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Recently, the Rastall–Rainbow gravity emerged as an intriguing modified gravity theory. This theory is a combination of two theories, namely, the Rastall theory and the Rainbow description. This study aims to investigate the potential existence of static, spherically symmetric wormholes in this gravity theory. Specifically, we provide precise solutions to asymptotically flat wormhole geometries for the specific choice of the redshift and shape functions. With the specific examples, we investigate some issues concerning energy conditions and adiabatic sound velocity. We also consider the “volume integral quantifier” to assess the total amount of energy-condition violation matter. Finally, we conclude that reducing Rastall’s parameters and adjusting the Rainbow functions may alleviate the violation of energy conditions.

This work examines whether evolving wormhole solution is possible or not in $f(R,T)$ modified gravity theory. In the background of inhomogeneous FLRW-type wormhole configuration, the field equations are investigated for different choices of scale factors and shape functions. For the power law and exponential choice of the scale factor from cosmological context and decoupled power law of $f(R,T)$ in each variable, wormhole configuration has been examined for two viable choices of shape function. Energy conditions are examined graphically for a range of values of the parameters involved. Finally, the possibility of emergent scenario at early cosmic evolution has been examined.

Using modified $f(T)$ gravity and the diagonal tetrad, we propose a new kind of analytical solution to describe anisotropic charged stellar structures in this study. We obtain precise solutions by applying the linear form of $f(T)$ as $f(T)=\gamma T+\delta$ in the framework of Tolman–Kuchowicz physically sound metric potentials. The stellar structures of the compact star EXO 1785-248 are then investigated using the model by incorporating a linear equation of state relating the radial pressure $p_r$ and the matter density $\rho$. We computed the closed-form expressions for the model parameters and illustrated their characteristics. The comprehensive graphical analysis demonstrates the scientific plausibility, causality, and dynamical stability of the model describing charged anisotropic stars. Finally, using the M-R curve, we estimate the numerical values of mass for different values of $\gamma$. The observational data of the neutron star candidates 4U 1820-30, PSR J1614-2230, and PSR J2215 + 5135 are covered by the maximum allowable masses for different values of $\gamma$ additionally, when $\gamma =2.5$, the charged compact star’s maximum permissible mass is calculated to be $2.56M_{\odot }$, which could indicate the secondary component of the GW190814 event discovered by LIGO/VIRGO experiments.

In this paper, we present a simple toy model for a possible Ricci–Gauss–Bonnet gravity universe in which a novel form of cyclic evolution occurs where the Hubble parameter remains positive and oscillates. In this model, we have used the form for $f(R,\mathcal{𝒢})$ gravity as $\alpha R+\beta {\mathcal{𝒢}}^2$. In order to simulate cosmic transit, we have considered a time-dependent deceleration parameter oscillating in between the two phases of deceleration and acceleration which leads to a specific form for the Hubble parameter. The current periodic model predicts the deceleration–acceleration cosmic transit to happen at approximately $8.7\text{Gyr}$. The evolution of different parameters with the redshift has been plotted and analyzed. The contributions of the entropy-corrected holographic dark energy and the modified holographic Ricci dark energy density to the total energy parameter have been investigated.

We investigate the cosmic evolution of the universe in context of $f(R,G)$ gravity with homogeneous and isotropic background, where $R$ represents the Ricci scalar, and $G$ denotes the Gauss–Bonnet invariant. With the field equations of the $f(R,G)$ gravity in the non-flat spacetime, we examine the characteristics of model with two distinct forms: $f_1(R,G)=\mu R^n{G}^m$ and $f_2(R,G)={\beta }_{1}R+{\beta }_2\mu R^n{G}^m$, where $n$, $m$, ${\beta }_1$ and ${\beta }_2$ are the model parameters. The power-law solutions for the field equations are obtained by constraining the model parameters by employing Bayesian analysis tools in conjunction with the Markov Chain Monte Carlo (MCMC) method. We constraint the parameters by utilizing the combined datasets (OHD$+$BAO$+$Pantheon) for open Friedmann–Lemaitre–Robertson–Walker (FLRW) model. The parameters of power-law solutions are determined as $H_0=70.76732_{-0.00088}^{+0.00010}$ km/(s ⋅ Mpc) and $q=-0.6478_{-0.000075}^{+0.000091}$. The present dark energy model estimates $H_0$ value higher than the $\mathrm{\Lambda }$CDM model. This is one of the motivations to consider the $f(R,G)$ gravity to describe dark energy era. The best-fit values of model parameters in an open model yield the power index of power-law solution as $\alpha =2.394949_{-0.00060}^{+.000089}$. In the present model, the joint analysis by incorporating data from OHD, BAO, and Pantheon datasets favors the open FLRW model with power-law solutions at the late times. The behavior of cosmological parameters has been studied to explore the evolution of dark energy. The equation of state parameter ($\omega \simeq -1$) supports the accelerated expansion of the Universe at late times. The energy conditions are also studied to test the cosmological viability of the model.

In this paper, I propose a static wormhole model within modified $f(R,T)$ gravity where $f(R,T)=R+2\lambda T$. The wormhole solutions have been evolved in four cases — three different shape function along with redshift $\varphi =\frac{{\varphi }_0}{r}$ and a variable EoS parameter $\omega (r)$ with constant redshift function. I also have explored the energy conditions and the behavior of exotic matter within the wormhole in all scenarios. The presence of exotic matter violates necessary energy conditions near wormhole throat which gives constraint on modified gravity parameter $\lambda$ in all different cases.

In this work, we construct time-dependent wormhole solutions in the context of f(R) theory of gravity. The background matter is considered to be traceless. By considering specific shape function and power-law expansion, exact solutions for f(R) are found. The null and the weak energy conditions (NEC and WEC) are checked for wormhole solutions. It is shown that the matter threading the wormhole spacetimes with either accelerated expansion or decelerated expansion satisfies the NEC and WEC.

Some properties of f(R, L_m) gravity are studied in this paper. Concretely, the energy conditions and the Dolgov–Kawasaki (DK) instability criterion in f(R, L_m) gravity are obtained, which are quite general and can degenerate to the ones in General Relativity (GR) and pure f(R) gravity with non-coupling and non-minimal coupling as well as in [J. Wang and K. Liao, Class. Quantum Grav. 29, 215016 (2012)] as special cases. Furthermore, in order to get some insight on the meaning of the energy conditions and the DK instability criterion, we apply them to the concrete type of f(R, L_m) gravity models and the corresponding constraints on the models are given.

We consider Heisenberg–Euler-type model of nonlinear electrodynamics with two parameters. Heisenberg–Euler electrodynamics is a particular case of this model. Corrections to Coulomb’s law at $r\to \infty$ are obtained and energy conditions are studied. The total electrostatic energy of charged particles is finite. The charged black hole solution in the framework of nonlinear electrodynamics is investigated. We find the asymptotic of the metric and mass functions at $r\to \infty$. Corrections to the Reissner–Nordström solution are obtained.

Morris and Thorne [M. S. Morris and K. S. Thorne, Am. J. Phys.56, 395 (1988)] proposed geometrical objects called traversable wormholes that act as bridges in connecting two spacetimes or two different points of the same spacetime. The geometrical properties of these wormholes depend upon the choice of the shape function. In the literature, these are studied in modified gravities for different types of shape functions. In this paper, the traversable wormholes having shape function $b(r)=\frac{r_{0}tanh(r)}{tanh(r_0)}$ are explored in $f(R)$ gravity with $f(R)=R+\alpha R^m-\beta R^{-n}$, where $\alpha$, $\beta$, $m$ and $n$ are real constants. For different values of constants in function $f(R)$, the analysis is done in various cases. In each case, the energy conditions, equation of state parameter and anisotropic parameter are determined.

Wormholes (WHs) are considered as hypothetical shortcuts or tunnels in spacetime. In general relativity (GR), the fundamental ingredient of WH geometry is the presence of exotic matter at the throat, which is responsible for the violation of null energy condition (NEC). However, the modified gravity theories have shown to be able to provide WH solutions satisfying energy conditions (ECs). In this paper, we study the static spherically symmetric WH solutions in modified $f(R,T)$ gravity for a phantom fluid case. The exact solutions of this model are obtained through the equation of state (EoS), $p=\omega \rho$, associated with phantom dark energy (DE) $\omega <-1$. We find the existence of spherically symmetric WH solution supported by phantom energy distribution. The shape function of the WH obtained in this model obeys all the WH metric conditions. In modified gravity scenario, the phantom fluid WH violates the NEC in radial case, unlike in the tangential case. Furthermore, using the “volume integral quantifier” (VIQ) method, the total amount of EC violating matter in spacetime is discussed briefly.

In this paper, we have studied Noether symmetries of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Solving the determining equations of Noether symmetries, it is concluded that the dimension of Noether algebra for these spacetimes is 5, 6, 7, 9, 10, 11 or 17. For all Noether symmetry generators, we have presented the corresponding conservation laws and the Lie algebra. Moreover, some physical implications of the obtained metrics are discussed, which include the study of different energy conditions.

In this paper, conformal symmetric Freidmann–Robertson–Walker (FRW) universe with perfect fluid in the framework of $f(R,T)$ gravitational theory is investigated. Firstly, field equations of FRW universe with perfect fluid are obtained for $f(R,T)=R+h(T)$ modified theory of gravity. The field equations of the model have been revised to understand physical nature between matter and geometry by means of conformal symmetry in $f(R,T)$ gravitational theory. The exact solutions of conformal FRW universe with perfect fluid are attained for matter part of the $f(R,T)$ model in the case of $h(T)=\lambda T$. The $f(R,T)$ gravitational theory is one of the acceptable modifications of General Relativity (GR) in order to expound cosmic acceleration of the universe with no needing any exotic component. Nevertheless, the obtained model indicates exotic matter distribution for the current selection of arbitrary constants. Also, different value selections of arbitrary constants for the obtained model are able to predicate expanding or contracting universe with zero deceleration. Besides, it is shown that the FRW universe under the influence of the conformal Killing vector preserves to isotropic nature. Energy conditions are investigated. Also, it is shown that the constructed model satisfies strong energy condition (SEC) in all cases.

This paper presents modeling of matter bounce in the framework of $f(R,T)$ gravity, where $f(R,T)=R+2\lambda T$. We start by defining a parametrization of scale factor which is non-vanishing. The geometrical parameters such as the Hubble parameter and deceleration parameter are derived, from which expressions of pressure, density and Equation of State (EoS) parameter and a qualitative understanding of the initial conditions of the universe at the bounce are ascertained. We found that the initial conditions of the universe are finite owing to the non-vanishing nature of the scale factor thus eliminates the initial singularity problem. Furthermore, we show the violation of energy conditions near the bouncing region and analyze the stability of our model with respect to linear homogeneous perturbations in Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime. We found that our model and hence matter bounce scenarios in general are highly unstable at the bounce in the framework of $f(R,T)$ gravity but the perturbations decay out rapidly away from the bounce safeguarding its stability at late-times.

In this paper, we have used the Karmarkar condition to the spherically symmetric non-static radiating star experiencing dissipative gravitational collapse with a heat flux in the framework of $f(R,T)$ gravity, (where $R$ is Ricci scalar which replaces Lagrangian density and $T$ is the trace of energy–momentum tensor). To obtain the ultimate results of the gravitational field equations in $f(R,T)$ scenario, we take a linear form of the function as $f(R,T)=R+2\lambda T$. In this connection, the Karmarkar condition along with boundary condition generates a model of radiating star and enables us to completely indicate the spatial presence of gravitational potentials. Vadiya’s exterior solution across a time-like hypersurface is smoothly matched to the interior solution which allows to study the physical conduct of our model under consideration. Furthermore, we have analyzed the energy conditions of radiating star in $f(R,T)$ gravity and analyzed the physical behavior of thermodynamics parameters which provide a detailed discussion of the model. For coupling parameter $\lambda =0$, we successfully obtain the standard results of General Relativity.

In this work, the possible existence of wormhole solutions have been investigated in the extended teleparallel $f(T)$ theory of gravity by incorporating the Lorentzian source of non-commutative geometry through the conformal motion. The physical concept of conformal symmetry becomes more arguable when it is discussed in the background of non-commutative geometry, especially with the Lorentzian source. In this context, two specific different models of the extended teleparallel theory, that is, $f_1(T)={\eta }_{1}T+\frac{{\eta }_2}{T}$, and $f_2(T)={\eta }_3{T}^n$ (where ${\eta }_1$, ${\eta }_2$, ${\eta }_3$ being real constants and $n$ a positive integer) have been studied. The corresponding energy conditions are worked out and are analyzed graphically in the presence of the conformal motion with Lorentzian source. The presence of the exotic matter has been confirmed due to the violation of null energy conditions under some particular conditions, thereby proving the existence of the wormhole geometries in both of the models under investigation. Moreover, the stability of the wormhole geometries via the Tolman-Oppenheimer-Volkov equation has been discussed. It is concluded that these wormhole solutions supported by the non-exotic matter truly exist and are well stable under the extended teleparallel gravity.

The paper deals with the static spherically symmetric wormhole solutions in $f(R)$-modified gravity theory with anisotropic matter field and for some particular choices for the shape functions. This work may be considered as an extension of the general formalism in [S. Halder, S. Bhattacharya and S. Chakraborty, Phys. Lett. B 791, 270 (2019)] for finding wormhole solutions. For isotropic matter distribution it has been shown that wormhole solutions are possible for zero tidal force and it modifies the claim in [M. Cataldo, L. Leimpi and P. Rodriguez, Phys. Lett. B 757, 130 (2016)]. Finally, energy conditions are examined and it is found that all energy conditions are satisfied in a particular domain with a particular choice of the shape function.

Considering an energy density of the form $\rho =q{\left(\frac{r}{r_0}\right)}^{-n}$ (where $q$ is an arbitrary positive constant with dimension of energy density and $n>0$), a shape function is obtained by using field equations of braneworld gravity theory in this paper. Under isotropic scenario wormhole solutions are obtained considering six different redshift functions along with the obtained new shape function. For anisotropic case, wormhole solutions are obtained under the consideration of five different shape functions along with the redshift function $\varphi =\beta ln\left(\frac{r}{r_0}\right)$, where $\beta$ is an arbitrary constant. In each case all energy conditions are examined and it is found that for some cases all energy conditions are satisfied in the vicinity of the wormhole throat and for the rest of the cases all energy conditions are satisfied except strong energy condition.

In this paper, we have explored the field equations of $f(T,B)$ gravity and determined the dynamical parameters with the hyperbolic function of Hubble parameter. The accelerating behavior has been observed and the behavior of equation of state parameter indicates the $\mathrm{\Lambda }$CDM model at late time. The role of model parameters in assessing the accelerating behavior has been emphasized. Interestingly, the term containing $\beta$, the coefficient of boundary term, in the model parameter vanishes during the simplification. The scalar perturbation has been presented to show the stability of the model.

This paper examines the behavior of the universe around the bouncing point in the background of $f(\mathcal{𝒬},\mathcal{𝒯})$ theory, where $\mathcal{𝒬}$ is the non-metricity and $\mathcal{𝒯}$ is the trace of the energy–momentum tensor. We derive the field equations that describe gravitational phenomena in the existence of non-metricity and matter source terms. By applying the reconstruction method for the Hubble parameter, a phenomenon of the bouncing universe for homogeneous spacetime filled with perfect fluid is studied. We consider specific models of this modified theory to evaluate the behavior of various cosmic parameters such as the Hubble, deceleration, equation of state and fluid parameters. When the null energy condition is violated, it follows a bouncing behavior. It is found that spacetime is composed of isotropic fluid, where a big bounce can occur and the universe turns into extremely unstable. We conclude that $f(\mathcal{𝒬},\mathcal{𝒯})$ gravity successfully explains the early and late time cosmic expansion and evolution.