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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]

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 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 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]

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]

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]

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]

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, 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]

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]