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The primary objective of this paper is to examine singularity-free solutions within the framework of anisotropic solutions for the Chaplygin equation of state in f (R , ϕ , X) modified gravity theory. Herein, R signifies the Ricci scalar, ϕ denotes the scalar field, and X represents the kinetic term associated with ϕ. The investigation employs the Krori–Barua metric to explore the characteristics of an anisotropic compact star. In the course of our analysis, we specifically consider observational data about three distinct stellar structures: Her X-I, LMC X-4, and 4U 1538-52. Our inquiry extends to the graphical examination of various physical parameters, encompassing energy density, pressure components, anisotropic components, equation of state parameters, equilibrium conditions, stability analysis, adiabatic index, and energy conditions. Furthermore, we delve into the intricacies of the mass-radius function, compactness factor, and surface redshift–integral features of charged compact stars. The culmination of our findings suggests that the f (R , ϕ , X) theory of gravity when subjected to observational scrutiny, manifests as realistic, stable, and devoid of singularities. [ABSTRACT FROM AUTHOR]

We study inflation in scalar–tensor perturbative quantum gravity driven by a one-loop effective potential. We consider effective potentials generated by three models. The first model describes a single scalar field with a nonvanishing mass. The second model describes a massless scalar field with nonminimal coupling to the Einstein tensor. The third model generalizes the Coleman–Weinberg model for the gravitational case. The first model can be consistent with the observational data for N∼70 e-foldings. The second model can be consistent with the observational data for N∼40 e-foldings. We did not find parameters that make the generalized Coleman–Weinberg model consistent with the observational data. We discuss the implications of these results and ways to improve them with other terms of effective action. [ABSTRACT FROM AUTHOR]

The f (R , T) theory of gravity investigated by Harko et al. [T. Harko, F. S. N. Lobo, S. Nojiri and S. D. Odintsov, Phys. Rev. D 84 (2011) 024020; T. Harko, Phys. Rev. D 90(4) (2014) 044067] serves as the inspiration for the homogeneous and isotropic cosmological model presented in generalized f (R , T ϕ) theories connected with a scalar field. Assuming that T ϕ is the trace of the energy-momentum tensor, f (R , T ϕ) gravity can be understood as f (R , T) gravity with a self-interacting scalar field ϕ. To address this, we provide a novel model-independent method for the parametrization of the Hubble parameter, and we apply it to the Friedmann equations in the FLRW Universe. The Markov Chain Monte Carlo (MCMC) approach is then used to estimate the best-fit values of the model parameters using a combination of the updated H (z) dataset, which comprises 57 points, and the Pantheon dataset, which contains 1048 points. The evolution of the deceleration parameter shows a transition from the universe's deceleration phase to its acceleration phase. We also investigate the behavior of the statefinder and the Om diagnostic parameter. Finally, a thorough discussion of the model's physical attributes has been carried out. [ABSTRACT FROM AUTHOR]

The aim of this paper is to examine the singularity-free solutions for anisotropic stellar structures in f (R , ϕ) theory of gravity, where R denotes the Ricci scalar and ϕ represents the scalar field. For this purpose, we consider the spherically symmetric spacetime to discuss the stellar structures with anisotropic fluid. Moreover, the Einstein field equations are solved by using Chaplygin equation of state, and the Karori–Barua metric. To analyze the charged stellar structure, we use the matching conditions of spherically symmetric spacetime with the Reissner–Nordstrom exterior metric and develop some expressions for finding the unknown parameters. We further investigate the graphical behavior of energy density, pressure components, anisotropic component, equation of state parameters, equilibrium condition, stability analysis, adiabatic index and energy conditions. Conclusively, our considered stellar structures under observations are realistic, stable, and are free from any singularities. [ABSTRACT FROM AUTHOR]

In the framework of f (R , T , R a b T a b) gravity theory, the slow-roll approximation of the cosmic inflation is investigated, where T is the trace of the energy–momentum tensor T a b , R and R a b are the Ricci scalar and tensor, respectively. After obtaining the equations of motion of the gravitational field from the action principle in the spatially flat FLRW metric, the fundamental equations of this theory are received by introducing the inflation scalar field as the matter and taking into account only the minimum curvature-inflation coupling term. Remarkably, after taking the slow-roll approximation, the identical equations as in f (R , T) gravity with a R T mixing term are derived. We study several potentials of interest in different domains. We perform analytical analyzes under various approximate conditions, and present numerical results and their comparison with existing observational data at the same time. In the appendix, we analyze the behavior of the inflation scalar field under perturbation while ignoring the effect of metric perturbations. This research complements the slow-roll inflation in the modified theory of gravity. [ABSTRACT FROM AUTHOR]

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting f (R ̄ , T ̄) gravity within the framework of a nonstandard theory, called K-essence theory, where R ̄ represents the Ricci scalar and T ̄ denotes the trace of the energy–momentum tensor associated with the K-essence geometry. The Dirac–Born–Infeld (DBI) nonstandard Lagrangian has been employed to generate the emergent gravity metric ( G ̄ μ ν) associated with the K-essence. This metric is distinct from the usual gravitational metric (g μ ν). It has been shown that under a flat Friedmann–Lemaître–Robertson–Walker (FLRW) background gravitational metric, the modified field equations and the Friedmann equations of the f (R ̄ , T ̄) gravity are distinct from the usual ones. In order to get the equation of state (EoS) parameter ω , we have solved the Friedmann equations by taking into account the function f (R ̄ , T ̄) ≡ f (R ̄) + λ T ̄ , where λ represents a parameter within the model. We have found a relationship between ω and time for different kinds of f (R ̄) by treating the kinetic energy of the K-essence scalar field ( ϕ ̇ 2 ) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on ϕ ̇ 2 . By presenting graphical representations of the EoS parameter with time, we show that our model is consistent with the data of SNIa + BAO + H (z) within a certain temporal interval. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the behavior of a scalar bosonic field within the backdrop of Eddington-inspired Born–Infeld gravity with a global monopole configuration. Additionally, we consider the presence of both scalar and vector potentials. To introduce the scalar potential, we perform a transformation on the mass term, replacing M 2 with (M + S) 2 . For the vector potential, we apply a minimal coupling scheme, transforming p μ → D μ ≡ (p μ − e A μ) within the relativistic Klein–Gordon equation. We opt for a harmonic oscillator scenario where the scalar and vector potentials are equal, i.e. S = V ∝ x 2 . Through this setup, we analytically solve the wave equation using the confluent Heun equation form. Subsequently, we delve into the quantum system in the absence of any potential, determining the permissible values for bound-state relativistic energy levels and the scalar field's wave function. Our analysis reveals that the energy levels and wave function are influenced by various parameters present in the eigenvalue expression. [ABSTRACT FROM AUTHOR]

In unimodular-like theories, the constants of nature are demoted from pre-given parameters to phase space variables. Their canonical duals provide physical time variables. We investigate how this interacts with an alternative approach to varying constants, where they are replaced by dynamical scalar fields. Specifically, we investigate the Brans–Dicke theory of gravity and its interaction with clocks dual to the cosmological constant, the Planck mass, etc. We crucially distinguish between the different role of Newton's G in this process, leading to the possibility of local Lorentz invariance violation. A large number of possible theories emerge, for example where the Brans–Dicke coupling, ω , depends on unimodular-like times (in a generalization of scalar-tensor theories), or even become the dual variable to unimodular-like clocks ticking variations in other demoted constants, such as the cosmological constant. We scan the space of possible theories and select those most interesting regarding the joint variations of the Brans–Dicke ω and other parameters, (such as the cosmological constant); and also regarding their energy conservation violation properties. This ground work is meant to provide the formalism for further developments, namely regarding cosmology, black holes and the cosmological constant problem. [ABSTRACT FROM AUTHOR]

We look into the cosmological uses of the new modified gravitational theory f ̂ (, G) , which is based on the torsion invariant and the teleparallel equivalent of the Gauss–Bonnet term G . The corresponding cosmology of f ̂ (, G) gravity is very intriguing because it varies from both f (T) theories and the f (R , G) class of curvature-modified gravity. In this paper, we have investigated the applicability of an alternative gravitational theory called f ̂ (, G) by applying the energy conditions. Here, we assumed the form of f ̂ (T , T G) = − + α ln β 1 ( 2 + β 2 G) n , where β 1 and β 2 are arbitrary constants. We have examined the cosmological applications of f ̂ (, G) gravity. Here, we consider two particular expressions of the time-dependent Hubble parameter. Both the model parameters are constrained jointly by the Observation Hubble dataset (OHD), the Pantheon dataset and the BAO data to constrain the model parameters using the Markov Chain Monte Carlo (MCMC) minimization technique. We determine the present values of Hubble constant for model ζ : ℋ 0 = 7 0 − 0. 3 4 + 0. 3 4 , ζ = 1. 2 − 0. 0 1 6 + 0. 0 1 6 and ℋ 0 = 1. 8 − 0. 0 1 3 + 0. 0 1 3 ; and model A 2 : ℋ 0 = 7 2 − 0. 4 1 + 0. 4 1 , ζ = 1. 5 − 0. 0 0 7 7 + 0. 0 0 7 6 and = 1. 3 − 0. 0 1 2 + 0. 0 1 2 for the OHD+BAO+Pantheon dataset. Using the most recent estimated values of Hubble parameter, we properly analyzed the energy conditions and looked at the final behavior of our model. Additionally, we have explored the ω D − ω D ′ plane and also we have extracted the scalar field as well as potential of f ̂ (, G) gravity and its relationship to the tachyon field. In addition, we find that, depending on the model parameters, the dark energy (DE) equation-of-state (EoS) parameter may be quintessence or phantom-like, or it may undergo phantom-divide crossing. Finally, we find that all the essential features of the model are satisfied successfully. [ABSTRACT FROM AUTHOR]

In this paper, we present an introduction to cosmic inflation in the framework of Palatini gravity, which provides an intriguing alternative to the conventional metric formulation of gravity. In the latter, only the metric specifies the spacetime geometry, whereas in the former, the metric and the spacetime connection are independent variables—an option that can result in a gravity theory distinct from the metric one. In scenarios where the field(s) responsible for cosmic inflation are non-minimally coupled to gravity or the gravitational sector is extended, assumptions about the underlying gravitational degrees of freedom can have substantial implications for the observational effects of inflation. We examine this explicitly by discussing various compelling scenarios, such as Higgs inflation with a non-minimal coupling to gravity, Higgs inflation with a non-minimal derivative coupling, ℛ 2 inflation, and beyond. We also comment on reheating in these models. Finally, as an application of the general results of Palatini ℛ 2 inflation, we review a model of successful quintessential inflation, where a single scalar field acts initially as the inflaton and then becomes dynamical dark energy, in agreement will all experimental constraints. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the localization of five-dimensional tensor gauge fields called Kalb–Ramond fields in the modified teleparallel braneworld models. The aforementioned branes are generated by gravity coupled to a real scalar field with nonstandard kinetic terms. For two specific forms of the noncanonical expressions, background scalar field solutions are particularly discussed in the presence of different forms of f (T) gravity. By applying nonminimal coupling functions in the tensor gauge field action, it is shown that massless zero modes of Kalb–Ramond gauge fields can be localized on the f (T) branes with noncanonical scalar fields. We also find that potentials of Kalb–Ramond massive modes are volcano-like regarding the equation of motion in the supersymmetric quantum mechanic scenario. Furthermore, the effects of parameters that control the deviation of the usual teleparallel theory are considered on the massless Kaluza–Klein mode and effective potential. [ABSTRACT FROM AUTHOR]

The quantum superposition principle states that quantum-mechanical systems such as atoms can be placed in a superposition of mass-energy eigenstates. Inspired by this idea and the seminal conjecture of Bekenstein, who proposed that black holes in quantum gravity must possess a discrete mass eigenspectrum, here we analyze the effects produced by a black hole in a superposition of masses. Analogous to using the electromagnetic field to probe atoms, we consider a quantum scalar field on the spacetime background sourced by the black hole mass superposition. From the resulting spectra, as measured by a hypothetical two-level system interacting with the field, we infer signatures of discretization of the black hole mass in support of Bekenstein's conjecture. [ABSTRACT FROM AUTHOR]

This paper is intended to review the consequences of assuming tachyon scalar field as a candidate for dark energy from dynamical system technique and observational cosmology point of views. In the contexts of general relativity and teleparallel gravity, a variety of non-minimally coupled tachyon fields have been taken into consideration. These models provide us subclasses of scalar-tensor and scalar-torsion theories. This review covers the tachyonic chameleon, the non-minimally coupled tachyon field to the Gauss–Bonnet invariant and the tachyonic teleparallel dark energy models. Type Ia supernovae and baryonic acoustic oscillations datasets are the observational data that have been used to constrain the model parameters. [ABSTRACT FROM AUTHOR]

In statistical theory, the Tsallis entropy is an extended form of the Boltzmann–Gibbs entropy. The dimensionless parameter δ is employed to state the quantitative difference from the standard scenario. The concepts of Tsallis entropy and the future event horizon are employed in formulating the present new Tsallis holographic dark energy (NTHDE) model. The model attempts to explain the properties of dark energy using the foundation of quantum gravity. The differential equation characterizing the evolution of the NTHDE density parameter is obtained. Expressions stating the dynamic behavior such as equation of state (EoS), deceleration and jerk parameters are obtained in terms of the NTHDE density parameter. For δ < 1 , the quintessence nature of scalar field could completely characterize the NTHDE. A reconstruction of the scalar field's dynamics and quintessence potential is attempted. We demonstrate that the diagnosis made by statefinder is adaptive enough to distinguish between quintessence and cosmological constant-based dark energy models. Additionally, observational data obtained from CC + SNIa + 5 8 0 union 2.1 sources are used to evaluate the model's effectiveness. [ABSTRACT FROM AUTHOR]

Black hole's quasinormal frequencies are basically the complex numbers which provide information about the relaxation of perturbations and depend on the characteristics of the spacetime and types of perturbations. In this paper, we evaluate the spectrum of the quasinormal modes of Hayward black hole in Einstein–Gauss–Bonnet gravity, Hayward black hole in anti-de Sitter space (AdS) spacetime, and 4-dimensional black hole in Einstein–Lovelock gravity. By utilizing the 6th-order WKB resonance technique, we examine the quasinormal modes frequencies ω by shifting the charge parameter Q (it is also identified with the cosmological constant), circular harmonic index l , and mass of scalar field m. We observe that 6th-order WKB method gives quite high accuracy when the multipole number l is larger than the overtone n. We observe that real and imaginary components of the quasinormal modes are not linear functions similar to Reisnner–Nordström-AdS. For large values of charge, quasinormal ringing becomes slower to settle down to thermal equilibrium and hence the frequency of the oscillation becomes smaller. [ABSTRACT FROM AUTHOR]

We investigated the stability condition of f (Q) gravity theory with interacting and noninteracting models by using dynamical system. We assume the f (Q) function as f (Q) = Q + M 2 2 , where M is the free parameter. We evaluated the critical points for this model and examined the stability behavior. We found two stable critical points for interacting model. The phase plots for this system are examined and the physical interpretation is discussed. We illustrate all the cosmological parameters such as Ω m , Ω ϕ , q and ω Tot at each fixed point and compare the parameters with observational values. Further, we assume hybrid scale factor and the equation of redshift and time is t (z) = μ ν W [ ν (1 + z) − m μ μ ]. We transform all the parameters in terms of redshift by using this equation and examine the behavior of these parameters. Our model represents the accelerated expansion of the universe. The energy conditions are examined in terms of redshift and strong energy conditions are not satisfied for the model. We also find the statefinder parameters { r , s } in terms of z and discuss the nature of r–s and r–q plane. For both pairs { r , s } and { r , q } our model represents the Λ CDM model. Hence, we determine that our f (Q) model is stable and it satisfies all the observational values. [ABSTRACT FROM AUTHOR]

A spatially homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I space-time is considered in the presence of a massive scalar field containing domain walls in the framework of the f (R , T) gravity proposed by Harko et al. [Phys. Rev. D 84, 024020, (2011)]. Solving the field equations of the model using a relation between metric potentials and power law between the scalar field and average scale factor of the model, an anisotropic cosmological model with massive scalar fields and domain walls in f (R , T) theory is presented. These conditions result in a model solution that provides a dynamic deceleration parameter. The model's geometrical and physical properties are also examined. The universe exhibits a smooth transition from its early decelerated phase to its current accelerated phase, as shown by the study of the deceleration parameter. The statefinder plane corresponds to the Chaplygin gas era and the model finally approaches Λ CDM model. [ABSTRACT FROM AUTHOR]

The inflationary 1-loop tensor power spectrum from a spectator scalar field with a sharp peak is calculated. Recent studies on primordial black holes suggest that the inflationary curvature perturbation may be huge on small scales. An enhanced curvature perturbation may arise from a drastic enhancement of spectator scalar field fluctuations. In this paper, using the in-in formalism, we calculate 1-loop quantum corrections to primordial gravitational waves by such a spectator field with a sharp peak in momentum space. We find scale-invariant loop corrections in this full quantum setup, in contrast to the sharply peaked corrections in the previously calculated scalar-induced tensor modes. Especially on super Hubble scales, the primordial gravitational waves are also amplified, which can be understood as a Bogoliubov transformation of the vacuum due to the enhanced scalar field. This mechanism allows us to probe the scalar field properties on extremely short-distance scales with the current and future cosmic microwave background and gravitational wave experiments, opening a novel window for inflationary cosmology. [ABSTRACT FROM AUTHOR]

In this paper, we worked in the framework of an inflationary f (R , T) theory in the presence of a canonical scalar field. More specifically, the f (R , T) = γ R + 2 κ α T gravity. The values of the dimensionless parameters α and γ are taken to be α ≥ 0 and 0 < γ ≤ 1. The motivation for this study was the striking similarities between the slow-roll parameters of the inflationary model used in this work and the ones obtained by the rescaled Einstein–Hilbert gravity inflation f (R) = α R. We examined a variety of potentials to determine if they agree with the current Planck Constraints. In addition, we checked whether these models satisfy the Swampland Criteria and we specified the exact region of the parameter space that produces viable results for each model. As we mention in Sec. 4, the inflationary f (R , T) theory used in this work cannot produce a positive n T which implies that the stochastic gravitational wave background will not be detectable. [ABSTRACT FROM AUTHOR]

Here, we discuss a topic that comes up more often than expected: A same theory or theoretical model arises in two different presentations which are assumed to be actually different theories so that these are independently developed. Sometimes this leads to an unwanted doubling of the results. In this paper, we illustrate this issue with the example of two apparently different gravitational theories: (i) the (minimally coupled) Einstein-massless-scalar (EMS) system and (ii) the Sáez–Ballester theory (SBT). We demonstrate that the latter is not a scalar–tensor theory of gravity, as widely acknowledged. Moreover, SBT is identified with the EMS theory. As illustrations of this identification we show that several known solutions of SBT are also solutions of the EMS system and vice versa. Cosmological arguments are also considered. In particular, a dynamical systems-based demonstration of the dynamical equivalence between these theories is given. The study of the asymptotic dynamics of the Sáez–Ballester-based cosmological model shows that there are no equilibrium points which could be associated with accelerated expansion, unless one includes a cosmological constant term or a self-interacting scalar field. This is a well-known result for cosmological models which are based on the Einstein-self-interacting-scalar theory, also known as quintessence. [ABSTRACT FROM AUTHOR]

In this paper, we have explored the field equations of f (T , B) gravity as an extension of teleparallel gravity in an isotropic and homogeneous space-time. In the basic formalism developed, the dynamical parameters are derived by incorporating the power law and exponential scale factor function. The models show accelerating behavior and approach Λ CDM at late time. The present value of the equation of state parameter for both the cases is obtained to be in accordance with the range provided by cosmological observations. The geometrical parameters and the scalar field reconstruction are performed to assess the viability of a late-time accelerating universe. Further, the stability of both the models is presented. It has been observed that both the models are parameter-dependent. Since most of the geometrically modified theories of gravity favor the violation of strong energy condition (SEC), we have derived the energy conditions both for the power law and exponential model. In both the models, the violation of SEC is established. [ABSTRACT FROM AUTHOR]

Horizonless compact objects with light rings are becoming more popular in recent years for numerous motives. In this paper, the conditions under which the throat of a Morris–Thorne wormhole can act as an effective photon sphere are worked out. A specific example which satisfies all the energy conditions in modified theory of gravity is considered and the formation of relativistic images is studied. We have detected photon spheres for the wormhole modeling due to the effect of strong gravitational lensing. Subsequently, we have found the expression for deflection angle in terms of the angular separation between the image and lens by determining the strong-field limit coefficients. It is found to diverge for the impact parameter corresponding to the photon sphere. We observed that the angle of Einstein ring 0 and relativistic Einstein ring n ≥ 1 are completely distinguishable. Given the configuration of the gravitational lensing and the radii of the Einstein ring and relativistic Einstein rings, we can distinguish between a black hole and a wormhole in principle. The stability of wormholes is examined from the positivity of the shape function and satisfaction of the flare-out condition. [ABSTRACT FROM AUTHOR]

This study investigates a bulk viscous fluid anisotropic cosmological model with f (Q) gravity. Here, Q stands for the nonmetricity factor that drives gravitational interaction. We reconstructed the associated parameters with Tsallis holographic dark energy (THDE). We have solved the modified Einstein's field equations by considering the bulk viscosity factor ξ = ξ 0 + ξ 1 H + ξ 2 (Ḣ + H 2). Under the viscous and nonviscous THDE frameworks, we have obtained the expressions of f (Q) using the power-law form of expansion. We have investigated the nature of various energy conditions for the stability analysis. The positive behavior of DEC and WEC indicates the model's validation; on the other hand, SEC is violating, indicating the universe's accelerated expansion. We have also investigated the reconstructed EoS parameter ω rec , T for bulk viscosity and obtained the one that lies in both quintessence and phantom regions. We also discussed the correspondence of the tachyon scalar field with THDE energy density in f (Q) gravity. This correspondence permits the reconstruction of potentials and dynamics for scalar field models describing accelerated expansion. [ABSTRACT FROM AUTHOR]

We explore the swampland conjectures of quintessence and tachyon scalar field models in f (T) and Einstein gravities, respectively. In f (T) gravity, we consider cold and warm (by assuming generalized dissipative coefficient) inflationary scenarios and develop constraints on de-Sitter conjectures through Bekenstein entropy relation. In usual inflation, the de-Sitter conjecture constraint becomes constant (in terms of models constant parameters) which can be easily analyzed for its validity (i.e., | V ′ | V ≤ O (1)). However, in warm inflation, we analyze the de-Sitter conjecture constraint through τ ′ V τ V ′ , i.e., if τ ′ V τ V ′ < 1 then | V ′ | V ≤ O (1) and hence we can obtain the required result. For evaluating this condition, we choose three well-known potentials such as monomial chaotic, hilltop and generalized exponential. It is observed that the condition τ ′ V τ V ′ < 1 satisfied for all three potentials in both regimes of dissipative coefficient for specific choice of constants. We also obtain satisfactory results of de-Sitter conjecture for tachyon and polytropic (with quintessence scalar field) in general relativity. We investigate the consistency of assumed potentials through inflationary parameters n s and r comparing with Planck's observational data 2018 and found them compatible with the recent observations. [ABSTRACT FROM AUTHOR]

The main idea behind this paper is to study f (, φ) theory of gravity, where is Gauss–Bonnet (GB) term and φ is the scalar field. Scalar field has been introduced to explore gravitational interaction between geometry and scalar field. Field equations in Friedmann–Robertson–Walker (FRW) cosmology are constructed and found to be coherent with the existing literature. Exponential solutions are reconstructed. The coupling of the scalar field to the GB term leads to viable results. Further, we probe the oscillating universe in the said gravity model using linear trace term. Energy conditions are explored and graphically analyzed in detail to substantiate our work. Behavior of the Hubble and deceleration parameter is also examined. It is evident from the results that our model provides us with acceptable bouncing solutions for chosen parameters. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to uncover a connection between the dynamics associated with cosmological models and the radially symmetric nonlinear Schrödinger (NLS) equation. The link is made possible due to the central role played by a nonlinear, second-order ordinary differential equation (ODE) known as Milne–Ermakov–Pinney (EMP) equation. To this end, we describe the standard Friedmann–Robertson–Walker (FRW) cosmology of canonical scalar field (CSF) with two barotropic fluids (BFs) in terms of time-independent NLS type formulation within Rastall's theory of gravity (RTG). We derive all cosmological dynamical quantities including scalar field ϕ (x) , scalar potential V (x) , total Schrödinger energy E (x) , wave function u (x) and NLS potential P (x) , of EMP equation in terms of Schrödinger quantities. We consider bouncing and power-law models to find the exact solutions to these quantities in terms of cosmic time. It is found that RTG is a good candidate to discuss NLS type FRW formulation as the obtained results are in good compatibility with the standard theory of gravity. [ABSTRACT FROM AUTHOR]

In this paper, we generalize our previous results on spin connection for the linear scalar cosmological perturbation in f (T) theory to a wider class of theories which includes a scalar field Φ non-minimally coupled to torsion, and allows Φ -dependence of the function f. The case of f T T = 0 , with a scalar field non-minimally coupled to torsion, needs a special treatment. In both considered cases we derive self-consistent equations of motion for cosmological perturbation using a solution for non-trivial spin connection. [ABSTRACT FROM AUTHOR]

The equivalence between f (R) and scalar–tensor theories is revisited, we consequently explored different f (R) models. After consideration of specific definition of the scalar field, we derived the potentials V (ϕ) for each f (R) model focusing on the early Universe, mostly the inflation epoch. For a given potential, we applied the slow-roll approximation approach to each f (R) model and obtained the expressions for the spectral index n s and tensor-to-scalar ratio r. We determined the corresponding numerical values associated with each of the f (R) models. Our results showed that for certain choice of parameter space, the values of n s and r are consistent with the Planck survey results and others produce numerical values that are in the same range as suggested by Planck data. We further constructed the Klein–Gordon equations (KGEs) of each f (R) model. We found numerical solutions to each KGE considering different values of free parameters and initial conditions of each f (R) model. All models showed that the scalar field decreases as time increases, an indication that there is less content of the scalar field in the late Universe. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the reconstruction formalism of the Dirac–Born–Infeld (DBI)-essence scalar field model in the background of non-metric gravity or f (Q) gravity which is controlled by the deformation or non-metricity scale Q. The deformation is caused by the fifth dimension of wrapped compact spaces in brane cosmology. The fifth dimension of that wrapped space is controlled by the D-Brane tension T (ϕ). Hence, we have reconstructed the formalism of DBI scalar field energy densities and pressures using the coupling of deformation geometry and brane scalar fields, i.e. f (Q) and DBI-Scalar fields. The accretion of dark energy onto black holes and wormholes and its critical analysis had been studied with this reconstructed model. The validity of energy conditions has been studied. We have assumed four types of singularity resolutions of the scale factor to investigate the nature of the black hole and wormhole masses due to accretion. Graphically, the physical quantities like mass, kinetic and potential energies have been analyzed for DBI-essence model in the background of f (Q) gravity. [ABSTRACT FROM AUTHOR]

We obtain the statistical entropy of a scalar field on the Schwarzschild black hole in holographic massive gravity by considering corrections on the density of quantum states to all orders in the Planck length from a generalized uncertainty principle (GUP). As a result, we find not only the generalized Bekenstein–Hawking entropy depending on holographically massive gravitons without any artificial cutoff, but also new additional correction terms, which are proportional to surface gravity. Moreover, we also observe that all order GUP corrected entropy is improved to have smaller GUP parameter λ than the previous results. [ABSTRACT FROM AUTHOR]

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 Λ 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 L m R ̃ 2 , where L m is the ordinary matter Lagrangian, and R ̃ is the Weyl scalar. The coupling explicitly satisfies the requirement of the conformal invariance of the theory. Expressing R ̃ 2 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 f (R , L m) -type theory, with the matter Lagrangian nonminimally coupled to geometry. [ABSTRACT FROM AUTHOR]

In this work, we shall study the late-time dynamics of several F(R) gravity models. By appropriately expressing the field equations in terms of the redshift and of a statefinder function, we shall solve numerically the field equations using appropriate physical motivated initial conditions. We consider models which, by construction, are described by a nearly R 2 -model at early epochs and we fine tune the parameters to achieve viability and compatibility with the latest Planck constraints at late times. Such models provide a unified description of inflation and dark energy era and notably a common feature of all the models is the presence of dark energy oscillations. Furthermore, we show that, in contrast to general relativistic fluids and scalar field descriptions, a large spectrum of different dark energy physics is generated by simple F(R) gravity models, varying from phantom, to nearly de Sitter and to quintessential dark energy eras. [ABSTRACT FROM AUTHOR]

Modern cosmology establishes the scenario of accelerated expansion of the universe and the reason for this is supposed to be the exotic negative pressure named dark energy. In light of this, investigation of dark energy models to explain the above scenario assumes paramount importance. Here we obtain dark energy models in the presence of massive scalar meson fields in the Lyra manifold [Math. Z. 54, 52 (1951)] corresponding to Bianchi type-IX space–time. We obtain deterministic models solving field equations using some relevant physical conditions. Dynamical properties of the model are presented and their relevance to the modern observational cosmology is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we study a cosmological model governed by a generalized scalar field nonminimally coupled to scalar torsion in the framework of teleparallel gravity. By applying the Noether symmetry approach, we attempt to explore the explicit forms of the coupling function and the scalar field potential in the Friedmann–Lemaitre–Robertson–Walker (FLRW) flat spacetime. The existence of such symmetry permits the equations of motion to take a simpler form and provides an exponential form cosmological solution for both the scale factor and scalar field. It is shown that the tachyon field behaves as the origin of inflation and contributes significantly to the accelerating expansion of the universe in the early times. While, in the late times, gravitational sources are a pressureless matter field together with the tachyon field, which plays the essential role of dark energy and is the origin of deceleration-acceleration phase transition. Later on, it is also shown that the present model contains a cosmological degeneracy in the sense that different coupling parameters and tachyonic potentials can contribute to the same cosmological behaviors such as the cosmic acceleration, age, equation of state and mean Hubble of FLRW universe. [ABSTRACT FROM AUTHOR]

In this paper, the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is proposed in which noncommutative geometry can emerge from "one-matrix multitrace scalar matrix models" by probing the statistical physics of commutative phases of matter. This is in contrast to the usual mechanism in which noncommutative geometry emerges from "many-matrix singletrace Yang–Mills matrix models" by probing the statistical physics of noncommutative phases of gauge theory. In this novel scenario, quantized geometry emerges in the form of a transition between the two phase diagrams of the real quartic matrix model and the noncommutative scalar phi-four field theory. More precisely, emergence of the geometry is identified here with the emergence of the uniform-ordered phase and the corresponding commutative (Ising) and noncommutative (stripe) coexistence lines. The critical exponents and Wigner's semicircle law are used to determine the dimension and the metric, respectively. Arguments from the saddle point equation, from Monte Carlo simulation and from the matrix renormalization group equation are provided in support of this scenario. [ABSTRACT FROM AUTHOR]

In recent times, it has been perceived that incorporation of branes in higher dimensional theories of quantum gravity is very effective to differentiate those theories which successfully satisfy the swampland criteria. Moreover, warm inflation is considered to be most appropriate single scalar field inflationary model in the framework of swampland criteria. In this regard, we study two well-known Chaplygin gas (CG) models embedded in Randall–Sundrum braneworld. It is known that the de Sitter constraint is derived by taking into account Bousso's covariant entropy bound. We discuss the application of this result in the context of Chaplygin-brane models and find the condition on the slope of the potential. Furthermore, it is demonstrated that in view of warm inflation dynamics this condition remains essentially unchanged indicating the compatibility of the models with swampland criteria. In addition, we investigate the constraint on the warm inflation parameter imposed by the de Sitter conjecture which shows that the warm inflation is in accordance with de Sitter bound in the strong as well as in weak dissipative regime for both models of Chaplygin gas. [ABSTRACT FROM AUTHOR]

It has been previously shown that a Gauss–Bonnet term nonminimally coupled to a scalar field produces a scalarised black hole solution which can be considered as having secondary scalar hair, parametrised in terms of the black hole's mass and charge. In this paper we extend a previously investigated linear coupling of the form f (ϕ) = ϕ to a nonminimally coupled Maxwell term, with the form 1 8 F μ ν F μ ν + β ϕ F μ ν F μ ν . By using numerical methods the solutions to the full differential equations are found, as well as a perturbative expansion in the r → ∞ limit and a perturbative expansion in couplings parameters such as β. These solutions describe scalarised black holes with modified electric field which have dependence not only on the electric charge of the black hole, but also the value of the nonminimal coupling constant. We also discuss the bounds imposed on the parameters of the black hole by the reality condition of the solution, giving some explicit numerical bounds. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the inflationary cosmology in f (R , ϕ) gravity by proposing different models of f (R , ϕ) , where ϕ is a noninteracting massive scalar field which is nonminimally coupled to gravity in the Jordan frame. In special cases of these models, we could reach the standard Starobinsky model. Further, we calculated the slow-roll parameters, scalar-to-tensor ratio, and spectral index for these models and compared them with observations. Our findings are located in the favorite area of Planck's recent results. On the other hand, the discovery of the gravitational waves in the range of r ≥ 5 × 1 0 − 3 would rule out the Starobinsky model or even the nondiscovery of gravitational wave in this range r ≥ 2 × 1 0 − 3 by PICO. Our models, specifically the second one, might be the proper generalization for the Starobinsky model in this regard. [ABSTRACT FROM AUTHOR]

In this paper, we study the properties of gravity and bulk fields living in a torsion warped braneworld. The torsion is driven by a background vector whose norm provides a source for the bulk cosmological constant. For a vector as the derivative of a scalar field, we find new isotropic thick brane geometry. We analyze the features of bosonic and fermionic fields in this scenario. The background vector provides nonminimal coupling between the fields and the geometry leading to modifications in the Kaluza–Klein (KK) states. For a scalar field, the background vector breaks the Z 2 symmetry, whereas for the vector gauge field, a geometric coupling to the torsion tensor traps the massless mode. The spinor connection is modified by the torsion and a geometric derivative Yukawa-like coupling is proposed. The effects of these new couplings are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we study the sparsity of Hawking radiation from nonrotating singularity-free black holes in conformal gravity. We give a rigorous bound on the greybody factor for massless scalar field and calculate the sparsity of Hawking radiation from the black hole. Besides, we investigate the dependence of the bound of the greybody factor and the sparsity of Hawking radiation on the conformal parameters, respectively. Our study shows that when the conformal parameters are large, the increase of conformal parameters will lead to a more sparse Hawking radiation, while to a less sparse Hawking radiation if the conformal parameters are small. [ABSTRACT FROM AUTHOR]

In this paper, we investigate Einstein's gravity induced from higher-derivative scalar field theories. We develop an approach utilizing an effective theory of multiple fields for the higher-derivative theory. The expressions for induced cosmological constant and the induced gravitational constant are obtained in the present scenario of induced gravity in D dimensions. We also show that finite values for the induced constants can be extracted in certain infinite-derivative theories. [ABSTRACT FROM AUTHOR]

We investigate the characteristic modifications in the evolving cosmological perturbations when dark energy interacts with dust-like matter, causing the latter's background energy density fall off with time faster than usual. Focusing in particular to the late-time cosmic evolution, we show that such an interaction (of a specific form, arising naturally in a scalar-tensor formulation, or a wide range of modified gravity equivalents thereof), can have a rather significant effect on the perturbative spectrum, than on the background configuration which is not expected to get distorted much from Ł CDM. Specifically, the matter density contrast, which is by and large scale-invariant in the deep sub-horizon limit, not only gets dragged as the interaction affects the background Hubble expansion rate, but also receives a contribution from the perturbation in the (scalar field induced) dark energy, which oscillates about a nonzero mean value. As such, the standard parametrization ansatz for the matter density growth factor becomes inadequate. So we modify it suitably, and also find a numerical fit of the growth index in terms of the background parameters, in order to alleviate the problems that arise otherwise. Such a fit enables direct estimations of the background parameters, as well as the growth parameter and the reduced Hubble parameter, which we duly carry out using a redshift space distortion (RSD) subsample and its combination with the observational Hubble data. On the whole, the parametric estimates show consistency with the general observational constraints on the background level cosmology, as well as the constraints on scalar-tensor gravity from astrophysical observations, apart from having significance in the domain of cosmological perturbations. [ABSTRACT FROM AUTHOR]

In this work, we shall study a class of f (R , ϕ) gravity models which during the inflationary era, which is the large curvature regime, result to an effective inflationary Lagrangian that contains a rescaled Einstein–Hilbert term α R in the presence of a canonical minimally coupled scalar field. The dimensionless parameter α is chosen to take values in the range 0 < α < 1 and the main motivation for studying these rescaled Einstein–Hilbert f (R , ϕ) gravities, is the fact that the rescaled action may render an otherwise incompatible canonical scalar field theory with the Swampland criteria, to be compatible with the Swampland criteria and specifically the distance conjecture and the de Sitter conjecture, without considering the refined de Sitter conjecture however. As we will show, by studying a large number of inflationary potentials appearing in the 2018 Planck collaboration paper for the constraints on inflation, the simultaneous compatibility with both the Planck constraints and the aforementioned two Swampland criteria is achieved for some models, and the main characteristic of the models for which this is possible is the small value that the parameter α must take. [ABSTRACT FROM AUTHOR]

The assumptions of the Hawking–Penrose singularity theorem are not covariant under field redefinitions. Following the works on the covariant formulation of quantum field theory initiated by Vilkovisky and DeWitt in the 80s, we propose to study singularities in field space, where the spacetime metric is treated as a coordinate along with the other fields in the theory. From this viewpoint, a spacetime singularity might be just a singularity in the field-space coordinates, analogously to the standard coordinate singularities in General Relativity. Objects invariant under field-space coordinate transformations can then reveal whether certain spacetime singularity is indeed singular. We recall that observables in quantum field theory are scalar functionals in field space. Therefore, in principle, spacetime singularities corresponding to regular field-space curvature invariants would not affect physical observables. In this paper, we show that the field-space Kretschmann scalar for a certain choice of the DeWitt field-space metric is everywhere finite. This fact could be interpreted as an indication that no singularities actually exist in pure gravity for any gravitational action. In particular, all vacuum singularities of General Relativity result from an unhappy choice of field variables. The extension to the case in which matter fields are present, as required by singularity theorems, is left for future development. [ABSTRACT FROM AUTHOR]

In this paper, we conduct a study on the scalar field obtained from f (R) gravity via Weyl transformation of the spacetime metric g μ ν from the Jordan frame to the Einstein frame. The scalar field is obtained as a result of the modification in the geometrical part of Einstein's field equation of General Relativity. For the Hu–Sawicki model of f (R) gravity, we find the effective potential of the scalar field and calculate its mass. Our study shows that the scalar field (also named as scalaron) obtained from this model has the chameleonic property, i.e. the scalaron becomes light in the low-density region, while it becomes heavy in the high-density region of matter. Then it is found that the scalaron can be regarded as a dark matter (DM) candidate since the scalaron mass is found to be quite close to the mass of ultralight axions, a prime DM candidate. Thus, the scalaron in the Hu–Sawicki model of f (R) gravity behaves as DM. Further, a study on the evolution of the scalaron mass with the redshift is also carried out, which depicts that scalaron becomes light with expansion of the Universe and with different rates at different stages of the Universe. [ABSTRACT FROM AUTHOR]

Within the framework of quantum gravity and modified entropy-area formalism, the Tsallis holographic dark energy is an effort to peep into a mysterious content of the Universe, the dark energy, to analyze its nature. The Tsallis parameter δ provides the main characteristic of the Tsallis holographic dark energy. Opting the value of Tsallis parameter δ ≤ 2 , a quintessence scalar field description of the Tsallis holographic dark energy model can be obtained. In this work, we present this quintessential explanation of the Tsallis holographic dark energy with δ ≤ 2 and reconstruct the dynamics of the scalar field and the potential of quintessence. [ABSTRACT FROM AUTHOR]

In both Newtonian gravity and Einstein gravity there is no force on a test particle located inside a spherical cavity cut out of a static, spherically symmetric mass distribution. Inside the cavity exterior matter is decoupled and there is no external field effect that could act on the test particle. However, for potentials other than the Newtonian potential or for geometries other than Ricci flat ones this is no longer the case, and there then is an external field effect. We explore this possibility in various alternate gravity scenarios, and suggest that such (Machian) external field effects can serve as a diagnostic for gravitational theory. [ABSTRACT FROM AUTHOR]

The hybrid expansion law (HEL) for average scale factor that yields power-law and exponential-law cosmologies is considered in spatially homogenous and anisotropic Bianchi type-I model in the context of Brans–Dicke (BD) Theory of gravitation. The solutions of the field equations have been calculated by assuming the power-law expression between the average scale factor (a (t)) and scalar field (ϕ). We studied both interacting and non-interacting forms of dark energy and dark matter and obtained respective solutions. The energy density Ω m decreases with time while energy densities Ω de increases with time. In both the cases, the physical acceptability and stability of the models are also studied. The coincidence problem in Λ CDM model can be ruled out with proper choice of coupling between dark matter (DM) and dark energy (DE). We also discussed the physical behaviors of the derived models with the current observations applied to late-time acceleration and beginning of the universe. In this model, it is observed that our HEL Bianchi type I universe is highly anisotropic in the beginning of universe and becomes isotropic and overlaps with flat Λ CDM model at late times. [ABSTRACT FROM AUTHOR]