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The main objective of this manuscript is to investigate the bouncing cosmology in the background of f (Q) gravity, where Q defines the non-metricity. For this purpose, we use the reconstruction approach and consider a flat Friedmann–Robertson–Walker spacetime with perfect matter configuration. We examine how the first contracting phase gives the expansion by using a temporal derivative of the scale factor, i.e., a ̇ < 0 , a ̇ = 0 and a ̇ > 0 give contraction, bounce point and expansion phases, respectively. Further, we use the order reduction method to solve the modified field equations as these are very difficult due to the presence of additional non-linear expressions. It is analyzed that the original singularity of the universe diminishes for the required bounce conditions. We conclude that the acceleration occurs near the bouncing point and the considered f (Q) models are consistent with the current cosmic accelerated expansion. • Investigate the bouncing cosmology in the background of f(Q) gravity. • We use the reconstruction approach for a flat FRW spacetime with perfect matter configuration. • Examine how the first contracting phase gives the expansion through the scale factor. • The original singularity of the universe diminishes for the required bounce conditions. • The considered models of this gravity are consistent with the current cosmic accelerated expansion. [ABSTRACT FROM AUTHOR]

This paper uses the gravitational decoupling through the minimal geometric deformation approach and extends a known isotropic solution for a self-gravitating interior to two types of anisotropic spherical solutions in Rastall gravity in the presence of electromagnetic field. By deforming only the radial metric component, the field equations are decoupled into two sets, the first of which corresponds to an isotropic distribution of matter while the second set contains the anisotropic source. We obtain a solution of the first set by employing the charged isotropic Finch-Skea ansatz, whereas a solution for the second set is obtained by adopting two mimic constraints on the pressure and density. The matching conditions at the stellar surface are explored with the exterior geometry given by the deformed Reissner–Nordström spacetime. For the two fixed values of the Rastall and charge parameters, we investigate physical features of both solutions through graphical analysis of the energy conditions, equation of state parameters, surface redshift and compactness function. The stability of both solutions is also studied through the Herrera cracking approach and causality condition. We deduce that while both solutions are physically viable, only the solution corresponding to the pressure-like constraint is stable. • Gravitational decoupling approach is used to find charged exact solutions in Rastall gravity. • We obtain a solution by employing charged isotropic Finch-Skea ansatz. • Investigate physical viability of both solutions through graphical analysis of the physical quantities. • Stability of both solutions is also studied through the Herrera cracking approach and causality condition. • We deduce that both solutions are physically viable but only the first solution is stable. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of curvature properties of Hayward black hole (briefly, HBH) spacetime, which is a solution of Einstein field equations (briefly, EFE) having non-vanishing cosmological constant. We have proved that the HBH spacetime is an Einstein manifold of level 2, 2-quasi Einstein, generalized quasi-Einstein and Roter type manifold. Also, it is shown that the nature of the HBH spacetime is pseudosymmetric and it obeys several types of pseudosymmetries, such as, pseudosymmetry due to concircular, conformal and conharmonic curvature (i.e., F ⋅ F = L Q (g , F) for F = W , C , K with a smooth scalar function L), and it also possesses the relation R ⋅ R − L Q (g , C) = Q (S , R). It is engrossing to mention that the nature of energy momentum tensor of the HBH spacetime is pseudosymmetric. On the basis of curvature related properties, we have made a comparison among Reissner–Nordström spacetime, interior black hole spacetime and HBH spacetime. It is noteworthy to mention that the gravitational force of the point-like global monopole spacetime is much stronger than that of HBH spacetime. Also, it is shown that the HBH spacetime admits an almost η -Ricci soliton as well as an almost η -Ricci-Yamabe soliton. Finally, an elegant comparative study is delineated between the HBH spacetime and the point-like global monopole spacetime with respect to different kinds of symmetry, such as, motion, curvature collineation, curvature inheritance etc. • This paper aims to the study of curvature properties of Hayward black hole spacetime. • We have proved that the spacetime is an Ein(2), 2-quasi Einstein and Roter type. • Also shown that the nature of the spacetime obeys several types of pseudosymmetries. • We have compared Reissner–Nordström, interior black hole and HBH spacetime. • Also, the HBH spacetime admits an almost η -Ricci and almost η -Ricci-Yamabe solitons. [ABSTRACT FROM AUTHOR]

The Vaidya and Tikekar (1982) ansatz has so far provided numerous stellar solutions which are useful for the description of compact stars like neutron stars and quark stars. We re-examine the impacts of the spacetime curvature parameter of the Vaidya–Tikekar ansatz on the physical properties of the relativistic anisotropic star. For a spherically symmetric, static and anisotropic stellar configuration, in the Vaidya–Tikekar background spacetime, we develop new exact solutions by assuming a polytropic type equation of state p r = k ρ 1 + 1 n − β. Recent data from observed pulsars are taken as input parameters to validate the developed model. We examine the impact of the spheroidal curvature parameter of the VT spacetime on the stellar behaviour and mass–radius (M–R) relationship. It is observed that with the increase in the departure from spherical geometry, values of physical quantities, such as density and pressure, increase. • We have found a stable model of compact stars and fulfils all the regularity conditions and physical requirements. • An interesting feature of the model is that it provides a free parameter K, which makes it suitable for the description of a wide range of compact stars. [ABSTRACT FROM AUTHOR]

In the standard cosmological model the dark energy (DE) and nonrelativistic (NR) matter densities are observationally determined to be comparable at the present time, in spite of their greatly different evolution histories. This 'cosmic coincidence' enigma – also referred to as the 'why now? problem' – relies, by its very definition, on the implicit prior expectation for our 'typicality' in the cosmic (expanding) spacetime volume. Otherwise, this conundrum does not exist in the first place. It is shown here that this apparent coincidence could be explained as a non-anthropic observational selection effect: for us to be typical observers in the comoving (static) spacetime volume, the cosmic energy budget must contain a non-vanishing DE component. In addition, it is shown that irrespective of the cosmological initial conditions and assuming no 'new physics', the Universe is most likely to be observed at a time when the conformal Hubble radius, H − 1 , attains a maximum. The latter takes place at the epoch when ρ D E and ρ m , the energy densities of DE and NR matter, respectively, are comparable. Specifically, our presumed 'typicality' along the conformal timeline, coupled to a few other plausible assumptions, implies that R ≡ ρ D E / ρ m is 'sampled' from a Beta Prime probability distribution function. A priori 68% (95%) confidence range for the ratio is 0. 20 < R < 3. 46 (0. 033 < R < 17. 20), with an expectation value of R ̄ = 3. 5. These are in agreement with the observationally inferred value, R o b s = 2. 23. • Cosmic Coincidence problem admits non-anthropic solutions. • Typical observers could be uniformly distributed in comoving spacetime. • Meaningful uniform distribution requires the existence of dark energy. • The distribution is peaked in redshift space thanks to the Friedmann equation. • Peak corresponds to crossover between decelerated and accelerated expansion. [ABSTRACT FROM AUTHOR]

Gravitational weak lensing around a hairy black hole has been deeply studied in the presence of a plasma medium. The obtained results have shown that the effect of parameters a and l 0 on the deflection angle of light rays around the black hole in hairy spacetime is perceptible. With an increase of parameter a the deflection angle of photon orbits decreases, and the effect of plasma on the deflection angle is the opposite. Here, we discussed different types of plasma distributions: uniform ω e = c o n s t , Singular Isothermal Sphere medium, 1 / r and Non-Singular Isothermal gas sphere plasma. Additionally, The total magnification of the image source due to gravitational lensing has been also studied taking into account the effect of deviation parameter a and parameter l 0 related to hairy spacetime in the presence of plasma around the black hole. • Gravitational weak lensing around a hairy black hole has been deeply studied in the presence of a plasma medium. • The obtained results have shown that the effect of parameters a and I 0 on the deflection angle of light rays around the black hole in hairy spacetime is perceptible. • Here, we discussed different types of plasma distributions: uniform ω e = const , Singular Isothermal Sphere medium, 1 /r, and Non-Singular Isothermal gas sphere plasma. • The total magnification of the image source due to gravitational lensing has been also studied. [ABSTRACT FROM AUTHOR]

The current study emphasizes the impact of electric charge for static spherically symmetric stellar structures using isotropic distribution in f (R , T) theory of gravity. For this purpose, we assume the Krori–Barua metric potential, ν (r) = B r 2 + C and λ (r) = A r 2 , where A , B and C are the unknowns constants. The simplified phenomenological MIT bag equation of state, p = 1 3 (ρ − 4 B g) , and a precise form of electrical charge distribution q (r) = Q (r R) 3 = χ r 3 to be evaluated for the solution of Einstein–Maxwell field equations. To get the value of unknown parameters of the compact structures, we compare the Krori–Barua spacetime to external Bardeen geometry. Moreover, we examine the physical attributes of compact objects by presuming three viable f (R , T) models. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkov equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars. [ABSTRACT FROM AUTHOR]

• Oscillations can be generated in neutron stars through tidal interactions. • These stellar oscillations can be detected through gravitational waves. • These oscillations can be studied using simulations of evolution of perturbed stars. • The fundamental mode varies for different equations of state of the stellar matter. In this study, we perform full three dimensional numerical relativity simulations of non-rotating general relativistic stars. Extending the studies for polytropic equation of state, we investigate the accuracy and robustness of numerical scheme on measuring fundamental (f)-mode frequency for realistic equations of state (EoS). We use various EoS with varying range of stiffness and numerically evolve perturbed stellar models for several mass configurations (in the range of 1.2 − 2.0 M ⊙) for each of these EoS. Using the gravitational waveform obtained from the simulations we extract the f -modes of the stars. The obtained results are tested against the pre-existing perturbation methods and find good agreement. Validity and deviation of universal relations have been carried out and are compared with earlier results under Cowling approximation as well as perturbative approaches. We also show that even using perturbed single star simulations can provide good agreement with f -modes extracted from inspiral phase of binary neutron star simulations which are computationally more expensive. [ABSTRACT FROM AUTHOR]

The two models of wormhole in f (R , T) gravity using relationship between radial and transverse pressure is discussed in the article. To obtain the wormhole model, we used a separable functional form given by f (R , T) = f 1 (R) + f 2 (T). R is the Ricci scalar, and T is the trace of the energy momentum tensor, with f 1 (R) and f 2 (T) being arbitrary functions of R and T , respectively. We also explored the possibility of wormhole (WH) solutions by assuming that the spacetime admits conformal killing vectors. Using different values for the coupling parameter γ , we studied the viable solutions and graphically analyzed the various features of these models. It can also be noted that the energy conditions are violated for our anisotropic model and isotropic model violates null energy condition (NEC) for γ = 0,−2,−4 while holds NEC for γ = 2,4. Hence, the anisotropic WH throat is supported by exotic matter and the isotropic by exotic/non-exotic (i.e. γ = 0,−2,−4 & γ = 2,4) although not an interesting model as there is no opening throat. • Two new models of wormhole in f (R , T) gravity are obtained • Wormhole solutions are obtained by assuming conformal motion. • Using different values for the coupling parameter graphically analyzed are done. • The energy conditions are violated for our anisotropic model. • For isotropic model, energy conditions are violated for positive coupling parameter. [ABSTRACT FROM AUTHOR]

In the present paper we have investigated the strong gravitational lensing phenomena in the exponential spacetime contributed by Papapetrou (1954 [1,2,3]). The lensing coefficients and angle of deflection have been studied and compared with a Schwarzschild metric for M = 0. 6 , 0. 8 , 0. 9 , 1. As the value of parameter M increases, the angle of deflection value also increases. We have also conducted an image analysis including a graphical study of the total, radial, and tangential magnification, and explored the image positions, Einstein rings, the RCC, and TCC for some values of the parameter M. [ABSTRACT FROM AUTHOR]

• Dynamical equations of thin-shell wormholes constructed from two identical copies of the Hayward-de Sitter regular black hole through cut and paste techniques are studied. • The stability of the Hayward-de Sitter wormhole is analyzed about the static solution of linear perturbation at the wormhole throat. • The variable modified generalized Chaplygin gas equation of state is considered. • The existence of Bardeen-de Sitter parameters and the equation of state parameters seems to • enlarge the stability regions. A dynamical equation of thin shell wormholes constructed by grafting together two identical copies of the Hayward-de Sitter regular black hole through cut and paste techniques are studied. The stability analysis under the linear perturbation around the static solution at the wormhole throat with two different equations of state, such as a variable modified generalized Chaplygin gas and a polytropic gas are discussed. It is observed that the stability configuration is possible for a suitable choice of the parameters involved in both equations of state as well as the metric spacetime. [ABSTRACT FROM AUTHOR]

In this paper we have investigated Einstein (E), Bergmann–Thomson (BT) and Landau–Lifshitz (LL) energy–momentum distributions for Texture metric in Teleparallel gravitation (TG) theory. Although these energy–momentum complexes have different definitions, Einstein and Bergmann–Thomson energy distributions give the same result for the Texture metric in TG, while different result is obtained for the Landau–Lifshitz energy distribution. Also, we get different results for the Einstein, BT and LL momentum (M) distributions in TG. In 2010, Aygün (2010) investigated the energy–momentum distributions of Texture and Monopole metrics in General Relativity (GR). However, the same results were obtained for the Einstein and BT energy distributions. These results are the same as those in TG theory for Texture metric. • Texture space–time. • Teleparallel gravitation theory. • Einstein (E), Bergmann–Thomson (BT) and Landau–Lifshitz (LL) energy–momentum distributions. [ABSTRACT FROM AUTHOR]

The present manuscript throws light on the existence of an electrically charged compact stellar model and explores the behavior of complexity factor, proposed by Herrera (2018), against the selected model in the background of f (R , T) gravity (R is the Ricci scalar, while T is the trace of energy–momentum tensor). The set of f (R , T) field equations has been solved by choosing Adler Finch–Skea solution, where the presence of electromagnetic radiations have also been considered in the stellar interior. For the space–time continuity, the boundary conditions have been described by taking Reissner–Nordström solution as exterior space–time. The physical analysis has been made by choosing the radii of PSR J 1614-2230 and SAX J 1808.4-3658, which shows that the model is physically consistent in the realm of f (R , T) gravity, and we obtain more compact stellar configurations for negative values of coupling constant λ. The implications of λ on the total mass and complexity factor of the stellar model have been explored in details. The total mass has been found maximum for λ = − 0. 4 and minimum for λ = 0. 4. The complexity factor is increased for negative values of λ as compared to the other scenarios (i.e., λ ≥ 0). The comparison of anisotropy factor and complexity factor has been made, which indicates the presence of less anisotropy in pressure distribution and more inhomogeneity in energy density of the fluid configuration for negative values of λ. • We explored the behavior of complexity factor for an electrically charged compact stellar model. • Alder Finch–Skea solution is considered in the stellar interior with Reissner–Nordström solution as an exterior. • The physical analysis has been made for radii of PSR J 1614-2230 and SAX J 1808.4-3658. • We obtain more compact stellar configurations for coupling constant λ < 0. • Moreover, the comparison of anisotropy factor and complexity factor has been made. [ABSTRACT FROM AUTHOR]

In this paper an explicit cosmological model which allows cosmological singularities are discussed in Kaluza–Klein space time. The generalized power-law and asymptotic expansions of the baro-tropic fluid index ω and equivalently the deceleration parameter q , in terms of cosmic time ‘ t ’ are considered. Finally, the strength of the found singularities is discussed. [ABSTRACT FROM AUTHOR]

In this paper, the semi-analytic numerical technique for the solution of time-space fractional telegraph equation is applied. This numerical technique is based on coupling of the homotopy analysis method and sumudu transform. It shows the clear advantage with mess methods like finite difference method and also with polynomial methods similar to perturbation and Adomian decomposition methods. It is easily transform the complex fractional order derivatives in simple time domain and interpret the results in same meaning. [ABSTRACT FROM AUTHOR]

Traversable wormholes in General Relativity (GR) require exotic matter sources that violate the null energy condition (NEC), and such behavior may be avoided in modified gravity. Moreover, the concept of non-commutative geometry as a gravitational source can be leveraged both in GR and modified gravity to realize non-trivial space–time configurations. In this study, we use f (R) gravity in conjunction with non-commutative geometry to analyze spherically symmetric traversable Morris–Thorne wormhole solutions from the aspect of energy condition violation, considering both constant and variable redshift functions. First, we use well constrained metric and model parameters in a viable f (R) gravity model to demonstrate that wormholes respecting the NEC can be obtained with suitable choices of parameters. Additionally, we check the strong and dominant energy conditions to further validate our results. We then leverage non-commutative geometry in the framework of f (R) gravity to show that wormholes respecting the different energy conditions with a phantom-like source can be realized with suitable choices of model parameters. Our comprehensive analyses using well-constrained model parameters show that wormholes satisfying the NEC can be realized in the framework of non-commutative geometry with modified gravity. • Wormhole sources respect null energy condition in f(R) gravity. • Redshift function affects energy condition profile near throat. • Non-commutative background in f(R) gravity can support wormholes. • Stable wormhole solutions obtained with suitable metric functions. • Solutions require arbitrarily small amounts of exotic matter. [ABSTRACT FROM AUTHOR]

• Dynamical equation of thin-shell wormhole joining two identical copies of non-singular Bardeen-de Sitter spacetime is constructed. • The stability of the Bardeen-de Sitter wormhole is analyzed about the static solution of linear perturbation at the wormhole throat. • The variable modified generalized Chaplygin gas equation of state is considered. • The existence of Bardeen-de Sitter parameters and the equation of state parameters seems to enlarge the stability regions. A dynamical equation of thin-shell wormhole joining two identical copies of non-singular Bardeen-de Sitter black hole spacetime through the cut and paste techniques is constructed. The stability of the Bardeen-de Sitter wormhole, as the static solution of linear perturbation at the wormhole throat and a variable modified generalized Chaplygin gas equation of state, is analyzed. The existence of stability configurations depends on the particular values of different parameters involved in the equation of state as well as the space-time metric performed. The existence of Bardeen-de Sitter parameters and the equation of state parameters to enlarge the stability regions may be obtained. [ABSTRACT FROM AUTHOR]

The thermodynamic viability of some dark energy models reconstructed through the cosmological jerk parameter is investigated. Some models, already available in the literature, are picked up for the purpose. The models are broadly classified in two categories, depending on whether there is an interaction in the dark sector or not. The validity of the Generalized Second law of Thermodynamics (GSL) is used as the diagnostics. Hayward–Kodama temperature is considered in place of Hawking temperature in order to account for the dynamical nature of the spacetime. It is found that depending on the parametrization ansatz for jerk, the total entropy is increasing with time, so it is quite possible to find viable models. This holds even with an interaction in the dark sector. • Reconstruction of dark energy models miss out on the viability of the models on the count of thermodynamics. • This work takes of this aspect of models reconstructed from the jerk parameter. • The other important point is that Hayward–Kodama temperature is used as the horizon temperature. [ABSTRACT FROM AUTHOR]

• We have formulated the new physical generalized polytropic models. • We have assumed the Finch-Skea spacetime to develop the compact star models. • The proposed models fulfills all criteria for physical adequacy. • Distinct physical features of the obtained models have been examined and evaluated. • We have used the linear, quadratic and polytropic equation of state. In present article, we have formulated the new physical generalized polytropic models with anisotropic matter distribution in the absence of electromagnetic field. We have assumed the Finch-Skea spacetime to develop the models, which fulfill all the criteria for the physical adequacy. Distinct physical features of the obtained models have been examined and evaluated. Furthermore, the physical quantities are presented graphically to meet the physical conditions of viable astronomical models. These results can be reduced to the different cases of uncharged anisotropic fluid such as linear, quadratic and polytropic equations of state. [ABSTRACT FROM AUTHOR]

• The purpose of this paper is to investigate the modified f (R , Φ , X) theory of gravity, where R , Φ and X represent the Ricci scalar, scalar potential and kinetic term respectively. • We consider the spherically symmetric space-time to discuss the existence of wormhole geometry for some realistic regions. • For our current study, we consider three different kinds of fluids: anisotropic fluid, isotropic fluid and barotropic fluid. • We determine some exact solutions by taking some specific shape function and red-shift function for anisotropic fluid and examine the behavior of energy conditions. • Furthermore, we discuss the geometry of shape functions by considering some numerical solution for isotropic and barotropic fluid respectively. • It is concluded that wormhole geometry exist f (R , Φ , X) in theory of gravity under some sensible conditions. The basic aim of this paper is to investigate the existence of traversable wormhole in the background of f (R , ϕ , X) theory of gravity, where the terms used in this theory are clarified as: R is the Ricci Scalar, ϕ represents the scalar potential and X denotes the kinetic term. For this purpose, we choose the spherically symmetric space-time to discuss the existence of wormhole geometry for some realistic regions. For our current study, we consider three different kinds of fluids: anisotropic fluid, isotropic fluid and barotropic fluid. We determine some exact solutions by taking some specific shape function and red-shift function for anisotropic fluid and examine the behavior of energy conditions. Furthermore, we discuss the geometry of shape functions by considering some numerical solution for isotropic and barotropic fluid respectively. It is noticed that energy conditions especially Null energy condition and Weak energy condition are violated for anisotropic fluid as well as for isotropic and barotropic fluid. The violation of these energy conditions indicates the presence of exotic matter, which is the main candidate for the existence of wormhole. Under some sensible conditions, the analysis may gives an assurance of the existence of wormhole geometries in f (R , ϕ , X) theory of gravity. [ABSTRACT FROM AUTHOR]

• Introducing a kind of symmetry in the conservation equation. • Introducing a new type of symmetry for the sign in the Euclidean metric. • Introducing a new role for Euclidean space-time in cosmology. • Unique scenario for universe with different space-times. In this paper, we consider conservation equation in cosmology and propose four possible forms of space-times for universe resulting from dual symmetry between scale factor and energy density in the universe with constant equation of state. We start to describe these four possible types of space-times for universe and it's possible consequences. Due to the uniformity of the metric signature in Euclidean space-time, for the first time, we introduce a new symmetry for Euclidean space-time and consider it as a transition unstable state between the visible 4D universe and the invisible world with an extra dimension. Finally, we schematically represent these four possible space-times in a unique scenario for the universe. [ABSTRACT FROM AUTHOR]

Abstract: The space–time distribution of asymmetry in the area and total number of sunspot groups was considered over the time interval 1874–2009. The time behavior of the asymmetry in these indices of sunspot activity was shown to be similar on both small and large time scales. Spectral variation analysis (SVAN) was applied to study the spectral characteristics. Quasi–biennial oscillations (QBO) were revealed in the asymmetry of both indices under discussion. The SVAN diagrams for the asymmetry of the areas and numbers of sunspots in the range of QBO periods display pronounced similarity. In the activity indices per se, these effects are much weaker: the mutual correlation of the indices is lower, the QBO are less pronounced, and the similarity of the SVAN diagrams in the QBO range is absent. The effect of negative correlation between the QBO power and absolute value of the asymmetry over a long time interval was revealed: the increase in asymmetry is accompanied by a decrease in QBO amplitude regardless of which hemisphere is more active at the moment. This underlines the global nature of QBO and the relation of asymmetry to the quadrupole component of the solar large-scale magnetic field. The asymmetry is an independent fundamental characteristic of solar activity, which does not reduce to the classical characteristics of the 11-year cycle. [Copyright &y& Elsevier]

Abstract: We investigated the light propagation by means of the Robertson–McVittie solution which is considered to be the spacetime around the gravitating body embedded in the FLRW (Friedmann–Lemaître–Robertson–Walker) background metric. We concentrated on the time delay and derived the correction terms with respect to the Shapiro’s formula. To relate with the actual observation and its reduction process, we also took account of the time transformations; coordinate time to proper one, and conversely, proper time to coordinate one. We applied these results to the problem of increase of astronomical unit reported by Krasinsky and Brumberg [Krasinsky, G.A., Brumberg, V.A., 2004. Celest. Mech. Dyn. Astrn. 90, 267]. However, we found the influence of the cosmological expansion on the light propagation does not give an explanation of observed value, [m/century] in the framework of Robertson–McVittie metric. [Copyright &y& Elsevier]

• We suggest the current assignments of spacetime geometries to the Friedmann-Lemaitre-Robertson-Walker (FLRW) model are probably incorrect and suggest more useful descriptions. • This new assignment is consistent with our Universe exhibiting sparse matter density and quasi-Euclidean geometry and the calculated matter density agrees with Big Bang nucleosynthesis calculations. • Assigning a value of 1 for flat spacetime geometry to Friedmann's normalised K is useful for estimating H 0 and will help resolve the "tension" surrounding current estimates by different investigators. • We extend the FLRW model towards the Big Bang and discover a simple explanation of how matter creation developed into the currently geometrically flat Universe with sparse, homogeneous, isotropic matter and energy distributions. The description of spacetime is an fundamental problem of cosmology. We explain why the current assignments of spacetime geometries for Ω k of the Friedmann-Lemaître-Robertson-Walker (FLRW) model are probably incorrect and suggest more useful descriptions. We show that Ω k represents not only curvature but the influence of matter density on the extent of spacetime between massive objects. Recent analyses of supernovae type Ia (SNe Ia) and HII/GEHR data with the FLRW model present the best fits with a small value for Ω m and a large Ω k. These results are consistent with our Universe exhibiting sparse matter density and quasi-Euclidean geometry and the small Ω m value agrees with Big Bang nucleosynthesis calculations. We suggest the geometry of our current Universe is better described by a value for Ω k ≈ 1 rather than 0. As an example we extend the FLRW model towards the Big Bang and discover a simple explanation of how matter creation developed into the currently geometrically flat Universe with sparse, homogeneous, isotropic matter and energy distributions. Assigning Ω k ≈ 1 to describe quasi-Euclidean spacetime geometry is also useful for estimating H 0 and should help resolve the "tension" surrounding current estimates by different investigators. [ABSTRACT FROM AUTHOR]

• Anisotropic universe in presence of perfect fluid and heat conduction have investigated. • Physical behavior of the model with Wet Dark Fluid (WDF) have discussed. • Results obtained here are in good agreement with the recent observations. • The Presented model represent expanding, shearing and anisotropic universe. • Useful to study the dynamic and physical behaviors of the universe during its accelerated phase of expansion. In this paper, we have constructed Wet Dark Fluid (WDF) model in an anisotropic homogeneous space-time namely Marder's space time. We discussed two type of models as: power law expansion model and exponential expansion model. Also some physical parameters of the model are obtained and discussed. [ABSTRACT FROM AUTHOR]

• Two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry are studied. • The validity of the solutions is verified by performing several physical tests. • The solutions satisfy all the physical requirements necessary for well-behaved models. • The models represent neutron star in Vela X-1. In this paper, we present two new exact and analytic solutions of the Einstein–Maxwell field equations describing compact anisotropic charged stars satisfying the Karmarkar condition in the background of Bardeen black hole geometry. The solutions are composed of two parts: The inner region of the star is described by class I Karmarkar space-time, while exterior of the star is characterized by both the Bardeen and the Reissner–Nordstrom space-times. Physical analysis of the matter and thermodynamical variables show that the models are well-behaved. For our parametric set of values, we conclude that the Bardeen black hole metric can be used as an alternate to the exterior Reissner–Nordstrom metric. [ABSTRACT FROM AUTHOR]

• f (R , T) = R + 2 f (T) model allows stiff matter form which indicates conservation of energy-momentum tensor in theory. • Different selection of f (R , T) models changes structure of space-time and cosmic matter. f (R , T) = f 1 (R , T) + f 2 (R) f 3 (T) model indicates both quintessence and phantom scalar field for Einstein-Rosen universe. Non-static Einstein–Rosen universe with scalar field is examined via two different selection of f (R , T) models. Firstly, we analyzed Einstein–Rosen universe with scalar field in f (R , T) = R + 2 f (T) model. Then, we constructed field equations for f (R , T) = f 1 (R) + f 2 (R) f 3 (T) model, as well. For both models, exact solutions of field equations have been attained without considering any approximation or restriction. Whether scalar field corresponds to phantom and/or quintessence scalar field are investigated for each models. [ABSTRACT FROM AUTHOR]

• The isotropic model universe undergoes super-exponential expansion. • The f (R , T) model behaves as a dark energy (vacuum energy) model. • The model is free from initial singularity and predicted to approach the de-Sitter phase dominated by vacuum energy or cosmological constant in the finite time future avoiding singularity. • The scalar curvature R is decreasing with time, which is consistent with the recent studies. • The model universe is nearly or close to flat. Within the limits of the present cosmological observations in f (R , T) gravity theory, we have analyzed a spherically symmetric space-time in 5D setting. The field equations have been carefully studied considering reasonable cosmological assumptions to obtain exact solutions. We have obtained an isotropic model universe undergoing super-exponential expansion. It is predicted that the model universe behaves like a dark energy (vacuum energy) model. In the present scenario, the model evolves with a slow and uniform change of shape. It is observed that the universe is close to or nearly flat. The model is free from an initial singularity and is predicted to approach the de-Sitter phase dominated by vacuum energy or cosmological constant in the finite-time future. A comprehensive discussion on the cosmological parameters obtained in view of the recent studies is presented in detail with graphs. [ABSTRACT FROM AUTHOR]

• The compact stars Construction with Tolman-Kuchowicz Spacetime in f (R , G) Gravity is discussed. • The anisotropic source of matter has considered for this study. • By making use of field equations, many physical aspects have been discussed. • Some physical aspects are explored under the particular parametric values. In this paper, we review some anisotropic stellar spheres in the framework of modified f (R , G) gravity. For this purpose, we have capitalized the Tolman-Kuchowicz spacetime Tolman (1939) ; Kuchowicz (1968). The equations of motion have been formulated by considering anisotropic matter distribution along with metric potentials, a = B r 2 + 2 l n C and b = l n (1 + α r 2 + β r 4). To determine the new constraints, observational data of 4 U 1538 − 52 , H e r X − 1 and S A X J 1808.4 − 3658 have been pre-owned. Dynamical equations have been evaluated by making use of Starobinsky model f (R , G) = R + λ R 2 + G 2. Many physical aspects have been enlightened, such as energy density, pressure evolutions, adiabatic index, TOV equations and surface redshift. The credibility of our presented model has been confirmed by observing the evolution of some physical aspects and it is concluded that our system is free from all singularities and is physically stable. [ABSTRACT FROM AUTHOR]

• The piece of the work is achieved towards power and exponential inflation cosmologies. • The perceived cosmologies are singular and singularity observed at an initial epoch. • The Gauss-Bonnet energy density is unity while Gauss-Bonnet matter-energy density is null i.e. not observed in the model. • The equation of state parameter of both the models are affected by the value of constant n. • Gauss-Bonnet term in linear and quadratic model is just like as cosmological constant which described Λ CDM model. Present investigation devoted to the dynamical study of isotropic and homogeneous FRW space-time filled with a Holographic dark energy fluid with cosmic string in the framework of numerous form of f (G) gravity models say linear, quadratic and inverse model. We determine the aspects of the model by considering the hybrid expansion law for the average scale factor that yields power and exponential inflation cosmologies, in its special cases. As per the observation, the model is singular and singularity observed at an initial epoch. The contribution of Gauss-Bonnet term in linear and quadratic model is just like as cosmological constant hence for whole expansion it is Λ CDM model which supports and resembles with the observational fact that the usual matter is about 4% and the dark energy occupies near about 73% of the energy also the results with several high precision observational experiments, especially the Wilkinson Microwave Anisotropic Probe (WMAP) satellite experiment. [ABSTRACT FROM AUTHOR]

• We have obtained a new parametric class of well-behaved solutions in embedding class I. • We use pressure anisotropy and Karmarkar condition for developing viable models of compact stars PSR J1614-2230 and SAX J1808.4-3658. • Our solutions satisfy the following stability conditions i.e., Herrera cracking condition, causality condition, Bondi condition, Zeldovich condition and stable static criteria (Harrison-Zeldovich-Novikov criterion) for both the stars in their respective ranges of parametric class. • Our solutions satisfy all energy conditions and equilibrium condition (TOV equation) which are essential for a physically viable stellar models. The aim of this paper is to explore a new parametric class of relativistic solutions to the Einstein field equations describing a spherically symmetric, static distribution of anisotropic fluid spheres to study the behavior of some of the cold stars in the setting of Karmarkar space-time continuum. We develop models of stellar objects for a range of parameter values of n and analyze their behavior through graphical representation. For each of these models, we have found that the metric potentials are well behaved inside the stellar interior and the physical parameters such as density, radial and tangential pressures, red-shift, radial speed, radial pressure density ratio and energy conditions display a continuous decrease from the center to surface of the stars whereas the mass, anisotropy, adiabatic indexes and compactification factor show a monotonous increase which imply that the proposed solution satisfy all the physical aspects of a realistic stellar objects. The stability of the solutions are verified by examining various stability aspects, viz., Zeldovich criteria, causality condition, Bondi condition, equilibrium condition (TOV-equation) and stable static criteria in connection to their cogency. [ABSTRACT FROM AUTHOR]