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This work comprises a study of the thermodynamic behavior of modified $f(\bar{R},\bar{T})$ gravity, which had been developed based on a non-canonical theory known as K-essence theory. In this development, we use the Dirac-Born-Infeld (DBI) type of non-standard Lagrangian. We develop a modified first law and generalized second law of thermodynamics (GSLT) within the modified $f(\bar{R},\bar{T})$ gravity, where we consider the background metric to be the usual Friedmann-Lema$\hat{\text{i}}$tre-Robertson-Walker (FLRW) type. A graphical analysis of surface gravity has been performed for the modified FLRW metric via the $f(\bar{R},\bar{T})$ theory, which is different from the usual FLRW gravity through the usual $f(R,T)$ gravity. Exponential and power law scale factors are used to analyze cosmic surface gravity. Through the investigation of the modified GSLT, using the relation of scale factor with the scalar field, we have seen that during the initial phase of the universe, the entropy's rate of change may be either negative or positive, contingent upon the value of the curvature constant. The negativity of the entropy change indicates that the modified GSLT is not feasible in that particular area for a particular curvature constant. These traits suggest that during the inflationary period, entropy might have been either negative or positive. It has also been seen that entropy saturates every curvature value at different time ranges, which indicates the heat death of the universe., Comment: 20 pages, 10 figures

In this article, we apply the Finsler spacetime to develop the Einstein field equations in the extension of modified geometry. Following Finsler geometry, which is focused on the tangent bundle with a scalar function, a scalar equation should be the field equation that defines this structure. This spacetime maintains the required causality properties on the generalized Lorentzian metric manifold. The matter field is coupled with the Finsler geometry to produce the complete action. In this work, we use modified gravity to develop the Einstein field equations from the variational principle. Developed Einstein field equations are employed on the strange stellar system to improve the study. The interior of the system is made of a strange quark, maintained by the MIT Bag equation of state. In addition, the modified Tolman-Oppenheimer-Volkov (TOV) equation is formulated. In particular, the anisotropic stress attains the maximum at the surface. The mass-central density variation justifies the stability of the system., Comment: Accepted for publication in EPJC

We try to find the possibility of a Bianchi V universe in the modified gravitational field theory of $f(R,T)$. We have considered a Lagrangian model in the connection between the trace of the energy-momentum tensor $T$ and the Ricci scalar $R$. In order to solve the field equations a power law for the scaling factor was also considered. To make a comparison of the model parameters with the observational data, we put constraints on the model under the datasets of the Hubble parameter, Baryon Acoustic Oscillations, Pantheon, joint datasets of Hubble parameter + Pantheon, and collective datasets of the Hubble parameter + Baryon Acoustic Oscillations + Pantheon. The outcomes for the Hubble parameter in the present epoch are reasonably acceptable, especially since our estimation of this $H_0$ is remarkably consistent with various recent Planck Collaboration studies that utilize the $\Lambda$-CDM model.

In this paper, we present a bibliometric analysis of the Mendeleev Periodic Table. We have conducted a comprehensive analysis of the Scopus-based database using the keyword "Mendeleev Periodic Table". Our findings suggest that the Mendeleev Periodic Table is an influential topic in the field of Inorganic as well as Organic Chemistry. Future researchers may focus on expanding our analysis to include other bibliometric indicators to gain a more comprehensive understanding of the impact of the Mendeleev Periodic Table in chemistry-based scientific investigations and even in the field of astrochemistry., Comment: 16 pages, 9 figures

We propose a novel cosmological framework within the $f(R,T)$ type modified gravity theory, incorporating a non-minimally coupled with the higher order of the Ricci scalar ($R$) as well as the trace of the energy-momentum tensor ($T$). Therefore, our well-motivated chosen $f(R,T)$ expression is $ R + R^m + 2 \lambda T^n$, where $\lambda$, $m$, and $n$ are arbitrary constants. Taking a constant jerk parameter ($j$), we derive expressions for the deceleration parameter ($q$) and the Hubble parameter ($H$) as functions of the redshift $z$. We constrained our model with the recent Observational Hubble Dataset (OHD), $Pantheon$, and $ Pantheon $ + OHD datasets by using the analysis of Markov Chain Monte Carlo (MCMC). Our model shows early deceleration followed by late-time acceleration, with the transition occurring in the redshift range $1.10 \leq z_{tr} \leq 1.15$. Our findings suggest that this higher-order model of $f(R,T)$ gravity theory can efficiently provide a dark energy model for addressing the current scenario of cosmic acceleration., Comment: 14 pages, 12 figures

Based on the work of Chandrasekhar [{\it The Mathematical Theory of Black Holes, Oxford Univ. Press (1992)}], we investigate the null geodesic structure of the emergent Barriola-Vilenkin spacetime in the context of {\bf k-}essence theory. For {\bf k-}essence, the emergent gravity metric is a one-to-one correspondence with the Barriola-Vilenkin (BV) metric connected to the Schwarzschild background, where the global monopole charge is replaced by the dark energy density. This equivalence holds specifically for a certain class of {\bf k-}essence scalar fields that have been constructed by Gangopadhyay and Manna [Euro. Phys. Lett., 100, 49001, (2012)]. We have traced out different trajectories for null geodesic in the presence of dark energy for the {\bf k-}essence emergent Barriola-Vilenkin spacetime. It is demonstrated that the outcomes deviate from the typical Schwarzchild spacetime owing to the fundamental configuration with a constant dark energy density., Comment: 10pages, 5figures, Accepted from IJMPD

In this paper, we review the theoretical basis for generation of gravitational waves and the detection techniques used to detect a gravitational wave. To materialize this goal in a thorough way we first start with a mathematical background for general relativity from which a clue for gravitational wave was conceived by Einstein. Thereafter we give the classification scheme of gravitational waves such as (i) continuous gravitational waves, (ii) compact binary inspiral gravitational waves and (iii) stochastic gravitational wave. Necessary mathematical insight into gravitational waves from binaries are also dealt with which follows detection of gravitational waves based on the frequency classification. Ground based observatories as well as space borne gravitational wave detectors are discussed in a length. We have provided an overview on the inflationary gravitational waves. In connection to data analysis by matched filtering there are a few highlights on the techniques, e.g. (i) Random noise, (ii) power spectrum, (iii) shot noise, and (iv) Gaussian noise. Optimal detection statistics for a gravitational wave detection is also in the pipeline of the discussion along with detailed necessity of the matched filter and deep learning., Comment: 23 pages, 9 figures, Accepted in International Journal of Modern Physics D (Special Issue)

In the present work we study the geodesic motion and accretion process of a test particle near an Anti-de Sitter (ADS) BH surrounded by a dark fluid with a Chaplygin-like equation. Within the defined paradigm, we investigate on the equatorial plane and examine circular geodesics along with their features related to stabilities, radiation energy flux, oscillations and orbits. The general form of the fluid accretion onto the AdS BH through dynamical analysis and mass expansion also has discussed in a depth. Additionally, a few more interesting topics, e.g. the effective potential, angular momentum, specific energy, radiation energy and epicyclic frequencies have also been examined thoroughly. All the attributes are physically acceptable within the observational signatures and ranges., Comment: 22 pages, 12 figures

This article investigates on the radial and non-radial geodesic structures of the generalized K-essence Vaidya spacetime. Within the framework of K-essence geometry, it is important to note that the metric does not possess conformal equivalence to the conventional gravitational metric. This study employs a non-canonical action of the Dirac-Born-Infeld kind. In this work, we categorize the generalized K-essence Vaidya mass function into two distinct forms. Both the forms of the mass functions have been extensively utilized to analyze the radial and non-radial time-like or null geodesics in great details inside the comoving plane. Indications of the existence of wormhole can be noted during the extreme phases of spacetime, particularly in relation to black holes and white holes, which resemble the Einstein-Rosen bridge. In addition, we have also detected the distinctive indication of the quantum tunneling phenomenon around the central singularity., Comment: 19 pages, 21 figures

This paper examines a power law solution under $f(R,T)$ gravity for an isotropic and homogeneous universe by considering its functional form as $f(R,T) = R + \xi RT$, where $\xi$ is a positive constant. In $f(R,T)$ gravity, we have built the field equation for homogeneous and isotropic spacetime. The developed model's solution is $a = \alpha t^{\beta}$. We have used the redshift in the range $0 \leq z \leq 1.965$ and obtained the model parameters $\alpha$, $\beta$, $H_0$ by using the Markov Chain Monte Carlo (MCMC) method. The constrained values of the model parameter are as follows: $H_0 = 67.098^{+2.148}_{-1.792}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 67.588^{+2.229}_{-2.170}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 66.270^{+2.215}_{-2.181}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 65.960^{+2.380}_{-1.834}$ km s$^{-1}$ Mpc$^{-1}$, $H_0 = 66.274^{+2.015}_{-1.864}$ km s$^{-1}$ Mpc$^{-1}$ which have been achieved by bounding the model with the Hubble parameter ($H(z)$) dataset, Baryon Acoustic Oscillations (BAO) dataset, Pantheon dataset, joint $H(z)$ + Pantheon dataset and collective $H(z)$ + BAO + Pantheon dataset, respectively. These computed $H_o$ observational values agree well with the outcomes from the Plank collaboration group. Through an analysis of the energy conditions' behaviour on our obtained solution, the model has been examined and analysed. Using the Om diagnostic as the state finder diagnostic tool and the jerk parameter, we have also investigated the model's validity. Our results show that, within a certain range of restrictions, the proposed model agrees with the observed signatures.

In this paper, we examine the universe's expansion in $ f(R, L_{m}) $ gravity for a particular form of $ f(R, L_{m})=\frac{R}{2}+L_{m}^{n}$. The field equations for flat FLRW metric with matter Lagrangian $ L_{m}=\rho$ are derive. Hubble parameter in terms of red-shift$(z)$ are derived using the linear form of Equation of State (EoS) parameter $ \omega=w_{0}+w_{1}z $. By using Bayesian statistical techniques based on $ \chi^{2}$-minimization technique, we have obtained the best fit values of the model parameters of this model for cosmic chronometer and supernovae Pantheon datasets. The evolution of the equation of state parameter$(\omega)$, energy density $ (\rho) $, pressure $\mathit{(p)}$ cosmographic parameters, and the impact of the energy conditions with best-fit values of the model parameters are all thoroughly examined. We have also analyze Om diagnostic's behavior and determine the present age of universe for this model., Comment: Accepted Manuscript, 27 pages, 13 figures

The paper investigates the collapse of the generalized emergent Vaidya spacetime in the setting of $f(\bar{R}, \bar{T})$ gravity, specifically in K-essence theory. In this study, the Dirac-Born-Infeld type non-standard Lagrangian is used to calculate the emergent metric $\bar{G}_{\mu\nu}$, which is not conformally equivalent to the conventional gravitational metric. We use the function $f(\bar{R}, \bar{T})$ to reflect the additive nature of the emergent Ricci scalar ($\bar{R}$) and the trace of the emergent energy-momentum tensor ($\bar{T}$). Our study demonstrates that certain choices of $f(\bar{R}, \bar{T})$ may result in the existence of a naked singularity caused by gravitational collapse. The alternative $f(\bar{R}, \bar{T})$ values resulted in an accelerating universe dominated by dark energy. Moreover, the investigation showed the presence of both positive and negative masses, which might suggest the coexistence of dark matter and dark energy. Furthermore, for a given quantity of kinetic part of the K-essence scalar field, mass is completely changed into energy, meaning that spacetime is Minkowskian. The K-essence theory may also be employed as a dark energy framework and a basic gravitational theory, making it possible for researchers to investigate a wide ranges of cosmic phenomena., Comment: 21 pages, 8 figures, 2 tables, Accepted from Chinese Journal of Physics

In this article, using gravitational decoupling by means of minimal geometric deformation approach, we obtain a new spherically symmetric and static black hole solution. To progress, we close the system by assuming that the average pressure of the $\theta$-sector is vanishing. Also, we tackle the problem regarding how, for a given minimally deformed black hole solution, one can connect it to a wormhole space-time., Comment: 15 pages, 6 figures, Accepted in European Physical Journal C (in press)

Quantum mechanical concept such as the Casimir effect is explored to model traversable wormholes in an extended teleparallel gravity theory. The minimal length concept leading to the generalized uncertainty principle (GUP) is used to obtain the Casimir energy density. The effect of the GUP correction in the geometrical and physical properties of traversable Casimir wormholes are investigated. It is noted that the GUP correction has a substantial effect on the wormhole geometry and it modifies the energy condition. From a detailed calculation of the exotic matter content of the GUP corrected Casimir wormhole, it is shown that, a minimal amount of exotic matter is sufficient to support the stability of the wormhole., Comment: 14 pages, 7 figures

In this work, we investigate for an analytical solution under modified gravity theory, specifically the $f(R,T)$ gravity for two different eras, i.e., matter and dark energy dominated accelerating universe from completely geometrical and mathematical point of view with the help of the Raychaudhuri equation. To construct $f(R,T)$ gravity model, we consider the functional form of $f(R,T)$ as the sum of two independent functions of the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$, respectively. Under the consideration of this type of power law expansion of the Universe we have studied the viability, stability and all the energy conditions. We note that the strong energy condition is not satisfied in our model, which is obvious for the present scenario of the Universe., Comment: 15 pages, 27 figures

We investigate how the Raychaudhuri equation behaves in the $k$-essence geometry. As far as we are concerned, both the early and current epochs of the universe are relevant to the $k$-essence theory. Here, we have studied the $k$-essence geometry using the Dirac-Born-Infeld (DBI) variety of non-standard action. The corresponding $k$-essence emergent spacetime is not conformally equivalent to the usual gravitational metric. We assume that the background gravitational metric is of the Friedmann-Lemaitre-Robertson-Walker (FLRW) type in this case. We have found that both the conditional singular and non-singular cosmological models of the universe through the modified Raychaudhuri equation are possible where we have used the spacetime as the flat $k$-essence emergent FLRW-type. We have also addressed to the Focusing theorem and conditional caustic universe construction. These conditional effects are caused by the additional interactions that arise as a result of the coupling that exists between the gravity and the $k$-essence scalar field., Comment: 5 figures

The propagation of fully nonlinear ion acoustic solitary waves (IASW) in a magneto-plasma with degenerate electrons was investigated by Abdelsalam et al. [[1] Physics Letters A 372 (2008) 4923]. Based on their work in the present work, a rigorous and general analytical study is presented. This confirms their implied assumption that (i) only hump and no cavity is possible and (ii) for humps, the algebraic equation for the maximum density N obtained by them determines it uniquely (naturally assumes N > 1). Here we confirm analytically their assertion that N decreases with lx (the direction cosine of the wave vector k along the x-axis) and N increases with the increase of the Mach number (M).

In this work, we present the Einstein field equations (EFE) in the framework of a modified matter source and thus find out the solutions for the Wormhole. To obtain characteristic solutions set, we employ two kinds of equations of states (EOS), i.e., the van der Waals and polytropic EOS to the EFE. We adopt embedding class as a general technique for the system and discuss several physical attributes of the stellar system under embedded wormhole solutions. Detailed discussion about the matter contents of the thin-shell developed around the obtained wormhole solutions in the background of Schwarzschild BH surrounded by cloud and quintessence-type fluid distribution by using a well-known cut and paste approach. We have also performed stability analysis using the linearized radial perturbation method for the van der Waals EOS and polytropic EOS. Several interesting points have evolved from the entire investigation along with the features of the thin shell around the wormhole., Comment: 24 figures and 4 tables

In Einstein's Field Equation(EFE) the geometry of the space-time is connected with the matter distribution. The geometry or the gravitational sector deals with classical macroscopic objects involving gravitational units while the matter sector can be better described by quantum theory involving atomic units. It has been argued by Bisabr that there exists an epoch-dependent conversion factor between these two unit systems present in two different conformal frames,i.e. the conformal factor is epoch dependent. We argue that the conformal transformation is a dynamical degree of freedom describing it's possible relevance in inflation in context to the graceful exit problem, dynamics of the cosmological constant {\Lambda} and justify the argument in the light of consequences of Dirac's Large Number hypothesis(LNH)., Comment: 11 Pages, Previously this version appeared as arXiv:2005.09458v2 which was submitted as a replacement work by accident

In this paper, we study the collapsing scenario for the k-essence emergent Vaidya spacetime in the context of massive gravity's rainbow. For this study, we consider that the background metric is Vaidya spacetime in massive gravity's rainbow. We show that the k-essence emergent gravity metric resembles closely to the new type of generalized Vaidya massive gravity metric with the rainbow deformations for null fluid collapse where we consider the k-essence scalar field as a function solely of the advanced or the retarded time. The k-essence emergent Vaidya massive gravity rainbow mass function is also different. This new type k-essence emergent Vaidya massive gravity rainbow metric has satisfied the required energy conditions. The existence of the locally naked central singularity, the strength and the strongness of the singularities for the rainbow deformations of the k-essence emergent Vaidya massive gravity metric are the interesting outcomes of the present work., Comment: 20 pages, 5 figures, to be published in Chinese Physics C

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting $f(\bar{R},\bar{T})$ gravity within the framework of a {\it non-standard} theory, called {\it {\bf K-}essence} theory, where $\bar{R}$ represents the Ricci scalar and $\bar{T}$ denotes the trace of the energy-momentum tensor associated with the {\bf K-}essence geometry. The Dirac-Born-Infeld (DBI) non-standard Lagrangian has been employed to generate the emergent gravity metric $(\bar{G}_{\mu\nu})$ associated with the {\bf K-}essence. This metric is distinct from the usual gravitational metric $(g_{\mu\nu})$. It has been shown that under a flat FLRW background gravitational metric, the modified field equations and the Friedmann equations of the $f(\bar{R},\bar{T})$ gravity are distinct from the usual ones. In order to get the equation of state (EOS) parameter $\omega$, we have solved the Friedmann equations by taking into account the function $f(\bar{R},\bar{T})\equiv f(\bar{R})+\lambda \bar{T}$, where $\lambda$ represents a parameter within the model. We have found a relationship between $\omega$ and time for different kinds of $f(\bar{R})$ by treating the kinetic energy of the {\bf K-}essence scalar field ($\dot{\phi}^{2}$) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on $\dot{\phi}^{2}$. 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., Comment: 12 pages, 20 figures, 4 tables, Accepted from IJMPD

In recent years, a class of compact objects called gravastars have drawn immense interest as regular solutions to end state stellar collapse. Since the energy density involved in collapse process is expected to be high, it is a natural choice to study such compact objects in context of modified gravity theories which reduce to General Relativity (GR) in the low energy regime. We have already framed a model of gravastar in such a modified gravity framework involving extra dimensional Randall-Sundrum (RS) single brane gravity~[Phys. Rev. D \textbf{102}, 024037 (2020)] \cite{Sengupta1}. As a sequel in the present paper we substantially improve our previous model by choosing the Kuchowicz function as one of the metric potentials, which leads to many new interesting results and physical features from our analysis as discussed in this paper. Also, we provide essential additional stability checks on our gravastar model to investigate the possibility of any instability creeping in due to the higher dimensional framework. Our present improved gravastar model is found to clear all the stability checks successfully. Very interestingly, the static spherically symmetric matter distributions are found to accommodate both classes of solutions obeying and violating the modified energy conditions on the RS brane as we find in this work. We can conclude from our analysis that the Kuchowicz metric potential is very effective for describing regular solutions to compact objects at substantially high energies on the 3-brane., Comment: 14 pages, 10 figures

In the work, we present investigation on decoupling gravitational sources under the framework of $f(R,T)$ gravity. Basically the complete geometric deformation technique has been employed here which facilitates finding exact solutions to the anisotropic astrophysical system smoothly without imposing any particular ansatz for deformation function. Along with this we have also used 5-dimensional Euclidean spacetime in order to describe the embedding Class I spacetime for getting a solvable spherical physical system. The solutions thus obtained show physically interesting as well as viable with new possibilities to sought for. Especially, from the present investigation it is worthy to note that the mixture $f(R,T)$ + CGD translate the scenario beyond the pure GR realm and hence clearly helps to enhance the features of the interior astrophysical aspects of compact stellar objects. Therefore to check the physical acceptability and stability of the stellar system based on the obtained solutions, we have performed a few physical tests which satisfy all the stability criteria, including nonsingular nature of the density as well as pressure., Comment: 11 Figures and 4 Tables

We present a model of compact astrophysical object under General Theory of Relativity using the anisotropic extension of Tolman IV solution. The anisotropy function, derived from the model, remains well behaved throughout the interior of the star. The model satisfies several necessary conditions for a physically realistic compact star. Physical viability of the model is verified specifically by plugging in the estimated parameter values of the Low Mass X-ray Binary (LMXB) candidate 4U 1608 - 52. Our stability analysis of this star, by using various criteria for stability, provide satisfactory results. In connection to anisotropy, we compute the Tidal Love Number (TLN) for the compact stellar model and compare the calculated values with existing literature., Comment: 18 pages, the manuscript is prepared in LaTex code. arXiv admin note: text overlap with arXiv:2102.07099

In the present investigation compact stellar models are dealt with in the framework of the modified gravity theory, specifically of $f(\mathbb{T},\mathcal{T})$ type. We have considered that the compact objects are following a spherically symmetric static metric and obtained the Einstein field equations in the spacetime of $f(\mathbb{T},\mathcal{T})$. To make the Einstein equations solvable we employ the methodology of conformal Killing vectors. Thereafter by using the MIT bag equation of state to the compact stars, considering that the stars are formed by strange quark, we find the solutions set. The solutions are examined via several physical tastings which exhibit viability of the model., Comment: 14 pages, 7 figures

In this brief review, we present some cosmological models with a Hybrid Scale Factor (HSF) in the framework of general relativity (GR). The hybrid scale factor fosters an early deceleration as well as a late time acceleration and mimics the present Universe. The dynamical aspects of different cosmological models with HSF in the presence of different matter fields have been discussed., Comment: 10 pages, Review Article Accepted for publication in IJMPD

In this paper we attempt to examine the possibility of construction of a traversable wormhole on the Randall-Sundrum braneworld with ordinary matter employing the Kuchowicz potential as one of the metric potentials. In this scenario, the wormhole shape function is obtained and studied, along with validity of Null Energy Condition (NEC) and the junction conditions at the surface of the wormhole are used to obtain a few of the model parameters. The investigation, besides giving an estimate for the bulk equation of state parameter, draws important constraints on the brane tension which is a novel attempt in this aspect and very interestingly the constraints imposed by a physically plausible traversable wormhole is in high confirmity with those drawn from more general space-times or space-time independent situations involved in fundamental physics. Also, we go on to claim that the possible existence of a wormhole may very well indicate that we live on a three-brane universe., Comment: 27 Pages, 5 figures

It is generally believed that wormholes are supported by exotic matter violating Null Energy Condition (NEC). However, various studies of wormhole geometries under Lovelock theories of gravity have reported existence of wormhole supported by matter satisfying NEC. Being inspired by these results, we explore the possibility of the existence of wormhole supported by normal quark matter in third order Lovelock gravity theory. Well known MIT Bag Model Equation of state is chosen for describing the quark matter. Taking physically acceptable approximations, we solve the field equations for shape function which satisfies flare out condition. The residual of the approximate solution is studied for accuracy and found to be acceptable., Comment: 15 pages, 6 figures

In this paper, we develop a new class of models for a compact star with anisotropic stresses inside the matter distribution. By assuming a linear equation of state for the anisotropic matter composition of the star we solve the Einstein field equations. In our approach, for the interior solutions we use a particular form of the ansatz for the metric function $g_{rr}$. The exterior solution is assumed as Schwarzschild metric and is joined with the interior metric obtained across the boundary of the star. These matching of the metrices along with the condition of the vanishing radial pressure at the boundary lead us to determine the model parameters. The physical acceptability of the solutions has verified by making use of the current estimated data available from the pulsar 4U1608-52. Thereafter, assuming anisotropy due to tidal effects we calculate the Love numbers from our model and compare the results with the observed compact stars, viz. KS 1731- 260,4U 1608- 52,4U 1724- 207,4U 1820- 30,SAX J1748.9-2021 and EXO 1745-268. The overall situation confirms physical viability of the proposed approach,which can shed new light on the interior of the compact relativistic objects., Comment: Major Revision based on the referee reports; 31 pages; 11 figures

The popularity of the Finch-Skea ansatz to describe relativistic stellar model have encouraged us to study the analytic solutions of the Einstein field equation. We have presented a class of exact solutions to the field equations after considering the corresponding two cases: (i) positive value of anisotropic parameter, and (ii) absence of any anisotropy. Smooth matching of the interior solutions with the Schwarzschild exterior solution helped us to determine constants. The physical features of the solutions thus obtained have been studied both graphically and numerically with the specific pulsar $4U~1608-52$ (Mass = $1.57^{+0.30}_{-0.29}~M_\odot$ and radius = $9.8\pm 1.8~km$). The stability conditions for the model have also been discussed, however the model is found to be stable for zero anisotropy., Comment: 26 pages, 19 figures, major revision in the text

In this work we present a few simple cosmological models under the modified theory of gravity in the particular form of $f(R,\mathcal{T})=R+2f(\mathcal{T})$, where $R$ is the Ricci Scalar and $\mathcal{T}$ is the trace of the energy-momentum tensor. Two special cosmological models are studied with (i) hyperbolic scale factor and (ii) specific form of the Hubble parameter. The models are observed to predict relevant cosmological parameters closer to the observational values. Both the models reduce to overlap with the $\Lambda$CDM model at late times. We have discussed some interesting results related to wormhole solutions as evolved from our model. The possible occurrence of Big Trip in wormholes for the models are also discussed., Comment: 17 pages, 10 figures. Accepted version IJMPD

In the {\bf K-}essence Vaidya Schwarzschild spacetime, we apply the dynamical horizon equation to measure the mass-loss due to Hawking radiation and the tunneling formalism (Hamilton-Jacobi method) to calculate the hawking temperature. Assuming the Dirac-Born-Infeld kind of non-standard action for the {\bf K-}essence here, the background physical spacetime is a static spherically symmetric black hole, and we constrain the {\bf K-}essence scalar field to be a function only of either forward or backward time. The {\bf K-}essence emergent gravity and the generalizations of Vaidya spacetime have been linked by Manna et al. In this paper, we use Sawayama's modified description of the dynamical horizon to show that the obtained findings deviate from the standard Vaidya spacetime geometry., Comment: 11 pages, 6 figures, Accepted from Fortschritte der Physik (2023)

In the current article, we study anisotropic spherically symmetric strange star under the background of $f(R,T)$ gravity using the metric potentials of Tolman-Kuchowicz type~\cite{Tolman1939,Kuchowicz1968} as $\lambda(r)=\ln(1+ar^2+br^4)$ and $\nu(r)=Br^2+2\ln C$ which are free from singularity, satisfy stability criteria and also well behaved. We calculate the value of constants $a$, $b$, $B$ and $C$ using matching conditions and the observed values of the masses and radii of known samples. To describe the strange quark matter (SQM) distribution, here we have used the phenomenological MIT bag model equation of state (EOS) where the density profile ($\rho$) is related to the radial pressure ($p_r$) as $p_r(r)=\frac{1}{3}(\rho-4B_g)$. Here quark pressure is responsible for generation of bag constant $B_g$. Motivation behind this study lies in finding out a non-singular physically acceptable solution having various properties of strange stars. The model shows consistency with various energy conditions, TOV equation, Herrera's cracking condition and also with Harrison-Zel$'$dovich-Novikov's static stability criteria. Numerical values of EOS parameter and the adiabatic index also enhance the acceptability of our model., Comment: 14 pages, 11 figures

We study power law inflation (PLI) with a monomial potential and find a novel exact solution. It is well known that conventional PLI with exponential potential is inconsistent with the Planck data. Unlike the standard PLI, present model does not suffer from graceful exit problem and it agrees fairly well with recent observations. We have calculated the spectral index and the tensor-to-scalar ratio which are in very good agreement with recent observational data and also comparable with other modified inflationary models. A technique has been used which shows that the large cosmological constant reduces with expansion of the Universe in case of the power law inflation. The coupling of the inflaton with gravitation is the main point in this technique. The basic assumption here is that the two metric tensors in the gravitational and the inflaton parts correspond to different conformal frames which is in contradiction with the conventional power law inflation where the inflaton directly coupled with the background metric tensor. This fact has direct application to different dark energy models and assisted quintessence theory., Comment: 14 pages; Replacement restores version 1 of arXiv:2005.09458 which was incorrectly replaced

The motto of this work is to generate a general formalism of $f(\bar{R}, L(X))-$gravity in the context of dark energy under the framework of the {\bf K-}essence emergent geometry with the Dirac-Born-Infeld (DBI) variety of action, where $\bar{R}$ is the familiar Ricci scalar, $L(X)$ is the DBI type non-canonical Lagrangian with $X={1\over 2}g^{\mu\nu}\nabla_{\mu}\phi\nabla_{\nu}\phi$ and $\phi$ is the {\bf K-}essence scalar field. The emergent gravity metric $\bar{G}_{\mu\nu}$ and the well known gravitational metric $g_{\mu\nu}$ are not conformally equivalent. We have constructed a modified field equation using the metric formalism in $f(\bar{R}, L(X))$-gravity incorporating the corresponding Friedmann equations in the framework of the background gravitational metric which is of Friedmann-Lema{\^i}tre-Robertson-Walker (FLRW) type. The solution of modified Friedmann equations have been deduced for the specific choice of $f(\bar{R}, L(X))$, which is of Starobinsky-type, using power law expansion method. The consistency of the model with the accelerating phase of the Universe has been shown, when we restrict ourselves to consider the value of the dark energy density, as $\dot\phi^{2}=\frac{8}{9}=0.888 <1$, which indicates that the present Universe is dark energy dominated. Graphical plots for the energy density ($\rho$), pressure ($p$) and equation of state parameter ($\omega$) w.r.t. time ($t$) based on parametric values are interestingly consistent with the dark energy domination and hence accelerating features. We also put some light on the corresponding energy conditions and constraints of the $f(\bar{R}, L(X))$ theory with one basic example., Comment: 21 pages, 4 figures, 1 Table