Energy-momentum Squared Gravity Research Articles

Impact of energy-momentum squared gravity on the geometry of stellar objects

This paper investigates the impact of energy–momentum squared gravity on the geometry of anisotropic compact stellar objects. In this perspective, we use the Tolman IV solution to examine the configuration of static spherically symmetric structures. The values of unknown constants are found by the first fundamental form of Darmois junction conditions. We consider four different models of this theory to analyze the behavior of physical quantities such as effective fluid parameters, anisotropy, energy constraints and equation of state parameters in the interior of considered compact stars. Sound speed and adiabatic index methods are used to determine the stability of proposed compact stars. It is found that the proposed compact stars are viable and stable in energy–momentum squared gravity.

Gravitationally induced matter creation in scalar–tensor [formula omitted] gravity

In this work, we analyze the possibility of gravitationally induced matter creation in the so-called Energy–Momentum-Squared gravity (EMSG), i.e. f(R,TμνTμν) gravity, in its dynamically equivalent scalar–tensor representation. Given the explicit nonminimal coupling between matter and geometry in this theory, the energy–momentum tensor is not generally covariantly conserved, which motivates the study of cosmological scenarios by resorting to the formalism of irreversible thermodynamics of open systems. We start by deriving the universe matter creation rates and subsequent thermodynamical properties, such as, the creation pressure, temperature evolution, and entropy evolution, in the framework of f(R,TμνTμν) gravity. These quantities are then analyzed for a Friedmann–Lemaître–Robertson–Walker (FLRW) background with a scale factor described by the de Sitter solution, under different assumptions for the mater distribution, namely a vacuum universe, a constant density universe, and a time-varying density universe. Finally, we explore cosmological solutions with varying Hubble parameters and provide a comparison with the standard cosmological model. Our results indicate that the cosmological evolution in the framework of EMSG is in close agreement with the observational cosmological data for low redshift.

Gravitational collapse in energy-momentum squared gravity: Nature of singularities

In this paper we explore a collapsing scenario in the background of energy-momentum squared gravity (EMSG). EMSG claims to have terms that originate from the quantum gravity effects mimicking loop quantum gravity. As a result the framework admits a bounce at a finite time thus avoiding a singularity. So the question that naturally arises: Is there any realistic chance of formation of a black hole or the quantum gravity effects are strong enough to totally avoid such a pathology? Motivated from this we are interested in studying a gravitational collapse mechanism in the background of EMSG and investigate the fate of such a process. We model the spacetime of a massive star by the Vaidya metric and derive the field equations in EMSG. Then using the equations we go on to study a gravitational collapse mechanism, on two specific models of EMSG with different forms of curvature-matter coupling. The prime objective is to probe the nature of singularity (if formed) as the end state of the collapse. We see that none of the models generically admit the formation of black holes as the end state of collapse, but on the contrary they support the formation of naked singularities. This can be attributed to the quantum fluctuations of the gravitational interactions at the fundamental level.

Anisotropic quark stars in energy-momentum squared gravity

At super-saturation densities, quarks in the core of neutron stars (NSs) have been a subject of intense investigation for last few decades. In particular, an intriguing conjecture has emerged suggesting that the true ground state of hadronic matter may be strange quark matter (SQM). In the present manuscript, we study internal structure and the physical properties of quark stars (QSs) in energy-momentum squared gravity (EMSG) with MIT bag model equations of state (EoS). An important feature of this theory is the addition of the term f(TμνTμν) to the Einstein-Hilbert action. This modification in the action lead to changes in the right-hand side of Einstein's field equations (EFE). We obtain mass-radius relations for a spherically symmetric configuration supported by the anisotropic fluid matter distribution and solved the hydrostatic equilibrium equations numerically in the framework of EMSG. In addition, we present and discuss the stability of stellar structure depending on the model parameters.

Formula omitted]- inflation: Sourced by energy–momentum squared gravity

In this paper, we examine chaotic inflation within the context of the energy–momentum squared gravity (EMSG) focusing on the energy–momentum powered gravity (EMPG) that incorporates the functional f(T2)∝(T2)β in the Einstein–Hilbert action, in which β is a constant and T2≡TμνTμν where Tμν is the energy–momentum tensor, which we consider to represent a single scalar field with a power-law potential. We also demonstrate that the presence of EMSG terms allows the single-field monomial chaotic inflationary models to fall within current observational constraints, which are otherwise disfavored by Planck and BICEP/Keck findings. We show that the use of a non-canonical Lagrangian with chaotic potential in EMSG can lead to significantly larger values of the non-Gaussianity parameter, fNlequi whereas EMSG framework with canonical Lagrangian gives rise to results similar to those of the standard single-field model.

Relativistic structure of charged quark stars in energy–momentum squared gravity

Within the context of energy–momentum squared gravity (EMSG), where non-linear matter contributions appear in the gravitational action, we derive the modified TOV equations describing the hydrostatic equilibrium of charged compact stars. We adopt two different choices for the matter Lagrangian density (Lm=p versus Lm=−ρ) and investigate the impact of each one on stellar structure. Furthermore, considering a charge profile where the electric charge density ρch is proportional to the standard energy density ρ, we solve numerically the stellar structure equations in order to obtain the mass–radius diagrams for the MIT bag model equation of state (EoS). For Lm=p and given a specific value of β (including the uncharged case when β=0), the maximum-mass values increase (decrease) substantially as the gravity model parameter α becomes more negative (positive). However, for uncharged configurations and considering Lm=−ρ, our numerical results reveal that when we increase α (from a negative value) the maximum mass first increases and after reaching a maximum value it starts to decrease. Remarkably, this makes it a less trivial behavior than that caused by the first choice when we take into account the presence of electric charge (β≠0).

Weak field and slow motion limits in energy–momentum powered gravity

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy–momentum powered gravity (EMPG), viz., the energy–momentum squared gravity (EMSG) of the form f(TμνTμν)=α(TμνTμν)η with α and η being constants. We have shown that EMPG with η≥0 and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, Mast, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass Meff(α,η,M)=M+Mempg(α,η,M), M being the actual physical mass and Mempg being the modification due to EMPG. Accordingly, while in GR we simply have the relation Mast=M, in EMPG we have Mast=M+Mempg. Within the framework of EMPG, if there is information about the values of {α,η} pair or M from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only Mast alone from astronomical observations, but M and Mempg separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by |peff/ρeff|≪1 (where peff=p+pempg and ρeff=ρ+ρempg), whereas this condition leads to |p/ρ|≪1 in GR.

Relativistic binary systems in scale-independent energy–momentum squared gravity

ABSTRACT In this paper, we study the gravitational-wave (GW) radiation and radiative behaviour of relativistic compact binary systems in the scale-independent energy–momentum squared gravity (EMSG). The field equations of this theory are solved approximately. The gravitational potential of a gravitational source is then obtained by considering two matter Lagrangian densities that both describe a perfect fluid in general relativity (GR). We derive the GW signals emitted from a compact binary system. The results are different from those obtained in GR. It is shown that the relevant non-GR corrections modify the wave amplitude and leave the GW polarizations unchanged. Interestingly, this modification depends on the choice of the matter Lagrangian density. This means that for different Lagrangian densities, this theory presents different predictions for the GW radiation. In this case, the system loses energy to modified GWs. This leads to a change in the secular variation of the Keplerian parameters of the binary system. In this work, we investigate the non-GR effects on the radiative parameter, that is, the first time derivative of the orbital period. Next, applying these results together with GW observations from the relativistic binary systems, we constrain/test the scale-independent EMSG theory in the strong-field regime. After assuming that GR is the valid gravity theory, as a priori expectation, we find that the free parameter of the theory is of the order 10−5 from the direct GW observation, the GW events GW190425 and GW170817, as well as the indirect GW observation, the double pulsar PSR J0737−3039A/B experiment.

Cosmological models in scale-independent energy-momentum squared gravity

Scale-independent EMSG is a particular model of energy–momentum squared gravity (EMSG) in which the new terms in the Einstein field equations arising from the EMSG theory enter with the same power as the usual terms from Einstein–Hilbert part of the action. However, the model violates the local energy–momentum conservation and matter-current conservation in general and hence, permits a process of matter creation/annihilation in an expanding universe. Consequently, the scale factor dependencies of the energy densities are modified by the dimensionless model parameter α. We revisit some nostalgias such as static universes and de Sitter/steady state universes. We reproduce the original ones, moreover, present some novelties, e.g., a spatially flat static universe, de Sitter expansion by negative vacuum energy, steady state universes in the presence of arbitrary fluids with constant equation of state (EoS) parameter other than dust, etc. We also investigate the possible dynamics of dust dominated and radiation dominated universes. Depending on the value of α, dust/radiation dominated universe exhibits power-law accelerated/decelerated expansion, corresponds to a steady state model or may end in a big rip. In the framework of anisotropic cosmology, we reproduce Barrow’s quiescent universe in the presence of stiff fluid and extend it to fluids with arbitrary constant EoS parameter. We also relax the condition for isotropic initial singularity (big bang) owing to that EMSG effectively allows ultra-stiff EoS parameters.

Anisotropic compact stars with Karmarkar condition in energy-momentum squared gravity

Anisotropic compact stars with Karmarkar condition in energy-momentum squared gravity

Dynamical analysis of logarithmic energy–momentum squared gravity

We perform the dynamical system analysis of a cosmological model in the energy–momentum squared gravity (EMSG) of the form f ( T μ ν T μ ν ) = α ln ( λ T μ ν T μ ν ) , which is known as energy–momentum log gravity (EMLG). In particular, we show that the analytical cosmological solution of EMLG presented by Akarsu et al. (Eur. Phys. J. C 79:846, 2019) is a future attractor. It includes new terms in the right-hand side of the Einstein field equations, which yield constant inertial mass density and provide a dynamical dark energy with a density passing below zero at large redshifts, accommodating a mechanism for screening Λ in the past for α < 0 , suggested for alleviating some cosmological tensions. We show that the second law of thermodynamics requires α ≤ 0 that allows the screening mechanism to take place. We also show that the model gives rise to an entire class of new stable late-time solutions with H → ( Λ + 2 α ) / 3 as a → ∞ , where the new term is due to the constant effective inertial mass density that arises from EMLG contribution of dust, whereas H → Λ / 3 as a → ∞ in the Λ CDM model. We also show the existence of new interesting features and trajectories that are absent in Λ CDM with or without spatial curvature.

The mass–radius relation for quark stars in energy–momentum squared gravity

We study the structure of quark stars (QSs) adopting homogeneously confined matter inside the star with a 3-flavor neutral charge and a fixed strange quark mass ms. We explore the internal structure, and the physical properties of specific classes of QSs in the recently proposed energy–momentum squared gravity (EMSG). Also, we obtain the mass–radius (M–R) and mass–central energy density (M–ρc) relations for QS using the QCD motivated EoS. The maximum mass for QSs in EMSG is investigated depending on the presence and absence of the free parameter α. Furthermore, the stability of stars is determined by the condition dMdρc>0. We observe that consideration of the EMSG has specific contributions to the structure of QSs.

Complexity factor for static cylindrical system in energy-momentum squared gravity

This paper investigates some physical features that give rise to complexity within the self-gravitating static cylindrical structure coupled with anisotropic distribution in the energy-momentum squared gravity. To accomplish this, we formulate the modified field equations and explore the structure of the astronomical body. The C-energy and Tolman mass are also calculated to discuss the matter distribution. We then obtain some structure scalars via orthogonal splitting of the Riemann tensor. Since, the complexity of the considered structure is influenced by a variety of variables, including anisotropic pressure and inhomogeneous energy density, etc. thus, we adopt the factor $\mathcal{Y}_{TF}$ as the complexity factor. Further, the complexity-free condition along with the Gokhroo-Mehra model and polytropic equation of state are taken to generate their corresponding solutions. We deduce that the inclusion of additional terms of this modified theory leads to a more complicated system.

Light bending and gravitational lensing in energy-momentum-squared gravity

In the present work, we derive the motion of light in the weak-field limit of energy-momentum-squared gravity (EMSG). To do so, we introduce the post-Newtonian expansion of this modified theory of gravity. It is shown that, in addition to the Newtonian potential, a new EMSG potential affects the trajectory of photons. As a result, in this theory, photons do not behave as predicted by general relativity (GR). To evaluate the EMSG theory by the Solar System tests, we study light deflection and Shapiro time delay. Regarding the results obtained in Bertotti et al. [Nature (London) 425, 374 (2003)] and Shapiro et al. [Phys. Rev. Lett. 92, 121101 (2004)], we restrict the free parameter of the theory and show that it lies within the range $\ensuremath{-}4.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}27}\text{ }\text{ }\mathrm{m}\text{ }{\mathrm{s}}^{2}\text{ }{\mathrm{kg}}^{\ensuremath{-}1}&lt;{f}_{0}^{\ensuremath{'}}&lt;8.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}26}\text{ }\text{ }\mathrm{m}\text{ }{\mathrm{s}}^{2}\text{ }{\mathrm{kg}}^{\ensuremath{-}1}$. This interval is in agreement with those derived in Nazari et al. [Phys. Rev. D 105, 044014 (2022)] and Akarsu et al. [Phys. Rev. D 97, 124017 (2018)]. This consistency manifests that this theory passes these Solar System tests with flying colors. Interestingly, it turns out that the magnitude of the EMSG correction strongly depends on the density of the deflector. So, we investigate the possible effects of EMSG on images of a light source microlensed by a compact dense object such as neutron stars. It is estimated that the EMSG correction to the position of lensed images could be as large as (1--0.1) microarcseconds, which may be detected by future high-resolution missions. Moreover, the total magnification and the shape of light curves are obtained in the EMSG theory. It is revealed that except for a small deviation, the overall behavior of the EMSG light curves is similar to that in GR. We also show that as long as the light source and the dense lens are aligned, the EMSG correction is effective, and the combined light of the lensed images is different from the GR case. This issue makes it possible to observe signatures of this theory in the microlensing regime.

Inflation in energy-momentum squared gravity in light of Planck2018

We study cosmological dynamics of the energy-momentum squared gravity. By adding the squared of the matter field’s energy-momentum tensor (\(\zeta \, \mathbf{T} ^{2}\)) to the Einstein–Hilbert action, we obtain the Einstein’s field equations and study the conservation law. We show that, the presence of \(\zeta \, \mathbf{T} ^{2}\) term, breaks the conservation of the energy-momentum tensor of the matter fields. However, an effective energy-momentum tensor in this model is conserved in time. By considering the FRW metric as the background, we find the Friedmann equations and by which we explore the cosmological inflation in \(\zeta \,\mathbf{T} ^{2}\) model. We perform a numerical analysis on the perturbation parameters and compare the results with Planck2018 different data sets at \(68\%\) and \(95\%\) CL, to obtain some constraints on the coupling parameter \(\zeta \). We show that, for \(0< \zeta \le 2.1\times 10^{-5}\), the \(\zeta \, \mathbf{T} ^{2}\) gravity is an observationally viable model of inflation.

Gravastars with Kuchowicz Metric in Energy-Momentum Squared Gravity

This paper investigates the geometry of a gravitational vacuum star (also known as a gravastar) from the perspective of f(R,T2) gravity. The gravastar can be treated as a black hole substitute with three domains: (i) the inner domain, (ii) the intrinsic shell, and (iii) the outer domain. We examine these geometries using Kuchowicz ansatz for temporal metric function corresponding to a specific f(R,T2) model. We compute a nonsingular radial metric potential for both the interior and intermediate domains. The matching of these domains with exterior Schwarzschild vacuum results in boundary conditions that assist in the evaluation of unknown constants. Finally, we examine various attributes of gravastar domains, such as the equation of state parameter, proper length, energy, and surface redshift. We conclude that the gravastar model is a viable alternative to the black hole in the background of this gravity.

Complexity of static sphere in energy–momentum squared gravity

In this paper, we study complexity of a static spherically symmetric object containing anisotropic fluid in the background of energy–momentum squared gravity (EMSG). We formulate the field equations and describe the energy content of the fluid via Misner–Sharp as well as Tolman mass definitions. In order to compute the complexity factor, the Riemann tensor is orthogonally split to produce structure scalars which incorporate the fundamental properties of the system. The scalar involving anisotropic pressure and inhomogeneous energy density is chosen as the complexity factor. We consider a minimally coupled model to formulate the condition for vanishing complexity which is employed to formulate two solutions. It is concluded that additional matter source terms appearing due to energy–momentum squared gravity increase the complexity of the system.

Constraining energy-momentum-squared gravity by binary pulsar observations

In this paper, we introduce the post-Minkowskian approximation of Energy-Momentum-Squared Gravity (EMSG). This approximation is used to study the gravitational energy flux in the context of EMSG. As an application of our results, we investigate the EMSG effect on the first time derivative of the orbital period of the binary pulsars. Utilizing this post-Keplerian parameter, the free parameter of the EMSG theory, $f_0'$, is estimated for six known binary pulsars. Taking the binaries that have the most accurate observations, it turns out that $-6\times 10^{-37}\text{m}\,\text{s}^2\text{kg}^{-1}<f_0'<+10^{-36}\text{m}\,\text{s}^2\text{kg}^{-1}$. This bound is in agreement with the precedent studies.

Energy Momentum Squared Gravity in Doneva-Jazadjiev anisotropic pressure model of non-rotating neutron stars

We implement the Doneva-Yazadjiev (DY) anisotropic model of neutron stars into Energy Momentum Squared Gravity (EMSG) theory. We have shown that the Tolmann-Oppenheimer-Volkoff (TOV) equation within this model can be expressed in the terms of effective pressure and energy density. The structure of neutron stars (NS) is then calculated by using Basic Standard Parameter equation of state with hyperons in the center. We found that the combined model is able to adjust the mass-radius relation of the NS. We also found that this model could affect boundary limit of EMSG parameter, α, in the term of stability.

Noether symmetries and anisotropic universe in energy-momentum squared gravity

This paper explores exact cosmological solutions of anisotropic universe model through Noether symmetry technique in energy-momentum squared gravity. This theory resolves the primordial singularity and provides viable cosmological consequences in the early universe. We consider specific models of this theory and evaluate Noether equations, symmetry generators and corresponding conserved parameters. We then find exact solutions through conserved parameters and analyze their graphical behavior for different cosmological parameters. It is found that the behavior of these parameters is consistent with recent observations indicating that this theory supports current cosmic accelerated expansion. We conclude that conserved parameters are very helpful to obtain exact cosmological solutions.