Friedmann Lemaitre Robertson Walker Model Research Articles

An [formula omitted] gravity based FLRW model and observational constraints

We attempt to construct a Friedmann–Lemaitre–Robertson–Walker (FLRW) cosmological model in f(R,T) gravity which exhibits a phase transition from deceleration to acceleration at present. We take f(R,T)=R+2λT, λ being an arbitrary constant. In our model, the λ parameter develops a negative pressure in the universe whose Equation of state is parameterized. The present values of model parameters such as density, Hubble, deceleration, Equation of state, and λ are estimated statistically by using the Chi-Square test. For this, we have used three different types of observational data sets: the 46 Hubble parameter data set, the SNeIa 715 data sets of distance modulus, and the 66 Pantheon data set (the latest compilation of SNeIa 40 bined plus 26 high red shift apparent magnitude mb data set in the red shift ranges from 0.014≤z≤2.26). We have calculated the transitional red shift and time. The estimated results for the present values of various model parameters are found as per expectations and surveys. Interestingly, we get the present value of the density ρ0, ≃1.5ρc. The critical density is estimated as ρc≃1.88h0210−29gm/cm3 in the literature. The higher value of the present density is attributed to the presence of some additional energies in the universe apart from baryon energy. We have examined the behavior of the pressure in our model. It is negative and produces acceleration in the universe. Its present value is obtained as p0≃−0.7ρ0.

Spinor Field in FLRW Cosmology

Within the scope of a Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model we study the role of a nonlinear spinor field in the evolution of the universe. In doing so, we exploit the FLRW models given in both Cartesian and spherical coordinates. It is found that if the FLRW model is given in the spherical coordinates the energy-momentum tensor (EMT) of the spinor field possesses nontrivial non-diagonal components, which is not the case for Cartesian coordinates. These non-diagonal components do not depend on either the spinor field nonlinearity or the parameter k that defines the type of curvature of the FLRW model. The presence of such components imposes some restrictions on the spinor field. The problem is studied for open, flat and close geometries and the spinor field is used to simulate different types of sources including dark energies. Some qualitative numerical solutions are given.

Reconstruction of an observationally constrained f(R,T) gravity model

In this paper, an attempt is made to construct a Friedmann–Lemaitre–Robertson–Walker model in [Formula: see text] gravity with a perfect fluid that yields acceleration at late times. We take [Formula: see text] as [Formula: see text]. As in the [Formula: see text]CDM model, we take the matter to consist of two components, viz., [Formula: see text] and [Formula: see text] such that [Formula: see text]. The parameter [Formula: see text] is the matter density (baryons [Formula: see text] dark matter), and [Formula: see text] is the density associated with the Ricci scalar [Formula: see text] and the trace [Formula: see text] of the energy–momentum tensor, which we shall call dominant matter. We find that at present [Formula: see text] is dominant over [Formula: see text], and that the two are in the ratio 3:1–3:2 according to the three data sets: (i) 77 Hubble OHD data set, (ii) 580 SNIa supernova distance modulus data set and (iii) 66 pantheon SNIa data which include high red shift data in the range [Formula: see text]. We have also calculated the pressures and densities associated with the two matter densities, viz., [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], respectively. It is also found that at present, [Formula: see text] is greater than [Formula: see text]. The negative dominant matter pressure [Formula: see text] creates acceleration in the universe. Our deceleration and snap parameters show a change from negative to positive, whereas the jerk parameter is always positive. This means that the universe is at present accelerating and in the past it was decelerating. State finder diagnostics indicate that our model is at present a dark energy quintessence model. The various other physical and geometric properties of the model are also discussed.

Noncommutative quantum cosmology for the FLRW model in Unimodular Gravity

It is well known that classical Unimodular Gravity (UG) is equivalent to General Relativity, but the equivalence at the quantum level is not clear. Here we exhibit, in the UG framework, the Quantum Cosmology (QC) for a Friedmann–Lemaitre–Robertson–Walker (FLRW) universe, considering an inflationary scenario and also introducing a deformation on the commutation relations for the minisuperspace variables (NCC).

Roles of a periodic time varying deceleration parameter in particle creation with (d+2) dimensional FLRW Universe

In the present paper, we investigate the cosmic behavior of particle creation (PC) in (d+2) dimensional FLRW (Friedmann–Lemaitre–Robertson–Walker) models with time dependent gravitational constant and cosmological constant. The gravitational field equations are solved by assuming a periodically time-varying deceleration parameter (PTVDP) i.e. q=mcoskt−1 (Shen and Zhao, 2014) which produces a scale factor a(t)=a0tankt21m, where a0 shows current scale factor and k displays the PTVDP periodicity and can be regarded as a parameter of cosmic frequency, m is an enhancement element that increases the PTVDP peak. Here, we studied the periodic time-varying behavior of a few quantities, such as the deceleration parameter q, the energy density ρ, the entropy S, PC rate ψ, the cosmological constant Λ, Newton’s gravitational constant G and discuss their physical significance. We have also discussed the density parameter, proper distance, angular distance, luminosity distance, apparent magnitude, age of the Universe, and the look-back time with redshift z and have observed the role of particle formation in universe evolution in early and late times. The periodic nature of various physical parameters is also discussed which are supporting the recent observations.

Observational backreaction in discrete black holes lattice cosmological models

Applying the Sachs formalism, the optical properties encoded in the distance modulus are studied along curves exhibiting local rotational symmetry for some closed inhomogeneous cosmological models whose mass content is discretized by Schwarzschild-like sources. These models may challenge the concordance model in its use of the distance modulus data of type Ia supernovae, because they do not violate any energy condition. This result relies only on the symmetry properties considered, and not on the way in which the mass is discretized. The models with different number of sources are then compared among themselves and with a Friedmann–Lemaitre–Robertson–Walker model with the same total mass content by introducing a compactness parameter. The analysis shows that observational backreaction occurs because increasing the number of sources the features of a universe with a continuous matter distribution are not recovered. Our models are shown to exhibit a non-trivial relationship between kinematical, dynamical and observational backreactions, the kinematical one being asymptotically decreasing while the latter two are present. Furthermore, the electric part of the Weyl tensor contributes to the luminosity distance by affecting the evolution of the scale factor, while the magnetic part has an indirect role by affecting only the evolution of the former.

Exact initial data for black hole universes with a cosmological constant

We construct exact initial data for closed cosmological models filled with regularly arranged black holes in the presence of . The intrinsic geometry of the 3-dimensional space described by this data is a sum of simple closed-form expressions, while the extrinsic curvature is just proportional to . We determine the mass of each of the black holes in this space by performing a limiting procedure around the location of each of the black holes, and then compare the result to an appropriate slice through the Schwarzschild–de Sitter spacetime. The consequences of the inhomogeneity of this model for the large-scale expansion of space are then found by comparing the lengths of curves in the cosmological region to similar curves in a suitably chosen Friedmann–Lemaitre–Robertson–Walker (FLRW) solution. Finally, we locate the positions of the apparent horizons of the black holes, and determine the extremal values of their mass, for every possible regular arrangement of masses. We find that as the number of black holes is increased, the large-scale expansion of space approaches that of an FLRW model filled with dust and , and that the extremal values of the black hole masses approach that of the Schwarzschild–de Sitter solution.

Differential cosmic expansion and the Hubble flow anisotropy

The Universe on scales 10–100 h−1Mpc is dominated by a cosmic web of voids, filaments, sheets and knots of galaxy clusters. These structures participate differently in the global expansion of the Universe: from non-expanding clusters to the above average expansion rate of voids. In this paper we characterize Hubble expansion anisotropies in the COMPOSITE sample of 4534 galaxies and clusters. We concentrate on the dipole and quadrupole in the rest frame of the Local Group. These both have statistically significant amplitudes. These anisotropies, and their redshift dependence, cannot be explained solely by a boost of the Local Group in the Friedmann-Lemaitre-Robertson-Walker (FLRW) model which expands isotropically in the rest frame of the cosmic microwave background (CMB) radiation. We simulate the local expansion of the Universe with inhomogeneous Szekeres solutions, which match the standard FLRW model on ≳ 100 h−1Mpc scales but exhibit nonkinematic relativistic differential expansion on small scales. We restrict models to be consistent with observed CMB temperature anisotropies, while simultaneously fitting the redshift variation of the Hubble expansion dipole. We include features to account for both the Local Void and the “Great Attractor”. While this naturally accounts for the Hubble expansion and CMB dipoles, the simulated quadrupoles are smaller than observed. Further refinement to incorporate additional structures may improve this. This would enable a test of the hypothesis that some large angle CMB anomalies result from failing to treat the relativistic differential expansion of the background geometry; a natural feature of solutions to Einstein's equations not included in the current standard model of cosmology.

Dark side of the universe in the Stephani cosmology

We investigate the late time acceleration of the universe in the context of the Stephani model. This solution generalizes those of Friedmann–Lemaitre–Robertson–Walker (FLRW) in such a way that the spatial curvature is a function of time. We show that the inhomogeneity of the models can lead to an accelerated evolution of the universe that is analogous to that obtained with FLRW models through a cosmological constant or any exotic component for matter.

A New Vision of the Big Bang Cosmology

In this paper we show how the inhomogeneity in the matter distribution produced until the time of the last scattering surface in the light of some spatially homogeneous but anisotropic models, produced anisotropies that on large angular scales (larger than ϑ<img src=image/18402315_001.png>2^。) not differ from those considered in Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. For these anisotropic models the mark left in the cosmic microwave background radiation by fluctuations density primordial, in the form of a fractional variation of temperature of this radiation, is governed by the same expression which is used for FLRW models. More specifically, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, since the anisotropy of the global expansion is small at the time of the last scattering surface. This conclusion is in agreement with previous work on the same anisotropic models, where they undergo a process of ‘isotropization’ to the extent that the observations are unable to distinguish them from the FLRW models, if the Hubble parameters along the orthogonal directions are assumed approximately equal to the current present epoch. We considered upper bounds for the current values of the anisotropic parameters imposed by COBE observations.

Thermodynamics of viscous matter and radiation in the early universe

Assuming that the background geometry is filled with a free gas consisting of matter and radiation and that no phase transitions are occurring in the early universe, we discuss the thermodynamics of this closed system using classical approaches. We find that essential cosmological quantities, such as the Hubble parameter H, scale factor a, and curvature parameter k, can be derived from this simple model. On one hand, it obeys the laws of thermodynamics entirely. On the other hand, the results are compatible with the Friedmann–Lemaitre–Robertson–Walker model and the Einstein field equations. The inclusion of a finite bulk viscosity coefficient derives important changes in all of these cosmological quantities. The thermodynamics of the viscous universe is studied and a conservation law is found. Accordingly, our picture of the evolution of the early universe and its astrophysical consequences seems to be the subject of radical revision. We find that the parameter k, for instance, strongly depends on the thermodynamics of the background matter. The time scale, at which a negative curvature might take place, depends on the relation between the matter content and the total energy. Using quantum and statistical approaches, we assume that the size of the universe is given by the volume occupied by one particle and one photon. Different types of interactions between matter and photon are taken into account. In this quantum treatment, expressions for H and a are also introduced. Therefore, the expansion of the universe turns out to be accessible.

Improved treatment of optics in the Lindquist-Wheeler models

We consider the optical properties of Lindquist-Wheeler (LW) models of the Universe. These models consist of lattices constructed from regularly arranged discrete masses. They are akin to the Wigner-Seitz construction of solid state physics, and result in a dynamical description of the large-scale Universe in which the global expansion is given by a Friedmann-like equation. We show that if these models are constructed in a particular way then the redshifts of distant objects, as well as the dynamics of the global space-time, can be made to be in good agreement with the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker (FLRW) solutions of Einstein's equations, at the level of <3% out to z~2. Angular diameter and luminosity distances, on the other hand, differ from those found in the corresponding FLRW models, while being consistent with the 'empty beam' approximation, together with the shearing effects due to the nearest masses. This can be compared with the large deviations found from the corresponding FLRW values obtained in a previous study that considered LW models constructed in a different way. We therefore advocate the improved LW models we consider here as useful constructions that appear to faithfully reproduce both the dynamical and observational properties of space-times containing discrete masses.

There was movement that was stationary, for the four-velocity had passed around

Is the Doppler interpretation of galaxy redshifts in a Friedmann-Lemaitre-Robertson-Walker (FLRW) model valid in the context of the approach to comoving spatial sections pioneered by de Sitter, Friedmann, Lemaitre and Robertson, i.e. according to which the 3-manifold of comoving space is characterised by both its curvature and topology? Holonomy transformations for flat, spherical and hyperbolic FLRW spatial sections are proposed. By quotienting a simply-connected FLRW spatial section by an appropriate group of holonomy transformations, the Doppler interpretation in a non-expanding Minkowski space-time, obtained via four-velocity parallel transport along a photon path, is found to imply that an inertial observer is receding from herself at a speed greater than zero, implying contradictory world-lines. The contradiction in the multiply-connected case occurs for arbitrary redshifts in the flat and spherical cases, and for certain large redshifts in the hyperbolic case. The link between the Doppler interpretation of redshifts and cosmic topology can be understood physically as the link between parallel transport along a photon path and the fact that the comoving spatial geodesic corresponding to a photon's path can be a closed loop in an FLRW model of any curvature. Closed comoving spatial loops are fundamental to cosmic topology.

The angular-diameter distance maximum and its redshift as constraints on Λ≠ 0 Friedmann-Lemaître-Robertson-Walker models

The plethora of recent cosmologically relevant data has indicated that our Universe is very well fitted by a standard Friedmann-Lemaitre-Robertson-Walker (FLRW) model, with Ω M ≈ 0.27 and Ω Λ ≈ 0.73 - or, more generally, by nearly flat FLRW models with parameters close to these values. Additional independent cosmological information, particularly the maximum of the angular-diameter (observer area) distance and the redshift at which it occurs, would improve and confirm these results, once sufficient precise Type Ia supernovae data in the range 1.5 < z < 1.8 become available. We obtain characteristic FLRW-closed functional forms for C = C(z) and M 0 = M 0 (z), the angular-diameter distance and the density per source counted, respectively, when A ≠ 0, analogous to those we have for A = 0. More importantly, we verify that for flat FLRW models z max - as is already known but rarely recognized - the redshift of C max , the maximum of the angular-diameter distance, uniquely gives Ω Λ , the amount of vacuum energy in the universe, independent of H 0 , the Hubble parameter. For non-flat models, determination of both z max and C max gives both Ω Λ and Ω M , the amount of matter in the universe, as long as we know H 0 independently. Finally, determination of C max automatically gives a very simple observational criterion for whether or not the universe is flat - presuming that it is FLRW.

Cosmology without dark energy: Weyl curvature solutions

To reconcile recent observations that the cosmological expansion has a positive acceleration with the standard Friedmann–Lemaitre–Robertson–Walker models of our Universe, as yet unseen sources of energy and (or) momentum are required for an explanation. This is due to the particular nature of spacetimes that assume homogeneity and isotropy where the curvature of the spacetime is linked to the energy-momentum content of the matter and fields in the spacetime. It is shown that more general cosmological models where Weyl (or vacuum) curvature is present can produce effects that might be responsible for the observed acceleration and other phenomena.PACS Nos.: 95.30.sf, 95.36.+x, 98.80.jk

The phase-space view of f(R) gravity

We study the geometry of the phase space of spatially flat Friedmann–Lemaitre–Robertson–Walker models in f(R) gravity, for a general form of the function f(R). The equilibrium points (de Sitter spaces) and their stability are discussed, and a comparison is made with the phase space of the equivalent scalar-tensor theory. New effective Lagrangians and Hamiltonians are also presented.

The Effects of Inhomogeneities on Evaluating the Mass Parameter Ωmand the Cosmological Constant Λ

Analytic expressions for distance-redshift relations that have been corrected for the effects of inhomogeneities in the Friedmann-Lemaitre-Robertson-Walker (FLRW) mass density are given in terms of Heun functions and are used to illustrate the significance of inhomogeneities on a determination of the mass parameter Ωm and the cosmological constant Λ. The values of these parameters inferred from a given set of observations depend on the fractional amount of matter in inhomogeneities and can significantly differ from those obtained by using the standard magnitude-redshift (m-z) result for pure dust FLRW models. As an example, a determination of Ωm made by applying the homogeneous distance-redshift relation to SN 1997ap at z = 0.83 could be as much as 50% lower than its true value.

The relationship between continuum homogeneity and statistical homogeneity in cosmology

Although the standard Friedmann–Lemaitre–Robertson–Walker (FLRW) Universe models are based on the concept that the Universe is spatially homogeneous, up to the present time no definition of this concept has been proposed that could in principle be tested by observation. We propose such a definition, based on a simple spatial averaging procedure, which relates observable properties of the Universe to the continuum homogeneity idea that underlies the FLRW models. It turns out that the statistical homogeneity often used to describe the distribution of matter on a large scale does not imply spatial homogeneity according to this definition, and so cannot be simply related to a FLRW Universe model. We propose values for the homogeneity parameter ε and length scale Lc of homogeneity of the Universe.