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The article examines the Islamic concept of space and time. Topics mentioned include the link of the vision of the cosmos to the existing realities of a city in time, a description of the shrines of Tabriz in Iran, the chronotopic theory of paradise, and the relation of emanationist cosmology to post-Mongol Sufi that was thought in the Iranian sphere.

In this paper, we have presented a cosmological model that represents spatially homogenous and isotropic accelerating universe from the perspective of the latest developments begun by Perlmutter and Riess in cosmology. For this, Friedmann–Robertson–Walker (FRW) space–time metric is considered and our universe is assumed to be filled with two types of fluids. One is ordinary baryonic perfect fluid and the other one is mysterious and bizarre dark energy perfect fluid with negative pressure. This creates a repulsive field that produces acceleration in the universe. We have used 581 Union 2.1 compilation data to statistically estimate present values of cosmological parameters Ωde, Ωm, Ωk and equation of state parameter ωde for our model. We have used 31 datasets of observed values of Hubble constant for various redshifts to estimate the present value of Hubble constant H0. On the basis of these we have calculated the present age of the universe, densities, and deceleration parameter. Evolution of deceleration parameter shows that our universe has gone through an accelerating phase two times. In the beginning, and at present. We have also calculated Particle horizon and the time at which acceleration began. Our results are close to latest surveys. [ABSTRACT FROM AUTHOR]

In this work, we investigate the n -dimensional charged static black hole solutions in the Einstein-æther theory. By taking the metric parameter k to be 1 , 0 , and − 1 , we obtain the spherical, planar, and hyperbolic spacetimes, respectively. Three choices of the cosmological constant, Λ > 0 , Λ = 0 and Λ < 0 , are investigated, which correspond to asymptotically de Sitter, flat and anti-de Sitter spacetimes. The obtained results show the existence of the universal horizon in higher dimensional cases which may trap any particle with arbitrarily large velocity. We analyze the horizon and the surface gravity of four- and five-dimensional black holes, and the relations between the above quantities and the electrical charge. It is shown that when the aether coefficient c 1 3 or the charge Q increases, the outer Killing horizon shrinks and approaches the universal horizon. Furthermore, the surface gravity decreases and approaches zero in the limit c 1 3 → ∞ or Q → Q e , where Q e is the extreme charge. The main features of the horizon and surface gravity are found to be similar to those in n = 3 case, but subtle differences are also observed. [ABSTRACT FROM AUTHOR]

The accelerating behavior of cosmic fluid opposes gravitational attraction at present epoch, whereas standard gravity is dominant at small scales. As a consequence, there exists a point where the effects are counterbalanced, dubbed turnaround radius, r ta . By construction, it provides a bound on maximum structure sizes of the observed universe. Once an upper bound on r ta is provided, i.e. R TA,max , one can check whether cosmological models guarantee structure formation. Here, we focus on f (R) gravity, without imposing a priori the form of f (R). We thus provide an analytic expression for the turnaround radius in the framework of f (R) models. To figure this out, we compute the turnaround radius in two distinct cases: (1) under the hypothesis of static and spherically symmetric spacetime, and (2) by using the cosmological perturbation theory. We thus find a criterion to enable large scale structures to be stable in f (R) models, circumscribing the class of f (R) theories as suitable alternative to dark energy. In particular, we get that for constant curvature, the viability condition becomes R dS f ′ (R dS ) ≤ 5. 4 8 Λ ⇒ f ′ (R dS ) ≤ 1. 3 7 , with Λ and R dS , respectively, the observed cosmological constant and the Ricci curvature. This prescription rules out models which do not pass the aforementioned R TA,max limit. [ABSTRACT FROM AUTHOR]

We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational action is discussed. On the experimental side, we recall the bounds on the scales of the geometry coming from particle physics, astrophysics and the cosmic microwave background. [ABSTRACT FROM AUTHOR]

The models of f (R , T) gravity are efficient in describing a non-minimal coupling between geometry and matter. In this paper, the extended theory of gravity describes the non-minimal coupling between matter and geometry using special cosmological model of f (R , T) = f 1 (R) + f 2 (R) f 3 (T) in Bianchi-V spacetime; whose functional relations are f 1 (R) = f 2 (R) = R and f 3 (T) = β T , where β is a constant. The Einstein's field equation has been solved by taking special choice of scale factor as a = { t m exp (λ t) } 1 n , where m , λ and n are constants. The energy and other stability conditions obtained in this paper explain the physical behavior of phase transition of universe and it also confirms the stability of the derived model. [ABSTRACT FROM AUTHOR]

We discuss again the approach to cyclic cosmology based on the 2007 Baum–Frampton model. By introducing the relationship between entanglement entropy and space–time connectivity first introduced by Van Raamsdonck (2010) we show how vanishing entropy at the turnaround, and hence at the bounce after adiabatic contraction, can be better understood in this solution to the Tolman entropy conundrum. [ABSTRACT FROM AUTHOR]

Abstract The paper deals with f (R) gravity theory in the background of inhomogeneous FLRW-type space–time model. With proper choice of the inhomogeneous metric function it is possible to have an emergent scenario for the f (R) -cosmology. Explicit form of f (R) is obtained for power law expansion. It has been shown that the present f (R) gravity model is equivalent to some particle creation mechanism in Einstein gravity. Further a complete cosmic evolution from inflation to present late time acceleration is possible with proper continuous choices of the f (R) -functions. Finally, in the perspective of thermodynamical analysis a form of f (R) has been evaluated using the unified first law. [ABSTRACT FROM AUTHOR]

Methods for obtaining exact solutions of the dynamical equations in Friedmann-Robertson-Walker spacetime for cosmological models with a scalar field and matter fields or nonzero curvature are considered on the basis of a representation of the main cosmological parameters as functions of the number of e-folds and direct substitution of the scale factor. [ABSTRACT FROM AUTHOR]

In this study, we investigate an anisotropic Bianchi type- I I I space-time in the presence of matter and holographic dark energy components within the framework of general relativity. We obtained the solution of the field equations by assuming (i) the expansion scalar ( 𝜃 ) in the model is proportional to shear scalar ( σ ) , (ii) hybrid expansion law for average scale factor (keeping an eye on the recent scenario of accelerating nature of the universe). We develop cosmological parameters like deceleration and equation of state parameters. These parameters are plotted versus redshift z for different values of power component of average scale factor l. We observe that the equation of state varies in quintessence region ( − 1 < ω Λ < − 1 / 3 ) and ultimately tends to Λ CDM model ( ω Λ = − 1 ). The deceleration parameter exhibits a smooth transition from early decelerated epoch to present accelerated era. In addition, we establish the correspondence between our holographic dark energy model and quintessence scalar field. We also express the self-interacting potential V ( φ ) and scalar field φ of quintessence model as functions of cosmic time t , which describes the accelerated expansion of the universe. [ABSTRACT FROM AUTHOR]

Recently, the role of energy conditions in f ( R ) -cosmology has been investigated. We generalize these results to BIonic systems in accelerating systems and show that the energy conditions can be changed in this system. We show that f ( R ) -gravity produces a wormhole between two universes and forms a BIonic system. On the other hand, the acceleration creates two regions in the Rindler space-time which BIon in each region acts reverse to other in another region. This means that by the expansion of universes of the BIon in one region, universes of another BIon in other regions contract. Also, in this model, by increasing the order of curvatures in f ( R ) -gravity, the energy and the entropy of system in one region increases and in other region decreases. Amount of this growth or decrease in the energy depends on the acceleration of universes. Finally, by calculating the dark energy equation of state, we observe that one universe enters to phantom phase and goes toward the big rip singularity and another goes out of phantom state. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to study ( n + 2)-dimensional collapse of perfect fluid spherically symmetric spacetime in the context of f( R, T) gravity. The matching conditions are acquired by considering a spherically symmetric non-static ( n + 2)-dimensional metric in the inner region and Schwarzschild ( n + 2)-dimensional metric in the outer region of the star. To solve the field equations for above settings in f( R, T) gravity, we choose the stress-energy tensor trace and the Ricci scalar as constants. It is observed that two physical horizons, namely, cosmological and black hole horizons appear as a consequence of this collapse. A singularity is also formed after the birth of both the horizons. It is also observed that the term f( R0, T0) slows down the collapsing process. [ABSTRACT FROM AUTHOR]

We consider a very general scenario of our universe where its geometry is characterized by the Finslerian structure on the underlying spacetime manifold, a generalization of the Riemannian geometry. Now considering a general energy-momentum tensor for matter sector, we derive the gravitational field equations in such spacetime. Further, to depict the cosmological dynamics in such spacetime proposing an interesting equation of state identified by a sole parameter which for isotropic limit is simply the barotropic equation of state ( being the barotropic index), we solve the background dynamics. The dynamics offers several possibilities depending on this sole parameter as follows: (i) only an exponential expansion, or (ii) a finite time past singularity (big bang) with late accelerating phase, or (iii) a nonsingular universe exhibiting an accelerating scenario at late time which finally predicts a big rip type singularity. We also discuss several energy conditions and the possibility of cosmic bounce. Finally, we establish the first law of thermodynamics in such spacetime. [ABSTRACT FROM AUTHOR]

One of the important quantities in cosmology and astrophysics is the 3-velocity of an object. Specifically, when the gravitational fields are strong, one should require the employment of general relativity both in its definition and measurement. Looking into the literature for GR-based definitions of 3-velocity, one usually finds different ad hoc definitions applied according to the case under consideration. Here, we introduce and analyze systematically the two principal definitions of 3-velocity assigned to a test particle following the timelike trajectories in stationary spacetimes. These definitions are based on the (threading) and (slicing) spacetime decomposition formalisms and defined relative to two different sets of observers. After showing that Synge's definition of spatial distance and 3-velocity is equivalent to those defined in the (threading) formalism, we exemplify the differences between these two definitions by calculating them for particles in circular orbits in axially symmetric stationary spacetimes. Illustrating its geometric nature, the relative linear velocity between the corresponding observers is obtained in terms of the spacetime metric components. Circular particle orbits in the Kerr spacetime, as the prototype and the most well known of stationary spacetimes, are examined with respect to these definitions to highlight their observer-dependent nature. We also examine the Kerr-NUT spacetime in which the NUT parameter, contributing to the off-diagonal terms in the metric, is mainly interpreted not as a rotation parameter but as a gravitomagnetic monopole charge. Finally, in a specific astrophysical setup which includes rotating black holes, it is shown how the local velocity of an orbiting star could be related to its spectral line shifts measured by distant observers. [ABSTRACT FROM AUTHOR]

In this paper, we search the existence of invariant solutions of Bianchi type I space-time in the context of gravity with special case . The exact solution of the Einstein's field equations are derived by using Lie point symmetry analysis method that yield two models of invariant universe for symmetries and . The model with symmetries begins with big bang singularity while the model with symmetries does not favor the big bang singularity. Under this specification, we find out at set of singular and nonsingular solution of Bianchi type I model which present several other physically valid features within the framework of gravity. [ABSTRACT FROM AUTHOR]

Three new cosmological models of the present Universe are obtained with modified theory of gravity proposed by Harko et al. [ Phys. Rev. D 84 (2011) 024020, [gr-qc]] in a general class of Bianchi space-time. In this paper, we have generalized the modified field equations with -gravity, where and denote the curvature scalar and the trace of the stress-energy-momentum tensor, respectively. To find the deterministic solutions we have considered the linearly varying deceleration parameter proposed by Akarsu and Dereli [Cosmological models with linearly varying deceleration parameter, Int. J. Theor. Phys. 51 (2011) 612]. We have made the analyses of the variation of pressure, energy density and cosmological term with cosmic time. It is observed that our derived models are unstable in early time whereas they are stable at late and future time (i.e. at present epoch). The physical and geometric properties of all three models are studied in detail. [ABSTRACT FROM AUTHOR]

The order horismos induces the Zeeman topology, which is coarser than the Fine Zeeman Topology . The causal curves in a spacetime under are piecewise null. is considered to be the most physical topology in a spacetime manifold , as the group of homeomorphisms of is isomorphic to the group of homothetic transformations of . was used in the a ambient boundary-ambient space cosmological model, in order to show that there is no possibility of formation of spacetime singularities. In this paper, we question this result, by reviewing the corresponding papers, and we propose new questions toward the improvement of this model. [ABSTRACT FROM AUTHOR]

The main goal of the present work is to analyze the cosmological scenario of the induced gravity theory developed in previous works. Such a theory consists on a Yang-Mills theory in a four-dimensional Euclidian spacetime with $${ SO}(m,n)$$ such that $$m+n=5$$ and $$m\in \{0,1,2\}$$ as its gauge group. This theory undergoes a dynamical gauge symmetry breaking via an Inönü-Wigner contraction in its infrared sector. As a consequence, the $${ SO}(m,n)$$ algebra is deformed into a Lorentz algebra with the emergency of the local Lorentz symmetries and the gauge fields being identified with a vierbein and a spin connection. As a result, gravity is described as an effective Einstein-Cartan-like theory with ultraviolet correction terms and a propagating torsion field. We show that the cosmological model associated with this effective theory has three different regimes. In particular, the high curvature regime presents a de Sitter phase which tends towards a $$\Lambda $$ CDM model. We argue that $${ SO}(m,n)$$ induced gravities are promising effective theories to describe the early phase of the universe. [ABSTRACT FROM AUTHOR]

The plane symmetric space-times with anisotropic dark energy and with constant deceleration parameter have been derived by solving the Rosen's field equations in the Bimetric theory of gravitation. We explored both models in power law as well as in exponential law. In power law, the model attains both phases accelerating as well as decelerating in the expansion with anisotropic fluid, which is in the form of dark energy, and there is no chance of real matter in this power law. In exponential law, the model is dust, isotropized in nature with constant acceleration in the expansion. Further, other geometrical and physical aspects of the models are also studied. [ABSTRACT FROM AUTHOR]

Before 1998, it was usually expected that the universe was expanding with a constant rate or the expansion was slowing down. In 1998, the surprising discovery based on type Ia supernovae, that the rate of expansion of the universe is increasing, forced the researchers to reconsider the various cosmological models proposed so far. The current study is also an effort to revisit the LRS Bianchi type-II, dark energy (DE) model by taking time-dependent deceleration parameter (DP) instead of constant DP. We have assumed the variable scale factor , which gives the variable DP as , with these considerations, the solutions of field equations are calculated. Various parameters of DE models are also calculated, and it is found that these are consistent with the recent observations. [ABSTRACT FROM AUTHOR]

Mathisson-Papapetrou-Tulczyjew-Dixon (MPTD) equations in the Lagrangian formulation correspond to the minimal interaction of spin with gravity. Due to the interaction, in the Lagrangian equations instead of the original metric emerges spin-dependent effective metric . So we need to decide, which of them the MPTD particle sees as the spacetime metric. We show that the MPTD equations, if considered with respect to the original metric (using the standard Landau-Lifshitz spacetime decomposition), have unexpected behavior: the acceleration in the direction of the velocity grows up to infinity in the ultra-relativistic limit. If considered with respect to , the theory does not have this problem. But the metric now depends on spin, so there is no unique spacetime manifold for the universe of spinning particles: each particle probes its own three-dimensional (3D) geometry. This can be improved by adding a nonminimal interaction, given the modified MPTD equations with reasonable behavior within the original metric. [ABSTRACT FROM AUTHOR]

The Raychaudhuri equation enables to examine the whole spacetime structure without specific solutions of Einstein's equations, playing a central role for the understanding of the gravitational interaction in cosmology. In General Relativity, without considering a cosmological constant, a non-positive contribution in the Raychaudhuri equation is usually interpreted as the manifestation of the attractive character of gravity. In this case, particular energy conditions-indeed the strong energy condition-must be assumed in order to guarantee the attractive character. In the context of f( R) gravity, however, even assuming the standard energy conditions one may have a positive contribution to the Raychaudhuri equation. Besides providing a simple way to explain the observed cosmic acceleration, this fact opens the possibility of a repulsive character of this kind of gravity. In order to discuss physical bounds on f( R) models, we address the attractive/non-attractive character of f( R) gravity considering the Raychaudhuri equation and assuming the strong energy condition along with recent estimates of the cosmographic parameters. [ABSTRACT FROM AUTHOR]

In this paper, we have considered spatially homogeneous and anisotropic Bianchi type-III space-time filled with matter and anisotropic modified holographic Ricci dark energy in general relativity. We have solved Einstein's field equations using the following possibilities: ( i) hybrid expansion law proposed by Akarsu et al. (JCAP, 01, 022 (2014)); ( ii) a varying deceleration parameter considered by Mishra et al. (Int. J. Theor. Phys. 52, 2546 (2013)); and ( iii) a linearly varying deceleration parameter given by Akarsu and Dereli (Int. J. Theor. Phys. 51, 612 (2012)). We have presented the cosmological models in each of the preceding cases and studied their evolutions. We have also discussed physical and kinematical properties of the models. [ABSTRACT FROM AUTHOR]

We present explicit expressions of the thermodynamic volume inside and outside the cosmological horizon of Eguchi–Hanson solitons in general odd dimensions. These quantities are calculable and well-defined regardless of whether or not the regularity condition for the soliton is imposed. For the inner case, we show that the reverse isoperimetric inequality is not satisfied for general values of the soliton parameter a , though a narrow range exists for which the inequality does hold. For the outer case, we find that the mass M o u t satisfies the maximal mass conjecture and the volume is positive. We also show that, by requiring M o u t to yield the mass of dS spacetime when the soliton parameter vanishes, the associated cosmological volume is always positive. [ABSTRACT FROM AUTHOR]

A study of cosmological solutions in the presence of Modified Chaplygin gas (MCG) with dissipative term described by Eckart, truncated and full causal theories proposed by Israel and Stewart for a flat homogeneous isotropic Friedman-Robertson walker spacetime are given here. The interesting feature of the models is that it admits present acceleration phase as well as early inflationary phase with intermediate past deceleration phase of the evolution of the universe. The models may also help to predict future evolution of the universe. Statefinder diagnostic is also performed for the Eckart, truncated and full causal theories. [ABSTRACT FROM AUTHOR]

Gödel’s remarks concerning the ideality of time are examined. In the literature, some of these remarks have been somewhat neglected while others have been heavily criticized. In this article, I propose a clear and defensible sense in which Gödel’s work bears on the question whether there is an objective lapse of time in our world. [ABSTRACT FROM AUTHOR]

We study a hypersurface homogeneous space-time in the framework of the f (R, T) theory of gravitation in the presence of a perfect fluid. Exact solutions of field equations are obtained for exponential and power law volumetric expansions. We also solve the field equations by assuming the proportionality relation between the shear scalar (σ ) and the expansion scalar (θ ). It is observed that in the exponential model, the universe approaches isotropy at large time (late universe). The investigated model is notably accelerating and expanding. The physical and geometrical properties of the investigated model are also discussed. [ABSTRACT FROM AUTHOR]

A self-gravitating Skyrmion is an analytic and globally regular solution of the Einstein-Skyrme system with nonvanishing topological charge. The spacetime is the direct product and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX and, through an analytic continuation, it can also be turned into a transversable asymptotically AdS Lorentzian wormhole. The stress-energy of this wormhole satisfies physically realistic energy conditions and the only 'exotic matter' required by it is a negative cosmological constant. [ABSTRACT FROM AUTHOR]

The paper deals with the calculation of the gravitational entropy in the context of teleparallel gravity for de Sitter space-time. In such a theory it is possible to define gravitational energy and pressure; thus we use those expressions to construct the gravitational entropy. We use the temperature as a function of the cosmological constant and write the first law of thermodynamics from which we obtain the entropy. In the limit Λ≪1 we find that the entropy is proportional to volume, for a specific temperature’s choice; we find that ΔS≥0 as well. We also identify a phase transition in de Sitter space-time by analyzing the specific heat. [ABSTRACT FROM AUTHOR]

Space is something. Space inherently contains laws of nature: universal rules (mathematics, space dimensions, types of forces, types of fields, and particle species), laws (relativity, quantum mechanics, thermodynamics, and electromagnetism) and symmetries (Lorentz, Gauge, and symmetry breaking). We have significant knowledge about these laws of nature because all our scientific theories assume their presence. Their existence is critical for developing either a unique theory of our universe or more speculative multiverse theories. Scientists generally ignore the laws of nature because they "are what they are" and because visualizing different laws of nature challenges the imagination. This article defines a conceptual model separating space (laws of nature) from the universe’s energy source (initial conditions) and expansion (big bang). By considering the ramifications of changing the laws of nature, initial condition parameters, and two variables in the big bang theory, the model demonstrates that traditional fine tuning is not the whole story when creating a universe. Supporting the model, space and "nothing" are related to the laws of nature, mathematics and multiverse possibilities. Speculation on the beginning of time completes the model. [ABSTRACT FROM AUTHOR]

We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson–Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On the other hand, we show that this family of spacetimes provides suitable models obeying the null convergence condition to explain accelerated expanding universes. [ABSTRACT FROM AUTHOR]

The class of nonstationary braneworld models generated by the coupled gravitational and scalar fields is reviewed. The model represents a brane in a spacetime with single time and one large (infinite) and several small (compact) spacelike extra dimensions. In some particular cases the model has the solutions corresponding to the bulk gravi-scalar standing waves bounded by the brane. Pure gravitational localization mechanism of matter particles on the node of standing waves, where the brane is placed, is discussed. Cosmological applications of the model is also considered. [ABSTRACT FROM AUTHOR]

A step-by-step foundation for the differential character of the Universe's rotation is presented. First, invoking the concept of spacetime foam with spin, it is reasonable to assume that the very early Universe can be described by the Dirac equation. Second, it is shown using the Ehrenfest theorem that, from a classical point of view, the early Universe can be described by the Papapetrou equations. Third, it is stressed that our Universe can perform only rotational motion. It is shown based on the spin part of the Papapetrou equations that the Universe's rotation depends appreciably on the physical properties of a specific cosmological epoch. The rotational angular velocity is calculated for three basic cosmological epochs: the matter-dominated epoch, the transition period (from domination of matter to domination of vacuum), and the vacuum-dominated epoch. [ABSTRACT FROM AUTHOR]

After an initial burst of excitement about its extraordinary implications for our concept of space and time, the theory of general relativity underwent a thirty-year period of stagnation, during which only a few specialists worked on it, achieving little progress. In the aftermath of World War II, however, general relativity gradually re-entered the mainstream of physics, attracting an increasing number of practitioners and becoming the basis for the current standard theory of gravitation and cosmology-a process Clifford Will baptized the Renaissance of General Relativity. The recent detection of gravitational radiation by the LIGO experiment can be seen as one of the most outstanding achievements in this long-lasting historical process. In the paper, we present a new multifaceted historical perspective on the causes and characteristics of the Renaissance of General Relativity, focusing in particular on the case of gravitational radiation in order to illustrate this complex and far-reaching process. [ABSTRACT FROM AUTHOR]

We consider the synchronization of the Einstein's flow with the Ricci-flow of the standard spatial slices of the Robertson-Walker space-time and show that associated perfect fluid solution has a quadratic equation of state and is either spherical and collapsing, or hyperbolic and expanding. [ABSTRACT FROM AUTHOR]

This paper addresses strong cosmic censorship for spacetimes with self-gravitating collisionless matter, evolving from surface-symmetric compact initial data. The global dynamics exhibit qualitatively different features according to the sign of the curvature k of the symmetric surfaces and the cosmological constant Λ. With a suitable formulation, the question of strong cosmic censorship is settled in the affirmative if Λ=0 or k≤0, Λ > 0. In the case Λ > 0, k=1, we give a detailed geometric characterization of possible 'boundary' components of spacetime; the remaining obstruction to showing strong cosmic censorship in this case has to do with the possible formation of extremal Schwarzschild-de Sitter-type black holes. In the special case that the initial symmetric surfaces are all expanding, strong cosmic censorship is shown in the past for all k,Λ. Finally, our results also lead to a geometric characterization of the future boundary of black hole interiors for the collapse of asymptotically flat data: in particular, in the case of small perturbations of Schwarzschild data, it is shown that these solutions do not exhibit Cauchy horizons emanating from i + with strictly positive limiting area radius.© 2016 Wiley Periodicals, Inc. [ABSTRACT FROM AUTHOR]