Noether symmetry approach in f(T, B) teleparallel cosmology

We consider the cosmology derived from f(T, B) gravity where T is the torsion scalar and B=2e∂μ(eTμ)B=2e∂μ(eTμ) a boundary term. In particular we discuss how it is possible to recover, under the same standard, the teleparallel f(T) gravity, the curvature f(R) gravity, and the teleparallel–curvature f(R, T) gravity, which are particular cases of f(T, B). We adopt the Noether Symmetry Approach to study the related dynamical systems and to find cosmological solutions

Teleparallel quintessence with a nonminimal coupling to a boundary term

We propose a new model in the teleparallel framework where we consider a scalar field nonminimally coupled to both the torsion T and a boundary term given by the divergence of the torsion vector B ¼ 2 e ∂μðeTμÞ. This is inspired by the relation R ¼ −T þ B between the Ricci scalar of general relativity and the torsion of teleparallel gravity. This theory in suitable limits incorporates both the nonminimal coupling of a scalar field to torsion, and the nonminimal coupling of a scalar field to the Ricci scalar. We analyze the cosmology of such models, and we perform a dynamical systems analysis on the case when we have only a pure coupling to the boundary term. It is found that the system generically evolves to a late time accelerating attractor solution without requiring any fine-tuning of the parameters. A dynamical crossing of the phantom barrier is also shown to be possible

Holographic Complexity and Fidelity Susceptibility as Holographic Information Dual to Different Volumes in AdS

The holographic complexity and fidelity susceptibility have been defined as new quantities dual to different volumes in AdS. In this paper, we will use these new proposals to calculate both of these quantities for a variety of interesting deformations of AdS. We obtain the holographic complexity and fidelity susceptibility for an AdS black hole, Janus solution and a solution with cylindrically symmetry, an inhomogeneous background and a hyperscaling violating background. It is observed that the holographic complexity depends on the size of the subsystem for all these solutions and the fidelity susceptibility does not have any such dependence.Comment: Slighly updated version. Accepted for publication in Phys. Letters

Constraining generalized non-local cosmology from Noether symmetries

We study a generalized non-local theory of gravity which, in specific limits, can become either the curvature non-local or teleparallel non-local theory. Using the Noether symmetry approach, we find that the coupling functions coming from the non-local terms are constrained to be either exponential or linear in form. It is well known that in some non-local theories, a certain kind of exponential non-local couplings is needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to be introduced by hand, instead, it appears naturally from the symmetries of the Lagrangian in flat Friedmann–Robertson–Walker cosmology. Finally, we find de Sitter and power-law cosmological solutions for different non-local theories. The symmetries for the generalized non-local theory are also found and some cosmological solutions are also achieved using the full theory

Generalized f(R,ϕ,X)f(R,\phi,X) gravity and the late-time cosmic acceleration

High-precision observational data have confirmed with startling evidence that the Universe is currently undergoing a phase of accelerated expansion. This phase, one of the most important and challenging current problems in cosmology, represents a new imbalance in the governing gravitational equations. Historically, physics has addressed such imbalances by either identifying sources that were previously unaccounted for, or by altering the gravitational theory. Several candidates, responsible for this expansion, have been proposed in the literature, in particular, dark energy models and modified gravity models, amongst others. Outstanding questions are related to the nature of this so-called "dark energy" that is driving this acceleration, and whether it is due to the vacuum energy or a dynamical field. On the other hand, the late-time cosmic acceleration may be due to modifications of General Relativity. In this work we explore a generalised modified gravity theory, namely $f(R,\phi,X)$ gravity, where $R$ is the Ricci scalar, $\phi$ is a scalar field, and $X$ is a kinetic term. This theory contains a wide range of dark energy and modified gravity models. We considered specific models and applications to the late-time cosmic acceleration.Comment: 13 pages, 1 figure; slightly revised version, displayed name corrected. arXiv admin note: text overlap with arXiv:1412.086

Generalized second law of thermodynamic in modified teleparallel theory

This study is conducted to examine the validity of the generalized second law of thermodynamics (GSLT) in flat FRW for modified teleparallel gravity involving coupling between a scalar field with the torsion scalar T and the boundary term B=2∇μTμB=2∇μTμ . This theory is very useful, since it can reproduce other important well-known scalar field theories in suitable limits. The validity of the first and second law of thermodynamics at the apparent horizon is discussed for any coupling. As examples, we have also explored the validity of those thermodynamics laws in some new cosmological solutions under the theory. Additionally, we have also considered the logarithmic entropy corrected relation and discuss the GSLT at the apparent horizon

Thermodynamics in f(R,RαβRαβ,ϕ) theory of gravity

First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in f(R,RαβRαβ,ϕ) gravity, where R, RαβRαβ and ϕ are the Ricci invariant, Ricci tensor and the scalar field respectively. In this modified theory, Friedmann equations are formulated for any spatial curvature. These equations can be presented into the form of first law of thermodynamics for ThdSˆh+ThdiSˆh+WdV=dE, where diSˆh is an extra entropy term because of the non-equilibrium presentation of the equations and ThdSˆh+WdV=dE for the equilibrium presentation. The generalized second law of thermodynamics (GSLT) is expressed in an inclusive form where these results can be represented in GR, f(R) and f(R,ϕ) gravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters

Hubble inflation in Randall-Sundrum type II model

We study a braneworld Randall–Sundrum type II (RSII) model using the Hamilton–Jacobi formalism. We extend the standard inflationary parameters and the flow equations for this braneworld scenario. We investigate the conditions that reduce the infinite number of flow equations into a finite number and confirm that by considering one of the inflationary parameters that vanishes, the Hubble expansion rate gets a polynomial form in both General Relativity (GR) and in the high-energy regime of RSII. We also show that if one sets this inflationary parameter to a constant value, the model features a nonpolynomial form of the Hubble expansion rate. The form of the Hubble parameter in this case is different in GR and RSII. Next, we consider a single-scalar field model with a Hubble expansion rate behaving as H∝ϕn and show that compared to GR, the RSII model has a smaller tensor-to-scalar ratio and larger spectral index for n>1. Therefore, RSII model leads to better predictions than GR

Dynamical system analysis of generalized energy-momentum-squared gravity

In this work we have investigated the dynamics of a recent modification to the general theory of relativity, the energy-momentum squared gravity model f ( R , T 2 ) , where R represents the scalar curvature and T 2 the square of the energy-momentum tensor. By using dynamical system analysis for various types of gravity functions f ( R , T 2 ) , we have studied the structure of the phase space and the physical implications of the energy–momentum squared coupling. In the first case of functional where f ( R , T 2 ) = f 0 R n ( T 2 ) m , with f 0 constant, we have shown that the phase space structure has a reduced complexity, with a high sensitivity to the values of the m and n parameters. Depending on the values of the m and n parameters, the model exhibits various cosmological epochs, corresponding to matter eras, solutions associated to an accelerated expansion, or decelerated periods. The second model studied corresponds to the f ( R , T 2 ) = α R n + β ( T 2 ) m form with α , β constant parameters. In this case a richer phase space structure is obtained which can recover different cosmological scenarios, associated to matter eras, de–Sitter solutions, and dark energy epochs. Hence, this model represent an interesting cosmological model which can explain the current evolution of the Universe and the emergence of the accelerated expansion as a geometrical consequence