The present work is to introduce a new kind of modified gravitational theory, named as $f(\mathcal{R,G,T})$ (also $f(\mathcal{R,T,G})$) gravity, where $\mathcal{R}$ is the Ricci scalar, $\mathcal{G}$ is Gauss-Bonnet invariant and $\mathcal{T}$ is the trace of the energy-momentum tensor. With the help of different models in this gravity, we investigate some physical features of different relativistic compact stars. For this purpose, we develop the effectively modified field equations, conservation equation, and the equation of motion for test particle. Then, we check the impact of additional force (massive test particle followed by a non-geodesic line of geometry) on compact objects. Furthermore, we took three notable stars named as $Her X-1$, $SAXJ1808.4-3658$ and $4U1820-30$. The physical behavior of the energy density, anisotropic pressures, different energy conditions, stability, anisotropy, and the equilibrium scenario of these strange compact stars are analyzed through various plots. Finally, we conclude that the energy conditions hold, and the core of these stars is so dense.
Here we propose the extended modified gravity theory named as $f(R,G,\mathcal{T})$ gravity where $R$ is the Ricci scalar, $G$ is the Gauss-Bonnet invariant and $\mathcal{T}$ is the trace of the stress-energy tensor. We derive the gravitational field equations in $f(R,G,\mathcal{T})$ gravity by taking least action principle. Next we construct the $f(R,G,\mathcal{T})$ in terms of $R$, $G$ and $\mathcal{T}$ in de Sitter as well as power law expansion. We also construct $f(R,G,\mathcal{T})$ if the expansion follows the finite time future singulary (big rip singularity). We investigate the energy c…
We extend the results of antecedent literature on quadratic Metric-Affine Gravity by studying a new quadratic gravity action in vacuum which, besides the usual (non-Riemannian) Einstein-Hilbert contribution, involves all the parity even quadratic terms in torsion and non-metricity plus a Lagrangian that is quadratic in the field-strengths of the torsion and non-metricity vector traces. The theory result to be equivalent, on-shell, to a Vector-Tensor theory. We also discuss the sub-cases in which the contribution to the Lagrangian quadratic in the field-strengths of the torsion and non-metricit…
In this paper, we analyze the modified $f(\mathcal{R})$ gravity models in Friedmann--Lema\^ıtre--Robertson--Walker (FLRW) background. The actions of bouncing cosmology are studied under consideration of different viable models in $f(\mathcal{R})$ gravity theory that can resolve the difficulty of singularity in standard Big-Bang cosmology. Under different viable models in $f(\mathcal{R})$ gravity theory, the cosmological constraints are plotted in provisions of cosmic-time, then investigated the bounce circumstance. In addition, the red-shift parameter is used to reconstruct the modified gravit…
The aim of this paper is to analyze the cosmological evolution of holographic dark energy in $f(\mathcal{G},T)$ gravity ($\mathcal{G}$ and $T$ represent the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively). We reconstruct $f(\mathcal{G},T)$ model through correspondence scheme using power-law form of the scale factor. The qualitative analysis of the derived model is investigated with the help of evolutionary trajectories of equation of state, deceleration as well as state-finder diagnostic parameters and $ω_{_{\mathcal{G}T}}-ω'_{_{\mathcal{G}T}}$ cosmological phase …
We present the coupling of the torsion scalar $T$ and the trace of energy-momentum tensor $\mathcal{T}$, which produces new modified $f(T,\mathcal{T})$ gravity. Moreover, we consider the functional form $f(T,\mathcal{T}) =α\mathcal{T}+βT^2$ where $α$ and $β$ are free parameters. As an alternative to a cosmological constant, the $f(T,\mathcal{T})$ theory may offer a theoretical explanation of the late-time acceleration. The recent observational data to the considered model especially the bounds on model parameters is applied in detail. Furthermore, we analyze the cosmological behavior of the de…
We show that the Lovelock type brane gravity is naturally holographic by providing a correspondence between bulk and surface terms that appear in the Lovelock-type brane gravity action functional. We prove the existence of relationships between the $\mathcal{L}_{\mbox{\tiny bulk}}$ and $\mathcal{L}_{\mbox{\tiny surf}}$ allowing $\mathcal{L}_{\mbox{\tiny surf}}$ to be determined completely by $\mathcal{L}_{\mbox{\tiny bulk}}$. In the same spirit, we provide relationships among the various conserved tensors that this theory possesses. We further comment briefly on the correspondence between geom…
We explore the cosmological viability of a theory of gravity defined by the Lagrangian $f(\mathcal{R})=\mathcal{R}^{n\left(\mathcal{R}\right)}$ in the Palatini formalism, where $n\left(\mathcal{R}\right)$ is a dimensionless function of the Palatini scalar curvature $\mathcal{R}$ that interpolates between general relativity when $n\left(\mathcal{R}\right)=1$ and a locally scale-invariant and superficially renormalizable theory when $n\left(\mathcal{R}\right)=2$. We refer to this model as asymptotically Weyl-invariant gravity (AWIG). We analyse perhaps the simplest possible implementation of AWI…
In this work we shall address the ghost issue of $F\left( R,\mathcal{G} \right)$ gravity, which is known to be plagued with ghost degrees of freedom. These ghosts occur due to the presence of higher than two derivatives in the field equations, and can arise even when considering cosmological perturbations, where superluminal modes may arise in the theory. If we consider the quantum theory, the ghosts generate the negative norm states, which give the negative probabilities, and therefore the ghosts are physically inconsistent. Motivated by the importance of $F\left( R,\mathcal{G} \right)$ gravi…
The observational evidence regarding the present cosmological aspects tells us about the presence of very little anisotropy in the universe on a large scale. Here, in this paper, we attempt to study locally rotationally symmetric (LRS) homogeneous Bianchi-I spacetime with the isotropic matter distribution. This is done within the framework of $f(\mathcal{R},\mathscr{L}_m)$ gravity. Particularly, we consider a non-linear $f(\mathcal{R},\mathscr{L}_m)$ model, $f(\mathcal{R},\mathscr{L}_m)=\dfrac{1}{2}\mathcal{R}+\mathscr{L}_m^{\,α}$. Furthermore, $ω$, the equation of state parameter, which is vi…
The field equations of $f(R,\mathcal{G})$ gravity are rewritten in the form of obvious wave equations with the stress-energy pseudotensor of the matter fields and the gravitational field, as their sources, under the de Donder condition. The linearized field equations of $f(R,\mathcal{G})$ gravity are the same as those of linearized $f(R)$ gravity, and thus, their multipole expansions under the de Donder condition are also the same. It is also shown that the Gauss-Bonnet curvature scalar $\mathcal{G}$ does not contribute to the effective stress-energy tensor of gravitational waves in linearized…
Using a convolutive field theoretic product, it is shown here that the "square" of an Abelian $D=6$, $\mathcal{N}=(2,0)$ theory yields the free $D=6$, $\mathcal{N}=(4,0)$ theory constructed by Hull, together with its generalised (super)gauge transformations. This offers a new perspective on the $(4, 0)$ theory and chiral theories of conformal gravity more generally, while at the same time extending the domain of the "gravity = gauge $\times$ gauge" paradigm.
In this paper, we consider static spherical structure to develop some anisotropic solutions by employing the extended gravitational decoupling scheme in the background of $f(\mathcal{R},\mathcal{T},\mathcal{R}_{γχ}\mathcal{T}^{γχ})$ gravity, where $\mathcal{R}$ and $\mathcal{T}$ indicate the Ricci scalar and trace of the energy-momentum tensor, respectively. We transform both radial as well as temporal metric functions and apply them on the field equations that produce two different sets corresponding to the decoupling parameter $ξ$. The first set is associated with isotropic distribution, i.e…
In this paper, we study the $f(T,\mathcal{T})$ gravity model in the presence of the bulk viscosity by the flat-FRW metric. The field equation is obtained by teleparallel gravity with tetrad field. The universe components are considered as matter and dark energy which the dark energy component associates from the viscous $f(T,\mathcal{T})$ gravity. After calculating the Friedmann equations, we obtain the energy density, the pressure and the EoS of dark energy in terms of the redshift parameter. Afterward, we plot the corresponding cosmological parameters versus the redshift parameter and examin…
A bouncing universe is a viable candidate to solve the initial singularity problem. Here we consider bouncing solutions in the context of $f(R,\mathcal{G})$ gravity by using an order reduction technique which allows one to find solutions that are perturbatively close to General Relativity. This procedure also acts as a model selection approach. Indeed, several covariant gravitational actions leading to a bounce are directly selected by demanding that the Friedmann equation derived within such gravity theories coincides with the one emerging from Loop Quantum Cosmology.
In this paper, we consider static self-gravitating spherical spacetime and determine various anisotropic solutions through the extended gravitational decoupling technique in $f(\mathcal{R},\mathcal{T},\mathcal{R}_{λξ}\mathcal{T}^{λξ})$ gravity to analyze the influence of electromagnetic field on them. We construct two different sets of modified field equations by employing the transformations on both radial as well as temporal metric potentials. The first set symbolizes the isotropic fluid distribution, thus we take Krori-Barua solution to deal with it. The indefinite second sector comprises t…
On thermal fluctuations and quantum regularities of $\mathcal{F}(R,\mathcal{G})$ gravity black holes with constant topological Euler density in nonlinear electrodynamics
We consider a model of Bose-Einstein condensate of weakly interacting off-shell gravitons in the regime that is far from the quantum critical point. Working in static spherically symmetric setup, recent study has demonstrated that the effective spacetime geometry of this condensate is a gravastar. In this paper we make three generalizations: introducing a composite of two sets of off-shell gravitons with different wavelength to enable richer geometries for the interior and exterior spacetimes, working in $f({\mathcal R})$ gravity, and extending the calculations to higher dimensions. We find th…
We investigate Palatini $f(\mathcal{R},\mathcal{L}_m, \mathcal{R}_{μν}T^{μν})$ modified theories of gravity wherein the metric and affine connection are treated as independent dynamical fields and the gravitational Lagrangian is made a function of the Ricci scalar $\mathcal{R}$, the matter Lagrangian density $\mathcal{L}_m,$ and a "matter-curvature scalar" $\mathcal{R}_{μν}T^{μν}$. The field equations and the equations of motion for massive test particles are derived, and we show that the independent connection can be expressed as the Levi-Civita connection of an auxiliary, energy-momentum dep…
Topological Static Spherically Symmetric vacuum Solutions in $\mathcal F(R,G)$ Gravity
给出了$\mathcal F (R,G)$ -修正引力中拓扑静态球对称度规运动方程的拉格朗日推导，并讨论了相应的解。特别地，我们找到了模型$\mathcal F (R,G)=R+\sqrt{G}$的一个新的拓扑解，并对黑洞解和热力学第一定律进行了分析。此外，还考虑了与电磁场的耦合，并推导出麦克斯韦解。
In this work, we study the existence of strange star in the background of $f(\mathbb{T},\mathcal{T})$ gravity in the Einstein spacetime geometry, where $\mathbb{T}$ is the torsion tensor and $\mathcal{T}$ is the trace of the energy-momentum tensor. The equations of motion are derived for anisotropic pressure within the spherically symmetric strange star. We explore the physical features like energy conditions, mass-radius relations, modified TOV equations, principal of causality, adiabatic index, redshift and stability analysis of our model. These features are realistic and appealing to furthe…
The manifesto of the current article is to investigate the compact anisotropic matter profiles in the context of one of the modified gravitational theories, known as $f(\mathcal{R}, \mathcal{T})$ gravity, where $\mathcal{R}$ is a Ricci Scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. To achieve the desired goal, we capitalized on the spherical symmetric space-time and utilized the embedding class-1 solution via Karmarkar's condition in modeling the matter profiles. To calculate the unidentified constraints, Schwarzschild exterior solution along with experimental statistics …
In this work we develop a theoretical framework for Gauss-Bonnet modified gravity theories, in which ghost modes can be eliminated at the equations of motion level. Particularly, after we present how the ghosts can occur at the level of equations of motion, we employ the Lagrange multipliers technique, and by means of constraints we are able to eliminate the ghost modes from Gauss-Bonnet theories of the form $f(\mathcal{G})$ and $F(R,\mathcal{G})$ types. Some cosmological realizations in the context of the ghost free $f(\mathcal{G})$ gravity are presented, by using the reconstruction technique…
In this work we study certain classes of $F(R,{\cal G})$ gravity which have appealing phenomenological features, with respect to the successful realization of the dark energy and of the inflationary era. Particularly, we discuss the general formalism and we demonstrate how several inflationary and dark energy evolutions can be described in the context of $F(R,{\cal G})$ gravity. Also we propose a unified model, in the context of which the early and late-time dynamics are controlled by the $F(R,{\cal G})$ gravity, thus producing inflation and the dark energy era, while the intermediate era is a…
Making use of the $1 + 3$ covariant formalism, we show explicitly the effect that nonmetricity has on the dynamics of the universe. Then, using the Dynamical System Approach, we analyze the evolution of Bianchi type-I cosmologies within the framework of $f(\mathcal{Q})$ gravity. We consider several models of function $f(\mathcal{Q})$, each of them manifesting isotropic eras of the universe, whether transitional or not. In one case, in addition to the qualitative analysis provided by the dynamical system method, we also obtain analytical solutions in terms of the average length scale $l$.
We present the first interior solutions representing compact stars in $κ(\mathcal{R},\mathcal{T})$ gravity, by solving the modified field equations in isotropic coordinates. Further, we have assumed the metric potentials in Schwarzschild's form and a few parameters along with the isotropic condition of pressure. For solving, we use specific choice of the running gravitational constant as $κ(\mathcal{R},\mathcal{T})=8π-λ\mathcal{T} ~~(G=\tilde{c}=1)$. Once arrived at the reduced field equations, we investigate two solutions with $c=1$ and $c \neq 1$, where $c$ denotes here another constant that…
The compact stars are promising candidates associated with the generation of gravitational waves (GWs). In this work, we study a special type of compact stars known as strange stars in the $f(\mathcal{R})$ gravity Palatini formalism. Here we consider three promising $f(\mathcal{R})$ gravity models viz., Starobinsky, Hu-Sawicki and Gogoi-Goswami models in the domain of MIT Bag model and linear equations of state (EoSs). We compute the stellar structures numerically and constrained the $f(\mathcal{R})$ model parameters with a set of probable strange star candidates. The study shows that the cons…
In this paper, we explicitly construct an asymptotic $\mathcal{W}_5$ symmetry algebra of the three-dimensional anti-de Sitter $(AdS_3)$ higher spin gravity. We use an $\mathfrak{sl}(5,R) \oplus \mathfrak{sl}(5,R)$ Lie algebra valued Chern-Simons gauge theory with a negative cosmological constant and its asymptotic symmetry algebra is explicitly calculated as two copies of the classical $\mathcal{W}_5$ algebra with central charge c. Our results can be interpreted as a spin $5$ extension of $AdS_3$ gravity and a proof of how the higher spin Ward identities and as well as the asymptotic $\mathcal…
