Search Results (90)

A Friedmann–Lemaitre–Robertson–Walker space–time model with all curvatures $k=0,\pm 1$ is explored in $f(R,T)$ gravity, where R is the Ricci scalar, and T is the trace of the energy–momentum tensor. The solutions are obtained via the parametrization of the scale factor that leads to a model transiting from a decelerated universe to an accelerating one. The physical features of the model are discussed and analyzed in detail. The study shows that $f(R,T)$ gravity can be a good alternative to the hypothetical candidates of dark energy to describe the present accelerating expansion of the universe. Full article

General relativity (GR) postulates have been verified with high precision, yet our understanding of how gravity interacts with matter fields remains incomplete. Various modifications to GR have been proposed in both classical and quantum realms to address these interactions within the strong gravity regime. One such approach is non-minimal coupling (NMC), where the space-time curvature (scalar and tensor) interacts with matter fields, resulting in matter fields not following the geodesics. To probe the astrophysical implications of NMC, in this work, we investigate non-minimally coupled electromagnetic (EM) fields in the presence of black holes. Specifically, we show that primordial black holes (PBHs) provide a possible tool to constrain the NMC parameter. PBHs represent an intriguing cosmological black hole class that does not conform to the no-hair theorem. We model the PBH as a Sultana–Dyer black hole and compare it with Schwarzschild. We examine observables such as the radius of the photon sphere, critical impact parameter, and total deflection angles for non-minimally coupled photons for Schwarzschild and Sultana–Dyer black holes. Both the black hole space-times lead to similar constraints on the NMC parameter. For a PBH of mass $M={10}^{-5}{M}_{\odot }$, the photon sphere will not be formed for one mode. Hence, the photons forming the photon sphere will be highly polarized, potentially leading to observable implications. Full article

This review considers the theoretical approaches to the understanding of dark energy, which comprises approximately 68% of the energy of our Universe and explains the acceleration in its expansion. Following a discussion of the main approach based on Einstein’s equations with the cosmological term, the explanations of dark energy using the concept of some kind of scalar field are elucidated. These include the concept of a quintessence and modifications of the general theory of relativity by means of the scalar–tensor gravity exploiting the chameleon, symmetron and environment-dependent dilaton fields and corresponding particles. After mentioning several laboratory experiments allowing us to constrain the hypothetical scalar fields modeling the dark energy, special attention is devoted to the possibility of constraining the parameters of chameleon, symmetron and environment-dependent dilaton fields from measuring the Casimir force. It is concluded that the parameters of each of these fields can be significantly strengthened in near future by using the next-generation setups in preparation suitable for measuring the Casimir force at larger separations. Full article

In this review article, we revisit the topic of baryogenesis, which is the physical process that generated the observed baryon asymmetry during the first stages of the primordial Universe. A viable theoretical explanation to understand and investigate the mechanisms underlying baryogenesis must always ensure that the Sakharov criteria are fulfilled. These essentially state the following: (i) baryon number violation; (ii) the violation of both C (charge conjugation symmetry) and CP (the composition of parity and C); (iii) and the departure from equilibrium. Throughout the years, various mechanisms have been proposed to address this issue, and here we review two of the most important, namely, electroweak baryogenesis (EWB) and Grand Unification Theories (GUTs) baryogenesis. Furthermore, we briefly explore how a change in the theory of gravity affects the EWB and GUT baryogenesis by considering Scalar–Tensor Theories (STT), where the inclusion of a scalar field mediates the gravitational interaction, in addition to the metric tensor field. We consider specific STT toy models and show that a modification of the underlying gravitational theory implies a change in the time–temperature relation of the evolving cosmological model, thus altering the conditions that govern the interplay between the rates of the interactions generating baryon asymmetry, and the expansion rate of the Universe. Therefore, the equilibrium of the former does not exactly occur as in the general relativistic standard model, and there are consequences for the baryogenesis mechanisms that have been devised. This is representative of the type of modifications of the baryogenesis processes that are to be found when considering extended theories of gravity. Full article

Unimodular gravity (UG) is often deemed comparable to General Relativity (GR) in many respects, despite the theory exhibiting invariance under a more limited set of diffeomorphic transformations. The discussion we propose in this work relies on the criteria for establishing the equivalence between these two formulations, specifically exploring UG’s application to static and spherically symmetric configurations with the energy-momentum tensor originating from either a scalar field or an electromagnetic field. We find that the equivalence between UG and GR might be disrupted when scrutinizing the stability of solutions at a perturbative level. Full article

The paper investigates the vacuum expectation value of the surface energy–momentum tensor (SEMT) for a scalar field with general curvature coupling in the geometry of two branes orthogonal to the boundary of anti-de Sitter (AdS) spacetime. For Robin boundary conditions on the branes, the SEMT is decomposed into the contributions corresponding to the self-energies of the branes and the parts induced by the presence of the second brane. The renormalization is required for the first parts only, and for the corresponding regularization the generalized zeta function method is employed. The induced SEMT is finite and is free from renormalization ambiguities. For an observer living on the brane, the corresponding equation of state is of the cosmological constant type. Depending on the boundary conditions and on the separation between the branes, the surface energy densities can be either positive or negative. The energy density induced on the brane vanishes in special cases of Dirichlet and Neumann boundary conditions on that brane. The effect of gravity on the induced SEMT is essential at separations between the branes of the order or larger than the curvature radius for AdS spacetime. In the considerably large separation limit, the decay of the SEMT, as a function of the proper separation, follows a power law for both massless and massive fields. For parallel plates in Minkowski bulk and for massive fields the fall-off of the corresponding expectation value is exponential. Full article

The accelerated expansion of the universe during recent times is well known in cosmology, whereas during early times, there was decelerated expansion. The $\mathsf{\Lambda }$CDM model is consistent with most observations, but there are some issues with it. In addition, the transition from early deceleration to late-time acceleration cannot be explained by general relativity. Hence, it is worthwhile to examine modified gravity theories to explain this transition and to get a better understanding of dark energy. In this work, dark energy in modified $f(R,T)$ gravity is investigated, where R is the Ricci scalar and T is the trace of the energy momentum tensor. Normally, the simplest form of $f(R,T)$ is used, viz., $f\left(R\right)=R+\lambda T$. In this work, the more complicated form $f(R,T)=R+RT$ is investigated in Friedmann–Lemaître–Robertson–Walker spacetime. This form has not been well studied. Since the jerk parameter in general relativity is constant and $j=1$, in order to have as small a departure from general relativity as possible, the jerk parameter $j=1$ is also assumed here. This enables the complete solution for the scale factor to be found. One of these forms is used for a complete analysis and is compared with the usually studied form $f(R,T)=R+RT$. The solution can also be broken down into a power-law form at early times (deceleration) and an exponential form at late times (acceleration), which makes the analysis simpler. Surprisingly, each of these forms is also a solution to the differential equation $j=1$ (though they are not solutions to the general solution). The energy conditions are also studied, and plots are provided. It is shown that viable models can be obtained without the need for the introduction of a cosmological constant, which reduces to the $\mathsf{\Lambda }$CDM at late times. Full article

A plane symmetric Bianchi-I model filled with strange quark matter (SQM) was explored in $f(R,T)=R+2\lambda T$ gravity, where R is the Ricci scalar, T is the trace of the energy-momentum tensor, and $\lambda$ is an arbitrary constant. Three different types of solutions were obtained. In each model, comparisons of the outcomes in $f(R,T)$ gravity and bag constant were made to comprehend their roles. The first power-law solution was obtained by assuming that the expansion scalar is proportional to the shear scalar. This solution was compared with a similar one obtained earlier. The second solution was derived by assuming a constant deceleration parameter q. This led to two solutions: one power-law and the other exponential. Just as in the case of general relativity, we can obtain solutions for each of the different eras of the universe, but we cannot obtain a model which shows transitional behavior from deceleration to acceleration. However, the third solution is a hybrid solution, which shows the required transition. The models start off with anisotropy, but are shear free at late times. In general relativity, the effect of SQM is to accelerate the universe, so we expect the same in $f(R,T)$ gravity. Full article

Herein, we investigate scalar–tensor and bi-scalar–tensor modified theories of gravity that can alleviate the $H_0$ tension. In the first class of theories, we show that by choosing particular models with a shift-symmetric friction term we are able to alleviate the tension by obtaining a smaller effective Newton’s constant at intermediate times, a feature that cannot be easily obtained in modified gravity. In the second class of theories, which involve two extra propagating degrees of freedom, we show that the $H_0$ tension can be alleviated, and the mechanism behind this is the phantom behavior of the effective dark-energy equation-of-state parameter. Hence, scalar–tensor and bi-scalar–tensor theories have the ability to alleviate the $H_0$ tension with both known sufficient late-time mechanisms. Full article

We sketch the main features of the Noether Symmetry Approach, a method to reduce and solve dynamics of physical systems by selecting Noether symmetries, which correspond to conserved quantities. Specifically, we take into account the vanishing Lie derivative condition for general canonical Lagrangians to select symmetries. Furthermore, we extend the prescription to the first prolongation of the Noether vector. It is possible to show that the latter application provides a general constraint on the infinitesimal generator $\xi$, related to the spacetime translations. This approach can be used for several applications. In the second part of the work, we consider a gravity theory, including the coupling between a scalar field $\varphi$ and the Gauss–Bonnet topological term $\mathcal{G}$. In particular, we study a gravitational action containing the function $F(\mathcal{G},\varphi )$ and select viable models by the existence of symmetries. Finally, we evaluate the selected models in a spatially flat cosmological background and use symmetries to find exact solutions. Full article

In this work, we explore the formalism of the irreversible thermodynamics of open systems and the possibility of gravitationally generated particle production in modified gravity. More specifically, we consider the scalar–tensor representation of $f(R,T)$ gravity, in which the matter energy–momentum tensor is not conserved due to a nonminimal curvature–matter coupling. In the context of the irreversible thermodynamics of open systems, this non-conservation of the energy–momentum tensor can be interpreted as an irreversible flow of energy from the gravitational sector to the matter sector, which, in general, could result in particle creation. We obtain and discuss the expressions for the particle creation rate, the creation pressure, and the entropy and temperature evolutions. Applied together with the modified field equations of scalar–tensor $f(R,T)$ gravity, the thermodynamics of open systems lead to a generalization of the $\mathrm{\Lambda }$CDM cosmological paradigm, in which the particle creation rate and pressure are considered effectively as components of the cosmological fluid energy–momentum tensor. Thus, generally, modified theories of gravity in which these two quantities do not vanish provide a macroscopic phenomenological description of particle production in the cosmological fluid filling the Universe and also lead to the possibility of cosmological models that start from empty conditions and gradually build up matter and entropy. Full article

We investigate the Chandrasekhar mass limit of white dwarfs in various models of $f\left(R\right)$ gravity. Two equations of state for stellar matter are used: the simple relativistic polytropic equation with polytropic index $n=3$ and the realistic Chandrasekhar equation of state. For calculations, it is convenient to use the equivalent scalar–tensor theory in the Einstein frame and then to return to the Jordan frame picture. For white dwarfs, we can neglect terms containing relativistic effects from General Relativity and we consider the reduced system of equations. Its solution for any model of $f\left(R\right)=R+\beta R^m$ ($m\ge 2$, $\beta >0$) gravity leads to the conclusion that the stellar mass decreases in comparison with standard General Relativity. For realistic equations of state, we find that there is a value of the central density for which the mass of a white dwarf peaks. Therefore, in frames of modified gravity, there is a lower limit on the radius of stable white dwarfs, and this minimal radius is greater than in General Relativity. We also investigate the behavior of the Chandrasekhar mass limit in $f\left(R\right)$ gravity. Full article

A scalar–tensor theory of gravity was considered, wherein the gravitational coupling G and the speed of light c were admitted as space–time functions and combined to form the definition of the scalar field $\varphi$. The varying c participates in the definition of the variation of the matter part of the action; it is related to the effective stress–energy tensor, which is a result of the requirement of symmetry under general coordinate transformations in our gravity model. The effect of the cosmological coupling $\Lambda$ is accommodated within a possible behavior of $\varphi$. We analyzed the dynamics of $\varphi$ in the phase space, thereby showing the existence of an attractor point for reasonable hypotheses on the potential $V\left(\varphi \right)$ and no particular assumption on the Hubble function. The phase space analysis was performed both with the linear stability theory and via the more general Lyapunov method. Either method led to the conclusion that the condition $\dot{G}/G=\sigma \left(\dot{c},/,c\right)$, where $\sigma =3$ must hold for the rest of cosmic evolution after the system arrives at the globally asymptotically stable fixed point and the dynamics of $\varphi$ ceases. This result realized our main motivation: to provide a physical foundation for the phenomenological model admitting $\left(G,/,G_0\right)={\left(c,/,c_0\right)}^3$, used recently to interpret cosmological and astrophysical data. The thus covarying couplings G and c impact the cosmic evolution after the dynamical system settles to equilibrium. The secondary goal of our work was to investigate how this impact occurs. This was performed by constructing the generalized continuity equation in our scalar–tensor model and considering two possible regimes for the varying speed of light—decreasing c and increasing c—while solving our modified Friedmann equations. The solutions to the latter equations make room for radiation- and matter-dominated eras that progress to a dark-energy-type of accelerated expansion. Full article

We analyze the behavior of relativistic spherical objects within the context of modified $f(R,T)$ gravity considering Tolman VI spacetime, where the gravitational Lagrangian is a function of the Ricci scalar (R) and trace of energy momentum tensor (T), i.e, $f(R,T)$ = R + 2βT, for some arbitrary constant β. For developing our model, we have chosen £_m = −p, where £_m represents the matter Lagrangian. For this investigation, we have chosen three compact stars, namely PSR J1614-2230 (Mass = (1.97 ± 0.4)M_⊙; Radius = ${9.69}_{+0.02}^{-0.02}$ km), Vela X-1 (Mass = (1.77 ± 0.08)M_⊙; Radius = ${9.560}_{+0.08}^{-0.08}$ km) and 4U 1538-52 (Mass = (9.69)M_⊙; Radius = 1.97 km). In this theory, the equation of pressure isotropy is identical to the standard Einstein’s theory. So, all known metric potential solving Einstein’s equations are also valid here. In this paper, we have investigated the effort of a coupling parameter (β) on the local matter distribution. The sound of speed and adiabatic index are higher with grater values of β, while on the contrary, the mass function and gravitational redshift are lower with higher values of β. For supporting the theoretical results, graphical representations are also employed to analyze the physical viability of the compact stars. Full article

A locally rotationally symmetric Bianchi-I model is explored both in general relativity and in f(R,T) gravity, where R is the Ricci scalar and T is the trace of the energy-momentum tensor. Solutions have been found by means of a special Hubble parameter, yielding a hyperbolic hybrid scale factor. Some geometrical parameters have been studied. A comparison is made between solutions in general relativity and in f(R,T) gravity, where in both the theories, the models exhibit rich behaviour from stiff matter to quintessence, phantom, then later mimicking the cosmological constant, depending on some parameters. Full article