Curvature-matter Coupling Research Articles

Bouncing universe scenarios in an extended gravitational framework involving curvature-matter coupling

Exploration of bouncing cosmic models in modified theories has gained much popularity in modern cosmology. This paper explores the Lagrangian function of a new theory namely F(R,Lm,T) framework by taking four renowned cosmic bouncing models, i.e., the exponential bounce, oscillatory bounce scenario, power law, and matter bouncing. Our primary objective is to fix the form of F(R,Lm,T) function for each model and investigate which kinds of reconstructed Lagrangian function have potential of regenerating bouncing scenario in terms of analytical form. It is seen that except power law model, the analytical solutions are conceivable only for certain cases of these bouncing models. For power law bounce, different cases of Lagrangian function may be rebuilt analytically while for some other bouncing scenarios, it is found that particular solutions are not always attainable and hence only the complimentary solutions can be explored. Further, we examine the behavior of energy constraints and stability of these analytically formed bouncing solutions. Additionally, we determine that the dark energy phase in F(R,Lm,T) gravity is compatible with the experimental data of BAO+Sne-Ia+CMB+H(z) and it is shown that cosmic bounce can be produced with dark energy eras in this gravity. We also present some constraints on the model parameters with Hubble parameter values and ΛCDM to determine the best-fit values of model via least square and reduced chi-squares methods. It is concluded that matter bounce model is the best fitted with the observational data set as well as ΛCDM model because it has least value of χm2.

Exploring wormhole solutions in curvature–matter coupling gravity supported by noncommutative geometry and conformal symmetry

This article explores new physically viable wormhole solutions within the framework of f(R,ℒm) gravity theory, incorporating noncommutative backgrounds and conformal symmetries. The study investigates the impact of model parameters on the existence and properties of wormholes. The derived shape function is found to obey all the required criteria. Specific attention is given to traceless wormholes with Gaussian and Lorentzian distributions, investigating the behavior of the shape functions and energy conditions. In both cases, the presence of exotic fluid is confirmed.

Chaplygin gas equation in curvature-matter coupling gravity

In this paper, we study the Chaplygin gas equation in curvature-matter coupling gravity to describe the observed expansion of the universe. We consider the Chaplygin gas equation of state in terms of the energy density [Formula: see text] and pressure [Formula: see text], by the relationship [Formula: see text] and the curvature-matter coupling gravity as [Formula: see text], where [Formula: see text] is a positive constant, [Formula: see text] and [Formula: see text] denote, respectively, the Ricci scalar and the trace of energy–momentum tensor. Considering the gravitational lagrangian in the form [Formula: see text], where we used two forms of [Formula: see text] and by assuming a perfect fluid as matter source, we determined through the modified Friedmann equations, the corresponding energy and pressure for each model. By using the free parameters of our models, we performed the numerical results of the energy conditions to study its viability. Furthermore, we have derived some cosmological parameters like deceleration parameter and statefinder parameters and graphically investigated the nature of these parameters in Chaplygin gas model.

Observational constraints on non-minimally coupled curvature–matter models of gravity from the analysis of Pantheon data

We considered non-minimally coupled curvature–matter models of gravity in a Friedmann–Robertson–Walker Universe filled with perfect fluid and investigated its cosmological implications in the light of Pantheon compilation of 1048 supernova Ia (SNe Ia) data points along with 54 data points from observed Hubble data. The non-minimal curvature–matter coupling has been introduced by adding a term to the usual action for Einstein gravity involving the Einstein–Hilbert action and minimally coupled matter action. We investigate the observational constraints on the non-minimal models by choosing two different kinds of parametrisation of fluid-pressure profiles using a dimensionless parameter k. The interplay of the three parameters plays a pivotal role in testing the consistency of non-minimally coupled fluid–curvature scenarios with the observed data. We found there exist large domains in the ()-parameter space for which models with non-minimal curvature–matter mixing stand as viable cosmological models reproducing the observed features of late-time cosmic evolution. We also commented on the possibility of ‘gravitationally induced particle creation’ in the context of SNe Ia data.

Non-commutative wormhole in non-minimal curvature–matter coupling of f(R) gravity with Gaussian and Lorentzian distributions

In this work, we construct two new wormhole solutions in the theory dealing with non-minimal coupling between curvature and matter. We take into account an explicitly non-minimal coupling between an arbitrary function of scalar curvature [Formula: see text] and the Lagrangian density of matter. For this purpose, we discuss the Wormhole geometries inspired by non-minimal curvature coupling in [Formula: see text] gravity for linear model in [Formula: see text] as well as nonlinear model in [Formula: see text]. To derive these solutions, we choose the Gaussian and Lorentzian density distributions. To check the viability of these solutions, we plot the graphs for energy conditions and wormhole parameters. It is found that obtained wormhole solutions in both distributions satisfy the energy condition. The resulting wormhole solutions for both non-commutative distributions are determined to be physically stable when we evaluate the stability of these wormhole solutions graphically. It is concluded that wormhole solutions exist with viable physical properties in the non-minimal curvature–matter coupling of [Formula: see text] gravity with Gaussian and Lorentzian distributions.

Irreversible Geometrothermodynamics of Open Systems in Modified Gravity.

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 ΛCDM 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.

Geometric structures of Morris-Thorne wormhole metric in f(, ℒ m ) gravity and energy conditions

The aim of this manuscript is to study the traversable wormhole (WH) geometries in the curvature matter coupling gravity. We investigate static spherically symmetric Morris-Thorne WHs within the context of gravity. To accomplish this, we examine the WH model in four different cases (i) linear model, with anisotropic matter distribution having the relation p r = mp t (ii) linear model having anisotropic matter distribution along with the equation of state parameter, p r = ω ρ, (iii) non-linear model with specific form of energy density and (iv) non-linear model, with isotropic matter distribution and having the linear relation between pressure and energy density, p = ω ρ. Additionally, in the latter case, we consider a specific power-law shape function . Furthermore, we analyze the energy conditions for each WH model to verify their physical viability. As a novel outcome, we can see the validation of the null energy condition for the model that suggests ruling out the necessity of exotic matter for the traversability of the WH. At last, an embedding diagram for each model is illustrated that describes the WH geometry.

Palatini formulation of the conformally invariant fleft( R,L_mright) gravity theory

We investigate the field equations of the conformally invariant models of gravity with curvature-matter coupling, constructed in Weyl geometry, using the Palatini formalism. We consider the case in which the Lagrangian is given by the sum of the square of the Weyl scalar, the strength of the field associated to the Weyl vector, and a conformally invariant geometry-matter coupling term, constructed from the matter Lagrangian and the Weyl scalar. After substituting the Weyl scalar in terms of its Riemannian counterpart, the quadratic action is defined in Riemann geometry and involves a nonminimal coupling between the Ricci scalar and the matter Lagrangian. For the sake of generality, a more general Lagrangian, in which the Weyl vector is nonminimally coupled with an arbitrary function of the Ricci scalar, is also considered. By varying the action independently with respect to the metric and the connection, the independent connection can be expressed as the Levi-Civita connection of an auxiliary Ricci scalar- and Weyl vector-dependent metric, which is related to the physical metric by means of a conformal transformation. The field equations are obtained in both the metric and the Palatini formulations. The cosmological implications of the Palatini field equations are investigated for three distinct models corresponding to different forms of the coupling functions. A comparison with the standard Lambda CDM model is also performed, and we find that the Palatini type cosmological models can give an acceptable description of the observations.

Gravitationally induced particle production in scalar-tensor f(R,T) gravity

We explore the possibility of gravitationally generated particle production in the scalar-tensor representation of $f(R,T)$ gravity. Due to the explicit nonminimal curvature-matter coupling in the theory, the divergence of the matter energy-momentum tensor does not vanish. We explore the physical and cosmological implications of this property by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, temperature evolution, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy-momentum tensor. We also consider specific models, and compare the scalar-tensor $f(R,T)$ cosmology with the $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ scenario and the observational data for the Hubble function. The properties of the particle creation rates, of the creation pressures, and entropy generation through gravitational matter production are further investigated in both the low and high redshift limits.

Curvature–matter couplings in modified gravity: From linear models to conformally invariant theories

In this paper, we review modified theories of gravity with a curvature–matter coupling between an arbitrary function of the scalar curvature and the Lagrangian density of matter. This explicit nonminimal coupling induces a nonvanishing covariant derivative of the energy–momentum tensor, that implies nongeodesic motion and consequently leads to the appearance of an extra force. Here, we explore the physical and cosmological implications of the nonconservation of the energy–momentum tensor by using the formalism of irreversible thermodynamics of open systems in the presence of matter creation/annihilation. The particle creation rates, pressure, and the expression of the comoving entropy are obtained in a covariant formulation and discussed in detail. Applied together with the gravitational field equations, the thermodynamics of open systems lead to a generalization of the standard [Formula: see text]CDM cosmological paradigm, in which the particle creation rates and pressures are effectively considered as components of the cosmological fluid energy–momentum tensor. Furthermore, we also briefly present the coupling of curvature to geometry in conformal quadratic Weyl gravity, by assuming a coupling term of the form [Formula: see text], where [Formula: see text] is the ordinary matter Lagrangian, and [Formula: see text] is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing [Formula: see text] with the use of an auxiliary scalar field and of the Weyl scalar, the gravitational action can be linearized in the Ricci scalar, leading in the Riemann space to a conformally invariant [Formula: see text]-type theory, with the matter Lagrangian nonminimally coupled to geometry.

Study of Decoupled Anisotropic Solutions in f(R, T, RρηTρη) Theory

In this paper, we consider isotropic solution and extend it to two different exact well-behaved spherical anisotropic solutions through minimal geometric deformation method in f(R,T,RρηTρη) gravity. We only deform the radial metric component that separates the field equations into two sets corresponding to their original sources. The first set corresponds to perfect matter distribution while the other set exhibits the effects of additional source, i.e., anisotropy. The isotropic system is resolved by assuming the metric potentials proposed by Krori-Barua while the second set needs one constraint to be solved. The physical acceptability and consistency of the obtained solutions are analyzed through graphical analysis of effective matter components and energy bounds. We also examine mass, surface redshift and compactness of the resulting solutions. For particular values of the decoupling parameter, our both solutions turn out to be viable and stable. We conclude that this curvature-matter coupling gravity provides more stable solutions corresponding to a self-gravitating geometry.

Testing an inflationary era in curvature–matter coupling gravity

In this paper, we investigate the cosmological inflation in the context of a minimal matter–geometry coupling, which is based on the [Formula: see text] gravity theory, where [Formula: see text] is a generic function of the curvature scalar [Formula: see text] and the trace [Formula: see text] of the energy–momentum tensor. Assuming that the slow-roll inflation conditions hold true in [Formula: see text] gravity, we obtain the various inflation-related observables such as the tensor-to-scalar ratio [Formula: see text], the scalar spectral index [Formula: see text], the running [Formula: see text] of the spectral index and the tensor spectral [Formula: see text] for two specific [Formula: see text] models from the Hubble slow-roll parameters. To observe the viability of these models, a numerical analysis of such parameters has been done. The results showed that, by using the various values of free parameters, it is possible to obtain a viable compatible with the observational data.

Thermodynamics of traversable wormholes in f(R,T) gravity

In this paper, we discuss thermodynamics for spherically symmetric and static traversable wormholes which include Morris–Thorne wormholes and charged wormholes in the background of [Formula: see text] gravity. The local coordinates have been used to find trapping horizons of these objects and generalized surface gravity has been worked out on the trapping horizons. The expression for the unified first law has also been derived from the gradient of Misner–Sharp energy with the help of gravitational field equations and from this law the first law of wormhole dynamics has been obtained. We have done this analysis for the simplest case of [Formula: see text] gravity where [Formula: see text], [Formula: see text] and [Formula: see text] being the traces of the Ricci and stress–energy tensors. Also, we have extended these thermodynamic results to non-minimal curvature-matter coupling.

Non-vacuum relativistic extensions of MOND using metric theories of gravity with curvature–matter couplings and their applications to the accelerated expansion of the universe without dark components

We discuss the advantages of using metric theories of gravity with curvature–matter couplings in order to construct a relativistic generalization of the simplest version of Modified Newtonian Dynamics (MOND), where Tully–Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature–matter couplings. Using the simplest two local constructions in an FLRW universe for dust, we show that there is no need for the introduction of dark matter and dark energy components into the Friedmann equation in order to account for type Ia supernovae observations of an accelerated universe at the present epoch.

Beyond Einstein’s General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings

Einstein’s General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation (now confirmed) to the cosmological models. Indeed, a central theme in modern Cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion, which represents a new imbalance in the governing gravitational equations. The cause of the late-time cosmic acceleration remains an open and tantalizing question, and has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation. This has spurred much research in modified theories of gravity, where extensions of the Hilbert–Einstein action describe the gravitational field, in particular, [Formula: see text] gravity, where [Formula: see text] is the curvature scalar. In this review, we perform a detailed theoretical and phenomenological analysis of specific modified theories of gravity and investigate their astrophysical and cosmological applications. We present essentially two largely explored extensions of [Formula: see text] gravity, namely: (i) the hybrid metric-Palatini theory; (ii) and modified gravity with curvature-matter couplings. Relative to the former, it has been established that both metric and Palatini versions of [Formula: see text] gravity possess interesting features but also manifest severe drawbacks. A hybrid combination, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and avoids some drawbacks of the original approaches. Relative to the curvature-matter coupling theories, these offer interesting extensions of [Formula: see text] gravity, where the explicit nonminimal couplings between an arbitrary function of the scalar curvature [Formula: see text] and the Lagrangian density of matter, induces a nonvanishing covariant derivative of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. We extensively explore both theories in a plethora of applications, namely, the weak-field limit, galactic and extragalactic dynamics, cosmology, stellar-type compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvature-matter coupling theory.

Black hole solutions and Euler equation in Rastall and generalized Rastall theories of gravity

Focusing on the special case of generalized Rastall theory, as a subclass of the non-minimal curvature-matter coupling theories in which the field equations are mathematically similar to the Einstein field equations in the presence of cosmological constant, we find two classes of black hole (BH) solutions including (i) conformally flat solutions and (ii) non-singular BHs. Accepting the mass function definition and by using the entropy contents of the solutions along with thermodynamic definitions of temperature and pressure, we study the validity of Euler equation on the corresponding horizons. Our results show that the thermodynamic pressure, meeting the Euler equation, is not always equal to the pressure components appeared in the gravitational field equations and satisfies the first law of thermodynamics, a result which in fact depends on the presumed energy definition. The requirements of having solutions with equal thermodynamic and Hawking temperatures are also studied. Additionally, we study the conformally flat BHs in the Rastall framework. The consequences of employing generalized Misner–Sharp mass in studying the validity of the Euler equation are also addressed.

Gravitational baryogenesis without CPT violation

We show that in theories with nonminimal curvature-matter couplings up to first order in the curvature, baryon number (B) conservation and CP are automatically violated, provided that the curvature scalar and its gradient do not vanish. Together with the associated gravitationally induced particle creation in a cosmological framework, which is an essentially out-of-equilibrium process, this implies that all of Sakharov's conditions are satisfied in the simplest extension of General Relativity, without the need of CPT violation. Here, derivatives of the curvature can be disregarded, thus evading the potential problems associated with the Gravitational Baryogenesis (GB) model in a cosmological context. Thanks to the particle creation pressure and the trace anomaly, the curvature scalar is nonzero even in a radiation-dominated Universe. Moreover, the trace anomaly or the energy density of a massive scalar field can amplify the baryon asymmetry at very high temperatures, even when the particle creation rate is very slow. As a result, a baryon asymmetry compatible with observations and a huge CP violation can be generated in the early Universe.

Analytic transport from weak to strong coupling in the O(N) model

In this work, a second-order transport coefficient (the curvature-matter coupling $\kappa$) is calculated exactly for the 3+1d O(N) model at large N for any coupling value. Since the theory is `trivial' in the sense of possessing a Landau pole, the result for $\kappa$ only is free from cut-off artifacts much below the Landau pole in the effective field theory sense. Nevertheless, this leaves a large range of coupling values where this transport coefficient can be determined non-perturbatively and analytically with little ambiguity. Along with thermodyamic results also calculated in this work, I expect exact large N results to provide good quantitative predictions for N=1 scalar field theory with $\phi^4$ interaction.

Viable wormhole solutions through Noether symmetry in [formula omitted] gravity

This paper explores static wormhole solutions through Noether symmetry technique in the framework of f(G,T) gravity, where G and T indicate the Gauss–Bonnet invariant and trace of the energy-momentum tensor, respectively. We consider isotropic fluid configuration to derive the symmetry generators with conserved parameters. We evaluate possible viable wormhole solutions and explore their stable behavior by considering the Tolman–Oppenheimer–Volkoff equation. For different forms of the red-shift parameter, we examine the effects of curvature-matter coupling as well as shape function on wormhole geometry. The graphical behavior of null/weak energy bounds for ordinary as well as effective energy-momentum tensor is investigated. We conclude that viable wormhole solutions exist for a specific functional form of this gravity.

Unified first law for traversable wormholes in non-minimal coupling of curvature and matter

In this paper thermodynamics of static Morris–Thorne wormholes has been discussed in the context of f(R) gravity. The generalized surface gravity, unified first law of thermodynamics and wormhole dynamics have been studied at trapping horizons. We have investigated thermodynamics in non-minimal coupling of curvature and matter which produces very complex equations. Our results generalize the results that have already been derived in Einstein’s gravity in the absence of curvature–matter coupling.