Showing papers on "Friedmann–Lemaître–Robertson–Walker metric published in 2018"
TL;DR: In this paper, a new holographic dark energy (HDE) model was proposed for the Friedmann-Robertson-Walker (FRW) universe in which there is no interaction between the cosmos sectors.
243 citations
TL;DR: In this paper, a generalized entropy model for holographic dark energy was proposed, where the Hubble horizon plays the role of IR cutoff, and there is no mutual interaction between the cosmos components.
172 citations
TL;DR: Using the first law of thermodynamics, the authors proposed a relation between the system entropy (S) and its IR (L) and UV (\\\\\\\\\Lambda $$ ) cutoffs.
Abstract: Using the first law of thermodynamics, we propose a relation between the system entropy (S) and its IR (L) and UV (
$$\Lambda $$
) cutoffs. In addition, applying this relation to the apparent horizon of flat FRW universe, whose entropy meets the Renyi entropy, a new holographic dark energy model is addressed. Thereinafter, the evolution of the flat FRW universe, filled by a pressureless source and the obtained dark energy candidate, is studied. In our model, there is no mutual interaction between the cosmos sectors. We find out that the obtained model is theoretically powerful to explain the current accelerated phase of the universe. This result emphasizes that the generalized entropy formalism is suitable for describing systems including the long-range interactions such as gravity.
136 citations
TL;DR: In this article, the RR model was used to model the dynamics of the quantum effective action of gravity in the infrared regime, where the nonlocal term acts as an effective dark energy with a phantom equation of state, providing accelerated expansion without a cosmological constant.
Abstract: Even if the fundamental action of gravity is local, the corresponding quantum
effective action, that includes the effect of quantum fluctuations, is a
nonlocal object. These nonlocalities are well understood in the ultraviolet
regime but much less in the infrared, where they could in principle give rise
to important cosmological effects. Here we systematize and extend previous work
of our group, in which it is assumed that a mass scale $\Lambda$ is dynamically
generated in the infrared, giving rise to nonlocal terms in the quantum
effective action of gravity. We give a detailed discussion of conceptual
aspects related to nonlocal gravity and of the cosmological consequences of
these models. The requirement of providing a viable cosmological evolution
severely restricts the form of the nonlocal terms, and selects a model (the
so-called RR model) that corresponds to a dynamical mass generation for the
conformal mode. For such a model: (1) there is a FRW background evolution,
where the nonlocal term acts as an effective dark energy with a phantom
equation of state, providing accelerated expansion without a cosmological
constant. (2) Cosmological perturbations are well behaved. (3) Implementing the
model in a Boltzmann code and comparing with observations we find that the RR
model fits the CMB, BAO, SNe, structure formation data and local $H_0$
measurements at a level statistically equivalent to $\Lambda$CDM. (4) Bayesian
parameter estimation shows that the value of $H_0$ obtained in the RR model is
higher than in $\Lambda$CDM, reducing to $2.0\sigma$ the tension with the value
from local measurements. (5) The RR model provides a prediction for the sum of
neutrino masses that falls within the limits set by oscillation and terrestrial
experiments. (6) Gravitational waves propagate at the speed of light, complying
with the limit from GW170817/GRB 170817A.
117 citations
TL;DR: In this article, the authors derived the Friedmann equation of the FRW universe with any spatial curvature and examined the time evolution of the total entropy and showed that the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon.
114 citations
TL;DR: In this article, a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology was studied and the Clausius relation was transformed to the form of Clausius relations T ˆ h S eff = − d E + W d V, where H is the horizon temperature and S eff is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the nonequilibrium.
101 citations
TL;DR: Using the first law of thermodynamics, a relation between the system entropy and its IR ($L$) and UV ($Lambda$) cutoffs was proposed in this article, and applied this relation to the apparent horizon of flat FRW universe, whose entropy met the Renyi entropy, a new holographic dark energy model was addressed.
Abstract: Using the first law of thermodynamics, we propose a relation between the system entropy ($S$) and its IR ($L$) and UV ($\Lambda$) cutoffs. In addition, applying this relation to the apparent horizon of flat FRW universe, whose entropy meets the Renyi entropy, a new holographic dark energy model is addressed. Thereinafter, the evolution of the flat FRW universe, filled by a pressureless source and the obtained dark energy candidate, is studied. In our model, there is no mutual interaction between the cosmos sectors. We find out that the obtained model is theoretically powerful to explain the current accelerated phase of the universe. This result emphasizes that the generalized entropy formalism is suitable for describing systems including the long-range interactions such as gravity.
91 citations
TL;DR: In this paper, the cosmological features of Tsallis holographic dark energy (THDE) in cyclic, DGP and RS II braneworlds were studied.
Abstract: We study some cosmological features of Tsallis holographic dark energy (THDE) in Cyclic, DGP and RS II braneworlds. In our setup, a flat FRW universe is considered filled by a pressureless source and THDE with the Hubble radius as the IR cutoff, while there is no interaction between them. Our result shows that although suitable behavior can be obtained for the system parameters such as the deceleration parameter, the models are not always stable during the cosmic evolution at the classical level.
66 citations
TL;DR: In this paper, the authors use dynamical system methods to explore the general behavior of $f(T)$ cosmology, which can describe the universe evolution in agreement with observations, starting from a Big Bang singularity, evolving into the subsequent thermal history and the matter domination, entering into a late-time accelerated expansion, and resulting to the de Sitter phase in the far future.
Abstract: We use dynamical system methods to explore the general behaviour of $f(T)$ cosmology. In contrast to the standard applications of dynamical analysis, we present a way to transform the equations into a one-dimensional autonomous system, taking advantage of the crucial property that the torsion scalar in flat FRW geometry is just a function of the Hubble function, thus the field equations include only up to first derivatives of it, and therefore in a general $f(T)$ cosmological scenario every quantity is expressed only in terms of the Hubble function. The great advantage is that for one-dimensional systems it is easy to construct the phase space portraits, and thus extract information and explore in detail the features and possible behaviours of $f(T)$ cosmology. We utilize the phase space portraits and we show that $f(T)$ cosmology can describe the universe evolution in agreement with observations, namely starting from a Big Bang singularity, evolving into the subsequent thermal history and the matter domination, entering into a late-time accelerated expansion, and resulting to the de Sitter phase in the far future. Nevertheless, $f(T)$ cosmology can present a rich class of more exotic behaviours, such as the cosmological bounce and turnaround, the phantom-divide crossing, the Big Brake and the Big Crunch, and it may exhibit various singularities, including the non-harmful ones of type II and type IV. We study the phase space of three specific viable $f(T)$ models offering a complete picture. Moreover, we present a new model of $f(T)$ gravity that can lead to a universe in agreement with observations, free of perturbative instabilities, and applying the Om(z) diagnostic test we confirm that it is in agreement with the combination of SNIa, BAO and CMB data at 1$\sigma$ confidence level.
64 citations
TL;DR: In this article, the authors show that the inclusion of cosmological perturbations translates into corrections to the estimate of astrophysical parameters derived for the merging binary systems, and that the amplitude of the corrections will be negligible for current instruments, mildly important for experiments like DECIGO, and very important for future ones such as the Big Bang Observer.
50 citations
TL;DR: In this paper, a new form of approximate L monotonicity was identified for the linear solutions that holds whenever the background Kasner solution is sufficiently close to the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution.
Abstract: We linearize the Einstein-scalar field equations, expressed relative to constant mean curvature (CMC)-transported spatial coordinates gauge, around members of the well-known family of Kasner solutions on (0,∞)×T. The Kasner solutions model a spatially uniform scalar field evolving in a (typically) spatially anisotropic spacetime that expands towards the future and that has a “Big Bang” singularity at {t = 0}. We place initial data for the linearized system along {t = 1} ≃ T and study the linear solution’s behavior in the collapsing direction t ↓ 0. Our main result is the identification of a new form of approximate L monotonicity for the linear solutions that holds whenever the background Kasner solution is sufficiently close to the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution. Using the approximate monotonicity, we derive sharp information about the asymptotic behavior of the linear solution as t ↓ 0. In particular, we show that some of its time-rescaled components converge to regular functions defined along {t = 0}. In addition, we motivate the preferred direction of the approximate monotonicity by showing that the CMCtransported spatial coordinates gauge can be realized as a limiting version of a family of parabolic gauges for the lapse variable. An approximate L monotonicity inequality also holds in the parabolic gauges, but the corresponding parabolic PDEs are locally well-posed only in the direction t ↓ 0. In a companion article, we use the linear stability results to prove a stable singularity formation result for the nonlinear equations. Specifically, we show that the FLRW solution is globally nonlinearly stable in the collapsing direction t ↓ 0 under small perturbations of its data at {t = 1}.
TL;DR: In this paper, an exact cosmological solution of Einstein's field equations (EFEs) is derived for a dynamical vacuum energy in f(R, T) gravity for Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time.
Abstract: An exact cosmological solution of Einstein’s field equations (EFEs) is derived for a dynamical vacuum energy in f(R, T) gravity for Friedmann–Lemaitre–Robertson–Walker (FLRW) space-time. A parametrization of the Hubble parameter is used to find a deterministic solution of the EFE. The cosmological dynamics of our model is discussed in detail. We have analyzed the time evolution of the physical parameters and obtained their bounds analytically. Moreover, the behavior of these parameters are shown graphically in terms of the redshift ‘z’. Our model is consistent with the formation of structure in the Universe. The role of the f(R, T) coupling constant $$\lambda $$
is discussed in the evolution of the equation of state parameter. The statefinder and Om diagnostic analysis is used to distinguish our model with other dark energy models. The maximum likelihood analysis has been reviewed to obtain the constraints on the Hubble parameter $$H_0$$
and the model parameter n by taking into account the observational Hubble data set H(z), the Union 2.1 compilation data set SNeIa, the Baryon Acoustic Oscillation data BAO, and the joint data set $$H(z) + \mathrm{SNeIa}$$
and $$H(z) + \mathrm{SNeIa} + \mathrm{BAO} $$
. It is demonstrated that the model is in good agreement with various observations.
TL;DR: In this article, a generalized Rastall theory of gravity and its cosmological consequences in the background of homogeneous and isotropic flat FLRW model with perfect fluid as the matter context are discussed.
Abstract: The paper deals with generalized Rastall theory of gravity and its cosmological consequences in the background of homogeneous and isotropic flat FLRW model with perfect fluid as the matter context. The model shows a non singular era (emergent scenario) at the early phase of expansion for a particular choice of the Rastall parameter. Also the model finds to be equivalent to the particle creation mechanism in Einstein gravity in the framework of non-equilibrium thermodynamics. Universal thermodynamics is briefly presented and it is found that the entropy function in Rastall theory is the usual Bekenstein entropy and there is no correction to it. Finally, a complete cosmic history starting from inflation to late time acceleration is presented for suitable choices of the Rastall parameter.
TL;DR: In this article, simple solutions of IKKT-type matrix models describing a quantized homogeneous and isotropic cosmology with k = − 1, finite density of microstates and a resolved Big Bang are presented.
TL;DR: In this article, a modified gravity of which the scalar field derivative couples to the Einstein tensor is considered, in which the connection field gives rise to relation, h μ ν = f gμ ν between effective metric, h ν and the usual metric g ν where f = 1 − κ ϕ, α ϕ, α ∕ 2.
TL;DR: In this paper, it was shown that the acceleration of a black hole in the vicinity of static and spherically symmetric black holes is also equivalent to the propagation of odd-parity perturbations along both radial and angular directions.
TL;DR: In this article, the effects of perturbations on the non-Gaussinity and their implication on the explanations of observed power asymmetry in CMB have also been explored.
Abstract: While loop quantum cosmology (LQC) predicts a robust quantum bounce of the background evolution of a Friedmann-Robertson-Walker (FRW) spacetime prior to the standard slow-roll inflation, whereby the big bang singularity is resolved, there are several different quantization procedures to cosmological perturbations, for instance, {\em the deformed algebra, dressed metric, and hybrid quantizations} This paper devotes to study the quantum bounce effects of primordial perturbations in the hybrid approach The main discrepancy of this approach is the effective positive mass at the quantum bounce for the evolution of the background that is dominated by the kinetic energy of the inflaton field at the bounce, while this mass is always nonpositive in the dressed metric approach It is this positivity of the effective mass that violates the adiabatic evolution of primordial perturbations at the initial moments of the quantum bounce With the assumption that the evolution of the background is dominated by the kinetic energy of the inflaton at the bounce, we find that the effective potentials for both scalar and tensor perturbations can be well approximately described by a Poschl-Teller (PT) potential, which allows us to find analytical solutions of perturbations, and from these analytical expressions we are able to study the non-adiabatic evolution of primordial perturbations in details In particular, we derive their quantum bounce effects and investigate their observational constraints In addition, the impacts of quantum bounce effects on the non-Gaussinity and their implication on the explanations of observed power asymmetry in CMB have also been explored
TL;DR: In this paper, an exact cosmological solution of EFEs is derived for a dynamical vacuum energy in $f(R,T)$ gravity for Friedmann-LemaitreRobertson-Walker (FLRW) space-time.
Abstract: An exact cosmological solution of Einstein field equations (EFEs) is derived for a dynamical vacuum energy in $f(R,T)$ gravity for Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time. A parametrization of the Hubble parameter is used to find a deterministic solution of EFE. The cosmological dynamics of our model is discussed in detail. We have analyzed the time evolution of physical parameters and obtained their bounds analytically. Moreover, the behavior of these parameters are shown graphically in terms of redshift $`z'$. Our model is consistent with the formation of structure in the Universe. The role of the $f(R,T)$ coupling constant $\lambda$ is discussed in the evolution of the equation of state parameter. The statefinder and Om diagnostic analysis is used to distinguish our model with other dark energy models. The maximum likelihood analysis has been reviewed to obtain the constraints on the Hubble parameter $H_0$ and the model parameter $n$ by taking into account the observational Hubble data set $H(z)$, the Union 2.1 compilation data set $SNeIa$, the Baryon Acoustic Oscillation data $BAO$, and the joint data set $H(z)$ + $ SNeIa$ and $H(z)$ + $SNeIa$ + $BAO $. It is demonstrated that the model is in good agreement with various observations.
TL;DR: In this paper, a new form of time crystal has been proposed, which is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections.
Abstract: A new form time crystal has been proposed, and some of its consequences have been studied. The model is a generalization of the Friedmann-Robertson-Walker (FRW) cosmology endowed with noncommutative geometry corrections. In the minisuperspace approach, the scale factor undergoes the time periodic behavior, or Sisyphus dynamics, which allows us to interpret this cosmological time crystal as a physically motivated toy model to simulate the cyclic universe. Analyzing our model purely from the time crystal perspective reveals many novelties such as a complex singularity structure (more complicated than the previously encountered swallowtail catastrophe) and a richer form of Sisyphus dynamics. In the context of cosmology, the system can serve as a toy model in which, apart from inducing a form of the cyclic universe feature, it is possible to generate an arbitrarily small positive effective cosmological constant. We stress that the model is purely geometrical without introduction of matter degrees of freedom (d.o.f.).
TL;DR: In this article, the existence of an "inflaton" described by an homogeneous scalar field in the Szekeres cosmological metric is considered and the gravitational field equations are reduced to two families of solutions which describe the homogeneous Kantowski-Sachs spacetime and an inhomogeneous FLRW(-like) spacetime with spatial curvature a constant.
Abstract: We consider the existence of an “inflaton” described by an homogeneous scalar field in the Szekeres cosmological metric. The gravitational field equations are reduced to two families of solutions which describe the homogeneous Kantowski–Sachs spacetime and an inhomogeneous FLRW(-like) spacetime with spatial curvature a constant. The main differences with the original Szekeres spacetimes containing only pressure-free matter are discussed. We investigate the stability of the two families of solution by studying the critical points of the field equations. We find that there exist stable solutions which describe accelerating spatially-flat FLRW geometries.
TL;DR: In this article, the authors investigated non-Ricci, non-compact Friedmann-Robertson-Walker type Kaluza-Klein cosmology in the presence of pressureless matter and modified holographic Ricci dark energy in the frame work of Brans and Dicke (Phys Rev 124:965, 1961) scalar-tensor theory of gravitation.
Abstract: In this paper, we investigate non-Ricci, non-compact Friedmann–Robertson–Walker type Kaluza–Klein cosmology in the presence of pressureless matter and modified holographic Ricci dark energy in the frame work of Brans and Dicke (Phys Rev 124:965, 1961) scalar–tensor theory of gravitation. We solve the field equations of this theory using a hybrid expansion law for the five dimensional scale factor. We have also used a power law and a form of logarithmic function of the scale factor for the Brans–Dicke scalar field. Consequently, we obtain two interesting cosmological models of the Kaluza–Klein universe. We have evaluated the cosmological parameters, namely, the equation of state parameter, the deceleration parameter, and the density parameters. To check the stability of our models we use the squared speed of sound. Some well-known cosmological (
$$\omega _{de}$$
–
$$\omega ^{\prime }_{de}$$
and statefinder) planes are constructed for our models. We have also analyzed the physical behavior of these parameters through graphical representation. It is observed that the FRW type Kaluza–Klein dark energy models presented are compatible with the present day cosmological observations.
TL;DR: In this paper, the authors considered a variety of time-dependent Λ(t) models focusing on their evolutions and singular behavior and found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) line element.
Abstract: Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann–Lemaitre–Robertson–Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a...
TL;DR: In this article, the authors investigated the cosmological evolution in a new modified teleparallel gravity that connects both f(T) and f(R) theories with a boundary term B, called F(T,B) gravity.
Abstract: In this paper, we investigate the cosmological evolution in a new modified teleparallel gravity that connects both f(T) and f(R) theories with a boundary term B, called f(T,B) gravity. To this purpose, we assume flat Friedmann-Robertson-Walker (FRW) geometry filled with perfect fluid matter contents. We formulate the general energy constraints for two cases in this gravity: one is for a general function of f(T,B), and the other is for a particular form of it given by - T + F(B). Further, we explore the validity of these energy bounds by specifying different forms of f(T, B) and F(B) functions obtained by the reconstruction scheme for de Sitter, power-law, $\Lambda$
CDM and phantom cosmological models. In order to constrain the free model parameters, we examine these energy bounds with the help of region graphs. We also explore the evolution of the effective equation of state (EoS) $\omega_{\rm eff}$
for both cases and compare theoretical results with the observational data. It is found that the effective EoS represents the phantom phase or the quintessence state of accelerating universe in all cases, which is consistent with observational data.
TL;DR: In this paper, the authors present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds.
Abstract: We present exact solutions to Vasiliev’s bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in space-time, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (A)dS4. We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.
TL;DR: In this article, a new phenomenological two-parameter parametrization of q(z) was proposed to constrain barotropic dark energy models by considering a spatially flat FRW universe, neglecting the radiation component, and reconstructing the effective equation of state (EoS).
Abstract: In this paper, we propose a new phenomenological two parameter parametrization of $q(z)$ to constrain barotropic dark energy models by considering a spatially flat FRW universe, neglecting the radiation component, and reconstructing the effective equation of state (EoS). This two free-parameter EoS reconstruction shows a non-monotonic behavior, pointing to a more general fitting for the scalar field models, like thawing and freezing models. We constrain the $q(z)$ free parameters using the observational data of the Hubble parameter obtained from cosmic chronometers, the joint-light-analysis type Ia Supernovae sample and a joint analysis from these data. We obtain a value of $q(z)$ today, $q_0=-0.48\substack{+0.10 -0.11}$, and a transition redshift, $z_t=0.71\substack{+0.12 -0.12}$ (when the Universe change from an decelerated phase to an accelerated one). The effective EoS reconstruction and the $\omega'$-$\omega$ plane analysis pointed out a quintom dark energy, which is consistent with a non parametric EoS reconstruction, reported by other authors, and using the latest cosmological observations.
TL;DR: In this paper, a generalization of two-field α-attractors with a positive constant α was proposed, where the scalar manifold is a non-compact geometrically finite surface with a Riemannian metric.
TL;DR: In this article, the authors studied the magnetized quark matter (QM) and strange quark mass (SQM), distributions in the presence of the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric.
Abstract: In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of $f(R,T)$
gravity in the background of Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. To get exact solutions of modified field equations we have used $f(R,T ) = R + 2 f(T)$
model given by Harko et al. with two different parametrization of geometrical parameters i.e. the parametrization of the deceleration parameter
$q $
, and the scale factor $a $
in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in $f(R,T)$
gravity and General Relativity (GR). All models in $f(R,T)$
gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Aktas and Aygun in $f(R,T)$
gravity. However, we have also discussed the physical consequences of our obtained models.
TL;DR: In this paper, the authors investigated the stability of the Rastall theory of gravity in the presence of perfect fluid and vacuum energy originating from conformally invariant fields and showed that this solution is stable.
Abstract: We investigate stability of the Einstein static solution against homogeneous scalar, vector and tensor perturbations in the context of the Rastall theory of gravity. We show that this solution in the presence of perfect fluid and vacuum energy originating from conformally invariant fields is stable. Using the fix point method and taking linear homogeneous perturbations, we find that the scale factor of the Einstein static universe for closed deformed isotropic and homogeneous FLRW universe depends on the coupling parameter $ \lambda$
between the energy-momentum tensor and the gradient of the Ricci scalar. Thus, in the present model and in the presence of vacuum energy, our universe can stay at the Einstein static state past-eternally, which means that the big bang singularity may be resolved successfully in the context of the Einstein static universe in the Rastall theory.
TL;DR: In this article, the authors studied the magnetized quark matter (QM) and strange quark mass (SQM), distributions in the presence of $ f(R,T)$ gravity in the background of Friedmann-Lema\^itre--Robertson--Walker (FLRW) metric.
Abstract: In this paper, we have studied the magnetized quark matter (QM) and strange quark matter (SQM) distributions in the presence of $ f(R,T)$ gravity in the background of Friedmann--Lema\^itre--Robertson--Walker (FLRW) metric. To get exact solutions of modified field equations we have used $f(R,T) = R + 2 f(T)$ model given by Harko et al. with two different parametrization of geometrical parameters \textit{i.e.} the parametrization of the deceleration parameter $ q $, and the scale factor $ a $ in hybrid expansion form. Also, we have obtained Einstein Static Universe (ESU) solutions for QM and SQM distributions in $f(R,T)$ gravity and General Relativity (GR). All models in $f(R,T)$ gravity and GR for FRW and ESU Universes with QM also SQM distributions, we get zero magnetic field. These results agree with the solutions of Akta{\c{s} and Ayg\"un in $f(R,T)$ gravity. However, we have also discussed the physical consequences of our obtained models.
TL;DR: In this article, a quasilocal version of holographic complexity adapted to terminal states such as spacelike singularities is introduced, which enjoys monotonicity properties after the addition of appropriate counterterms.
Abstract: We introduce a quasilocal version of holographic complexity adapted to ‘terminal states’ such as spacelike singularities. We use a modification of the action-complexity ansatz, restricted to the past domain of dependence of the terminal set, and study a number of examples whose symmetry permits explicit evaluation, to conclude that this quantity enjoys monotonicity properties after the addition of appropriate counterterms. A notion of ‘complexity density’ can be defined for singularities by a coarse-graining procedure. This definition assigns finite complexity density to black hole singularities but vanishing complexity density to either generic FRW singularities or chaotic BKL singularities. We comment on the similarities and differences with Penrose’s Weyl curvature criterion.