Friedmann-Robertson-Walker Research Articles

Emergence of cosmic space and horizon entropy maximization from Tsallis and Cirto entropy

In this note by use of the idea of the emergence of cosmic space suggested by Padmanabhan (Emergence and expansion of cosmic space as due to the quest for holographic equipartition; Res Astro Astrophys 12:891, 2012), we derive the modified Friedmann equation of a Friedmann-Robertson-Walker (FRW) Universe from Tsallis and Cirto entropy in (n+1) dimension with any spatial curvature. We investigate further the consistency of the law of emergence with the maximization of horizon entropy in the context of Tsallis and Cirto horizon entropy. Our results reveal the deep connection between the law of emergence and horizon thermodynamics.

Non-flat and non-extensive thermodynamic effects of Møller tetradic theory of gravitation on cosmology

We derive non-flat cosmological models for two cases (i.e., dust and radiation) in the context of Møller’s tetradic theory (MTT) of gravitation using the tetrad that creates the non-flat Friedmann–Robertson–Walker (FRW) metric. These two models are affected by the free dimensional parameter, λ, that characterized MTT, which approaches zero in the flat case for both models. Using standard definitions of thermodynamics, we calculate the radius horizon, Hawking temperature, and entropy of our non-flat models in the framework of cosmology and show the effect of λ on open and closed universes. We then use the first law of thermodynamics to construct non-flat cosmological models via the non-extensive thermodynamic approach. The resulting models are affected by λ and the extensive parameter, δ, which quantifies the effect of non-extensive thermodynamics. When we set, λ=0 and δ=1, we return to Einstein’s general relativity models. We study the evolution of our models in the presence of collisionless non-relativistic matter and describe precise forms of the dark energy density and equation-of-state parameter constraining the non-extensive thermodynamic parameter. We show that insertion of the non-extensive thermodynamic parameter affects the non-flat FRW universe in a manner that noticeably differs from that observed under normal thermodynamics. We also show that the deceleration of the open universe behaves as dark energy in a future epoch, i.e., when the redshift approaches −1, i.e., z≈−1.

An Enhanced Lemaitre Model and Fracture Map for Cr5 Alloy Steel during High-Temperature Forming Process

To effectively control and predict crack defects in the high-temperature forming process of Cr5 alloy steel, based on the traditional Lemaitre damage model, a new high-temperature damage model of Cr5 alloy steel was proposed which considered the change of material elastic modulus with temperature, the influence of material hydrostatic pressure as well as temperature and strain rate on material damage. Because Cr5 alloy steels are usually forged at high temperatures, tensile testing is an important method to study the damage behaviour of materials. Through the high-temperature tensile test and elastic modulus measurement test of the Cr5 alloy steel, the stress–strain curves and the relationship curves of the elastic modulus value with the temperature of Cr5 alloy steel under different temperatures and strain rates were obtained. A new high-temperature damage model of Cr5 alloy steel was built by introducing the Zener–Hollomon coefficient considering the influence of temperature and strain rate. The established high-temperature damage model was embedded in Forge® finite element software through the program’s secondary development method to numerically simulate the experimental process of Cr5 alloy steel. Comparing the difference between the displacement–load curves of the numerical simulation and the actual test of the tensile process of the experimental samples, the correlation coefficient R2 is 0.987 and the difference between the experimental value and the simulated value of the tensile sample elongation at break is 1.28%. The accuracy of the high-temperature damage model of Cr5 alloy steel established in this paper was verified. Finally, the high-temperature damage map of Cr5 alloy steel was constructed to analyse the variation law of various damage parameters with the temperature and strain rate of the high-temperature damage model of Cr5 alloy steel.

Cosmological Redshift and Cosmic Time Dilation in the FLRW Metric

The paper shows that the commonly used Friedmann-Lemaitre-Robertson-Walker (FLRW) metric describing the expanding Universe must be modified to properly predict the cosmological redshift. It is proved that the change in the frequency of redshifted photons is always connected with time dilation, similarly as for the gravitational redshift. Therefore, the cosmic time runs differently at high redshifts than at present. Consequently, the cosmological time must be identified with the conformal time and the standard FLRW metric must be substituted by its conformal version. The correctness of the proposed conformal metric is convincingly confirmed by Type Ia supernovae (SNe Ia) observations. The standard FLRW metric produces essential discrepancy with the SNe Ia observations called the ‘supernova dimming’, and dark energy has to be introduced to comply theoretical predictions with data. By contrast, the conformal FLRW metric fits data well with no need to introduce any new free parameter. Hence, the discovery of the supernova dimming actually revealed a failure of the FLRW metric and introducing dark energy was just an unsuccessful attempt to cope with the problem within this false metric. Obviously, adopting the conformal FLRW metric for describing the evolution of the Universe has many fundamental cosmological consequences.

Density Perturbation and Cosmological Evolution in the Presence of Magnetic Field in f R Gravity Models

In this paper, we have investigated the density perturbations and cosmological evolution in the FLRW universe in the presence of a cosmic magnetic field, which may be assumed to mimic primordial magnetic fields. Such magnetic fields have sufficient strength to influence galaxy formation and cluster dynamics, thereby leaving an imprint on the CMB anisotropies. We have considered the FLRW universe as a representative of the isotropic cosmological model in the 1 + 3 covariant formalism for f R gravity. The propagation equations have been determined and analyzed, where we have assumed that the magnetic field is aligned uniformly along the x -direction, resulting in a diagonal shear tensor. Subsequently, the density perturbation evolution equations have been studied, and the results have been interpreted. We have also indicated how these results change in the general relativistic case and briefly mentioned the expected change in higher-order gravity theories.

Effect of peculiar velocities of inhomogeneities on the shape of gravitational potential in spatially curved universe

We investigate the effect of peculiar velocities of inhomogeneities and the spatial curvature of the universe on the shape of the gravitating potential. To this end, we consider scalar perturbations of the FLRW metric. The gravitational potential satisfies a Helmholtz-type equation which follows from the system of linearized Einstein equations. We obtain analytical solutions of this equation in the cases of open and closed universes, filled with cold dark matter in presence of the cosmological constant. We demonstrate that, first, peculiar velocities significantly affect the screening length of the gravitational interaction and, second, the form of the gravitational potential depends on the sign of the spatial curvature.

Constraints on cosmologies inside black holes

We study the construction of holographic models with closed FRW cosmologies on the worldvolume of a constant-tension brane inside a Schwarzschild-AdS black hole. In dimensions d > 2, having a smooth Euclidean solution where the brane does not self-intersect limits the brane tension to T < T*, preventing us from realising a separation of scales between the brane and bulk curvature scales. We show that adding interface branes to this model does not relax the condition on the brane tension.

Cosmic scenario of early universe in context of Euclidean wormhole in dilatonic Einstein–Gauss–Bonnet gravity

In this paper, we present some wormhole configurations using analytic and numerical solutions of the Euclidean field equations considering Einstein–Gauss–Bonnet dilaton coupled interaction in the Robertson–Walker metric. Analytic solutions invoking slow-roll type approximation for some potentials yield identical wormholes in the early era. Eventually, in later era, the universe enters to an expanding era much faster than usual inflation accompanied by oscillations with analytic continuation [Formula: see text]. The numerical solutions of wormholes in terms of the scale factor [Formula: see text] are almost identical for some standard potentials of the dilaton field, except for the evolution of potentials. The Hubble parameter and deceleration parameter obtained by curve fit of [Formula: see text] of the numerical solution of wormhole yield an inflationary era away from the throat of the wormhole using [Formula: see text]. A sharp decay of the potential is also observed.

Analysis of generalized ghost dark energy and new holographic dark energy in Chameleon Brans–Dicke theory

In this work, we discuss the stability analysis of generalized ghost dark energy (GGDE) and new holographic dark energy (NHDE) in the framework of Chameleon Brans–Dicke (CBD) gravity. The adiabatic squared sound speed [Formula: see text] plays a crucial role to analyze the stability of the models. We know that the models are stable if [Formula: see text] and unstable if [Formula: see text]. We study the interacting and noninteracting versions of GGDE and NHDE with dark matter in CBD model in a nonflat FLRW universe. We also try to show that in all cases of investigation, the models are classically stable with suitable choices of parameters. Finally, we analyze the perturbative analysis for both GGDE and NHDE models in the background of CBD gravity.

Partial reduction and cosmology at defect brane

Partial reduction is a Karch-Randall reduction for only part of the AdS region between finite tension brane and zero tension brane. This is interesting in AdS/BCFT where the AdS bulk contains a defect brane. We employ partial reduction for a AdS bulk with a brane evolving as a 2d Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalence between defect extremal surface and island formula for a large subregion fine grained entropy in boundary CFT. We then move to higher dimensions and demonstrate the existence of 4d massless graviton on AdS4 brane in partial reduction. We also propose a partial reduction for a 4d FRW cosmology at defect brane and obtain the Newton constant by computing boundary entropy.

Cosmology in f(R,Lm) gravity

In this letter, we investigate the cosmic expansion scenario of the universe in the framework of f(R,Lm) gravity theory. We consider a non-linear f(R,Lm) model, specifically, f(R,Lm)=R2+Lmn+β, where n and β are free model parameters. Then we derive the motion equations for flat FLRW universe and obtain the exact solution of corresponding field equations. Then we estimate the best fit ranges of model parameters by using updated H(z) datasets consisting of 57 points and the Pantheon datasets consisting of 1048 points. Further we investigate the physical behavior of density and the deceleration parameter. The evolution of deceleration parameter depicts a transition from deceleration to acceleration phases of the universe. Moreover, we analyze the stability of the solution of our cosmological model under the observational constraint by considering a linear perturbation. Lastly, we investigate the behavior of Om diagnostic parameter and we observe that our model shows quintessence type behavior. We conclude that our f(R,Lm) cosmological model agrees with the recent observational studies and can efficiently describe the late time cosmic acceleration.

Cosmic and growth matter analysis of deformed Hořava–Lifshitz gravity

Hořava–Lifshitz gravity is a very fascinating proposal of modified gravity for explaining the current acceleration and other cosmic issues. In continuation to this discussion, we explore the consequences of Tsallis dark energy with Hubble and particle horizons in the framework of deformed Hořava–Lifshitz gravity for flat FRW universe. The interaction between Tsallis holographic dark energy and dark matter is also taken into account to discuss the underlying scenario. It is found that fractional dark energy density ([Formula: see text]) approaches to [Formula: see text] as redshift goes to zero (present epoch) for both cases of horizons. The cosmic parameter ([Formula: see text]) shows phantom crossing behavior in both models, i.e. it evolutes the universe from quintessence phase to phantom phase by crossing the vacuum horizon. In both cases of horizons, the deceleration supports the cosmic acceleration by exhibiting the negative values. The perturbation sound speed also favors the viability of our models through positive behavior. The coincidence parameter supports the exchange of dark matter to dark energy phenomenon through positivity. We also discuss the behavior of growth rate and growth index in the growth of matter density perturbations for both horizons. These parameters mimic the [Formula: see text]CDM behavior of the universe.

A study on exact solutions of einstein’s field equations in different cosmological models

The paper deals with the exact solutions of the Einstein’s field equations in various cosmo-logical models based on Lyra’s geometry: (i) Bianchi type III cosmological model in a perfect fluid by considering the Equation of State (EoS) of the type p = αρ 2 − ρ, where α > 0 is constant (ii) Spatially flat FRW model with constant deceleration parameter q and time dependent displacement field vector β for the specific choice of particle creation function (iii) FRW model with variable β and time dependent q. The conditions for attaining an accelerated power-law expansion of the universe in the matter dominated era have also been discussed.

Cosmological sudden singularities in f(R, T) gravity

In this work, we study the possibility of finite-time future cosmological singularities appearing in f(R, T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We present the theory in both the geometrical and the dynamically equivalent scalar–tensor representation and obtain the respective equations of motion. In a background Friedmann–Lemaître–Robertson–Walker (FLRW) universe with an arbitrary curvature and for a generic C^infty function f(R, T), we prove that the conservation of the stress-energy tensor prevents the appearance of sudden singularities in the cosmological context at any order in the time-derivatives of the scale factor. However, if this assumption is dropped, the theory allows for sudden singularities to appear at the level of the third time-derivative of the scale factor a(t), which are compensated by divergences in either the first time-derivatives of the energy density rho (t) or the isotropic pressure p(t). For these cases, we introduce a cosmological model featuring a sudden singularity that is consistent with the current measurements for the cosmological parameters, namely, the Hubble constant, deceleration parameter, and age of the universe, and provide predictions for the still unmeasured jerk and snap parameters. Finally, we analyse the constraints on a particular model of the function f(R, T) that guarantees that the system evolves in a direction favorable to the energy conditions at the divergence time.

Non-extensive statistical mechanics and the thermodynamic stability of FRW universe

In this article, we investigate the thermodynamic stability of the FRW universe for two examples, Tsallis entropy and loop quantum gravity, by considering non-extensive statistical mechanics. The heat capacity, free energy and pressure of the universe are obtained. For the Tsallis entropy model, we obtained the constraint for β, namely, . The free energy of a thermal equilibrium universe must be less than zero. We suggest that the reason for the accelerated expansion of the universe is not because of Tsallis entropy. Similar results are obtained for loop quantum gravity. However, since the values of and q cannot be determined in this model, the results become more subtle than that in the Tsallis entropy model. In addition, we compare the results for the universe with those for a Schwarzschild black hole.

Tsallis holographic dark energy reconsidered

We consider the interacting Tsallis Holographic Dark Energy (THDE), with the Granda–Oliveros (GO) scale as the infrared (IR) cutoff, as dynamical vacuum. We analytically solved for the Hubble parameter, in a spatially flat FLRW universe with dark energy and matter as components, and the solution traces the evolutionary path from the prior decelerated to the late accelerated epoch. Without interaction, the model predicts a varLambda CDM like behavior with an effective cosmological constant. We used Pantheon Supernovae type Ia, observational Hubble data (OHD), cosmic microwave background (CMB), and baryon acoustic oscillation (BAO) data to constrain the free parameters of the model. The estimated values of the cosmological parameters were consistent with observational results. We analyzed the behavior of the model using the statefinder and omega ^prime _{e}-omega _{e} plane where omega _{e} and omega ^prime _{e} corresponds to the effective equation of state and its evolution, respectively. The model shows a quintessence behavior in general, and the model trajectory ends in a point that corresponds to the de Sitter phase. We performed a dynamical analysis of the model, concluding that the prior decelerated and late accelerated phases are unstable and stable equilibria, respectively. We also investigated the thermodynamical nature of the model and found that the generalized second law remains valid in the dynamical vacuum treatment of the model.

Cosmic bounce with α(e −β G − 1) + 2λ T model

We consider a model of f(G, T) gravity to study the bouncing phenomenon of our universe with FLRW metric. We take f(G, T) = α(e −β G − 1) + 2λ T and develop field equations for a particular form of Hubble parameter. The explicit forms of energy density and pressure are formulated for a perfect cosmic fluid, that gives energy conditions and well explained the bouncing. The role of deceleration parameter, jerk, and snap are explored. The graphical demonstration is also done for these terms with fixed values of model parameters. Finally, we discuss a special form of f(G, T) gravity model that ensures the bouncing universe.

Cosmological dynamics of dark energy in teleparallel gravity

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.

Non-minimally coupled transit cosmology in f(R, T) gravity

A non-minimally coupled cosmological model is studied in [Formula: see text] gravity for a particular choice of the function in the background of flat Friedmann–Robertson–Walker universe. The modified field equations are solved with the help of a varying deceleration parameter. The time evolution of the model is analyzed for both the dynamic and kinematic quantities. For testing the viability of the results, energy conditions and the statefinder diagnostic are used. It has been shown that this model, which we discussed to examine the phase transition in the expansion of the universe, is compatible with current astrophysical observations, and that the DE model dominating the early universe is Chaplygin gas, while the model dominating the late universe is quintessence.

Einstein Field Equation, Recursion Operators, Noether and Master Symmetries in Conformable Poisson Manifolds

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian–Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson–Schwarzschild and Friedmann–Lemaître–Robertson–Walker (FLRW) manifolds, and derive the related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion.