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In this paper, we examine static spherically symmetric wormhole solutions in generalized f(R, ϕ) gravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore different f(R, ϕ) models and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. The discussion about the conditions where the standard energy conditions (WEC and NEC) are valid for the fluids is discussed in details. From our results and for our cases, we conclude that for anisotropic and isotropic fluids, realistic wormhole geometries satisfying the energy conditions can be constructed.

The exact solutions of spherically symmetric space-times are explored by using Noether symmetries in $f(R,��,X)$ gravity with $R$ the scalar curvature, $��$ a scalar field and $X$ the kinetic term of $��$. Some of these solutions can represent new black holes solutions in this extended theory of gravity. The classical Noether approach is particularly applied to acquire the Noether symmetry in $f(R,��,X)$ gravity. Under the classical Noether theorem, it is shown that the Noether symmetry in $f(R,��,X)$ gravity yields the solvable first integral of motion. With the conservation relation obtained from the Noether symmetry, the exact solutions for the field equations can be found. The most important result in this paper is that, without assuming $R=\textrm{constant}$, we have found new spherically symmetric solutions in different theories such as: power-law $f(R)=f_0 R^n$ gravity, non-minimally coupling models between the scalar field and the Ricci scalar $f(R,��,X)=f_0 R^n ��^m+f_1 X^q-V(��)$, non-minimally couplings between the scalar field and a kinetic term $f(R,��,X)=f_0 R^n +f_1��^mX^q$ , and also in extended Brans-Dicke gravity $f(R,��,X)=U(��,X)R$. It is also demonstrated that the approach with Noether symmetries can be regarded as a selection rule to determine the potential $V(��)$ for $��$, included in some class of the theories of $f(R,��,X)$ gravity., Accepted for publication in JCAP. The title and the abstract have been changed and new exact solutions have been added with more cases. The existence of horizons of our solutions has been discussed too

In this paper, we examine static spherically symmetric wormhole solutions in generalized $f(R,��)$ gravity. To do this, we consider three different kinds of fluids: anisotropic, barotropic and isotropic. We explore different $f(R,��)$ models and inspect the energy conditions for all of those three fluids. It is found that under some models in this theory, it is possible to obtain wormhole solutions without requiring exotic matter. The discussion about the conditions where the standard energy conditions (WEC and NEC) are valid for the fluids is discussed in details. From our results and for our cases, we conclude that for anisotropic and isotropic fluids, realistic wormhole geometries satisfying the energy conditions can be constructed., Matches published version

First and second laws of black hole thermodynamics are examined at the apparent horizon of FRW spacetime in $f(R,R_{����}R^{����} ,��)$ gravity, where $R$, $R_{����}R^{����}$ and $��$ are the Ricci scalar, Ricci invariant 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 $T_{h}d\hat{S}_{h}+ T_{h}d_{i}\hat{S}_{h}+W dV=dE$, where $d_{i}\hat{S}_{h}$ is an extra entropy term because of the non-equilibrium presentation of the equations and $T_{h}d\hat{S}_{h}+W dV=dE$ 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 $f(R, ��)$ gravities. Finally to check the validity of GSLT, we take some particular models and produce constraints of the parameters., 29 pages, 4 figures

Recently, it was formulated a teleparallel theory called $f(T,B)$ gravity which connects both $f(T)$ and $f(R)$ under suitable limits. In this theory, the function in the action is assumed to depend on the torsion scalar $T$ and also on a boundary term related with the divergence of torsion, $B=2\nabla_{\mu}T^{\mu}$. In this work, we study different features of a flat Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation $\hat{T}_hS_{\rm eff}=-dE+WdV$, where $\hat{T}_h$ is the horizon temperature and $S_{\rm eff}$ is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium. We also formulate the constraint for the validity of the generalised second law of thermodynamics (GSLT). Additionally, using a cosmological reconstruction technique, we show that both $f(T,B)$ and $-T+F(B)$ gravity can mimic power-law, de-Sitter and $\Lambda$CDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions., Comment: Accepted for publication in Physics of the Dark Universe. Some notations and definitions have been changed but the conclusions are the same

We study the finite time singularity correspondence between the Jordan and Einstein frames for various $F(R)$ gravity theories. Particularly we investigate the ordinary pure $F(R)$ gravity case and the unimodular $F(R)$ gravity cases, in the absence of any matter fluids. In the ordinary $F(R)$ gravity cases, by using specific illustrative examples, we show that it is possible to have various correspondences of finite time singularities, and in some cases it is possible a singular cosmology in one frame might be non-singular in the other frame. In the unimodular $F(R)$ gravity case, the unimodular constraint is affected from the conformal transformation, so this has an effect on the metric we choose. Moreover, we study the Einstein frame counterpart theory of the unimodular $F(R)$ gravity case, and we investigate the correspondences of the singularities in the two theories by considering specific illustrative examples. Finally, a brief dynamical system analysis is performed for the vacuum unimodular $F(R)$ gravity and we demonstrate how the dynamical system behaves near the future Big Rip singularity.

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 $f(R,��,X)$ gravity, where $R$ is the Ricci scalar, $��$ 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., 13 pages, 1 figure; slightly revised version, displayed name corrected. arXiv admin note: text overlap with arXiv:1412.0867

General Relativity and the $\Lambda$CDM framework are currently the standard lore and constitute the concordance paradigm. Nevertheless, long-standing open theoretical issues, as well as possible new observational ones arising from the explosive development of cosmology the last two decades, offer the motivation and lead a large amount of research to be devoted in constructing various extensions and modifications. All extended theories and scenarios are first examined under the light of theoretical consistency, and then are applied to various geometrical backgrounds, such as the cosmological and the spherical symmetric ones. Their predictions at both the background and perturbation levels, and concerning cosmology at early, intermediate and late times, are then confronted with the huge amount of observational data that astrophysics and cosmology are able to offer recently. Theories, scenarios and models that successfully and efficiently pass the above steps are classified as viable and are candidates for the description of Nature. This work is a Review of the recent developments in the fields of gravity and cosmology, presenting the state of the art, high-lighting the open problems, and outlining the directions of future research. Its realization was performed in the framework of the COST European Action ``Cosmology and Astrophysics Network for Theoretical Advances and Training Actions''., Comment: 543 pages

We study a generalized nonlocal 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 are needed in order to achieve a renormalizable theory. In this paper, we explicitly show that this kind of coupling does not need to by 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 nonlocal theories. The symmetries for the generalized non-local theory is also found and some cosmological solutions are also achieved under the full theory., 15 pages, to be published in Eur.Phys.J. C

A gravitational theory of a scalar field non-minimally coupled with torsion and boundary term is considered with the aim to construct Lorentzian wormholes. Geometrical parameters including shape and redshift functions are obtained for these solutions. We adopt the formalism of Noether Gauge Symmetry Approach in order to find symmetries, Lie brackets and invariants (conserved quantities). Furthermore by imposing specific forms of potential function, we are able to calculate metric coefficients and discuss their geometrical behavior., Comment: Slightly updated version. Accepted for publication in PRD