories see [91].…”

Instability of a Reissner-Nordström-AdS black hole under perturbations of a scalar field coupled to the Einstein tensor

“…One important term appearing in the Horndeski Lagrangian is the kinetic coupling of a scalar field to curvature. This derivative coupling of matter to gravity has interesting cosmological implications, acting as a friction term in the early inflationary cosmological evolution [5][6][7][8][9]. Observational tests of inflation with a field coupled to Einstein tensor were presented in [10].…”