Robertson Walker Research Articles

Cosmic dynamics of isotropic models with inhomogeneous EoS: A dynamical system perspective

We examine the homogeneous and isotropic models sourced by the fluid having an inhomogenous equation of state (EoS) using qualitative methods. The flat Friedmann–Lemaitre–Robertson–Walker (FLRW) model explains the accelerating universe expansion of the present era having past of decelerating era dominated by radiation and matter. The open FLRW model incorporates the radiation, matter and dark energy dominated era in order with the spatial curvature playing role just before the accelerated universe evolution. The dominating behaviors of radiation, matter and spatial curvature affect the evolution trajectories of the deceleration and effective EoS parameter, which are obtained by the numerical solutions of autonomous system. The model parameters affect the nature of dark energy and therefore the EoS parameter may also lie in the quintessence or phantom regions. The closed FLRW model having constant positive curvature may yield the bouncing and turnaround universe evolution with dark energy-dominated phase at late-times. The application of statefinder diagnostic in the cosmological dynamical systems highlights that the universe may approach the [Formula: see text] cold dark matter ([Formula: see text]CDM) universe as a particular case in the future.

Exiting Inflation with a Smooth Scale Factor

The expectation that the physical expansion of space occurs smoothly may be expressed mathematically as a requirement for continuity in the time derivative of the metric scale factor of the Friedmann–Robertson–Walker cosmology. We explore the consequences of imposing such a smoothness requirement, examining the forms of possible interpolating functions between the end of inflation and subsequent radiation- or matter-dominated eras, using a straightforward geometric model of the interpolating behavior. We quantify the magnitude of the cusp found in a direct transition from the end of slow-roll inflation to the subsequent era, analyze the validity of several smooth interpolator candidates, and investigate equation-of-state and thermodynamic constraints. We find an order-of-magnitude increase in the size of the universe at the end of the transition to a single-component radiation or matter era. We also evaluate the interpolating functions in terms of the standard theory of preheating and determine the effect on the number of bosons produced.

Frequency–Redshift Relation of the Cosmic Microwave Background

We point out that a modified temperature–redshift relation (T-z relation) of the cosmic microwave background (CMB) cannot be deduced by any observational method that appeals to an a priori thermalisation to the CMB temperature T of the excited states in a probe environment of independently determined redshift z. For example, this applies to quasar-light absorption by a damped Lyman-alpha system due to atomic as well as ionic fine-splitting transitions or molecular rotational bands. Similarly, the thermal Sunyaev-Zel’dovich (thSZ) effect cannot be used to extract the CMB’s T-z relation. This is because the relative line strengths between ground and excited states in the former and the CMB spectral distortion in the latter case both depend, apart from environment-specific normalisations, solely on the dimensionless spectral variable x=hνkBT. Since the literature on extractions of the CMB’s T-z relation always assumes (i) ν(z)=(1+z)ν(z=0), where ν(z=0) is the observed frequency in the heliocentric rest frame, the finding (ii) T(z)=(1+z)T(z=0) just confirms the expected blackbody nature of the interacting CMB at z>0. In contrast to the emission of isolated, directed radiation, whose frequency–redshift relation (ν-z relation) is subject to (i), a non-conventional ν-z relation ν(z)=f(z)ν(z=0) of pure, isotropic blackbody radiation, subject to adiabatically slow cosmic expansion, necessarily has to follow that of the T-z relation T(z)=f(z)T(z=0) and vice versa. In general, the function f(z) is determined by the energy conservation of the CMB fluid in a Friedmann–Lemaitre–Robertson–Walker universe. If the pure CMB is subject to an SU(2) rather than a U(1) gauge principle, then f(z)=1/41/3(1+z) for z≫1, and f(z) is non-linear for z∼1.

Lie symmetries for the cosmological field equations in brane-world gravitywith bulk scalar field

We address the group classification problem for gravitational field equations within the context of brane-world cosmology, considering the presence of a bulk scalar field. Our investigation revolves around a five-dimensional spacetime, with the four-dimensional Friedmann–Lemaître–Robertson–Walker geometry embedded within it. Additionally, we assume that the scalar field exists in this five-dimensional geometry (bulk) and possesses a nonzero mass. The resulting field equations constitute a system of nonlinear partial differential equations. We apply the Lie symmetry condition to identify all functional forms of the scalar field potential, ensuring that the field equations remain invariant under one-parameter point transformations. Consequently, we find that only the exponential potential exhibits Lie symmetries. Finally, the Lie invariants are used to construct similarity transformations, which enable us to derive exact solutions for the system.

Timelike geodesic congruence in the simplest solutions of general relativity with quantum-improved metric tensor

A recent quantum-geometrical approach for the possible reconciliation of the principles of general relativity and quantum mechanics extends the fundamental tensor to the relativistic (quantum) scales, in which additional geometric structures and curvatures, i.e., additional sources of gravitation, are emerged. This paper introduces some characteristics of the emerged curvatures and their consequences on regulating the space and initial singularities. We analyze the timelike geodesic congruence in the simplest solutions of the Einstein field equations; the homogeneous, isotropic, and spherically symmetric Schwarzschild, de Sitter–Schwarzschild, and Friedmann–Lemaitre–Robertson–Walker (FLRW) metrics. From the expansion of the trajectory congruence that follows the change in the shape of the volume which keeps the same set of geodesics in the bundle along the flow lines which are generated by the velocity fields, we conclude that the analytical and numerical analyses give an unambiguous signature that the space and initial singularities are attenuated or even regulated, especially in the relativistic (quantum) regime. This means that the regulation of the singularity in Einstein’s general relativity (GR) would not be possible until quantum-mechanical ingredients are properly imposed on it.

Galaxy rotation curve in hyperconical universes: a natural relativistic MOND

Abstract Modified Newtonian dynamics (MOND) and similar proposals can (at least partially) explain the excess rotation of galaxies or the equivalent mass-discrepancy acceleration, without (or by reducing) the requirement of dark matter halos. This paper develops a modified gravity model to obtain local limit to the general relativity (GR) compatible with a cosmological metric different to the standard Friedmann–Lemaître–Robertson–Walker metric. Specifically, the paper uses a distorted stereographic projection of hyperconical universes, which are 4D hypersurfaces embedded into 5D Minkowski spacetime. This embedding is a key in the MOND effects found in galactic scales. To adequately describe the mass-discrepancy acceleration relation, centrifugal force would present a small time-like contribution at large-scale dynamics due to curvature of the Universe. Therefore, the Lagrangian density is very similar to the GR but with subtracting the background curvature (or vacuum energy density) of the perturbed hyperconical metric. Results showed that the proposed model adjusts well to 123 galaxy rotation curves obtained from the Spitzer Photometry and Accurate Rotation Curves database, using only a free parameter.

Teleparallel Robertson-Walker Geometries and Applications

In teleparallel geometries, the coframe and corresponding spin connection are the principal geometric objects and, consequently, the appropriate definition of a symmetry is that of an affine symmetry. The set of invariant coframes and their corresponding spin connections that respect the full six dimensional Lie algebra of Robertson–Walker affine symmetries are displayed and discussed. We will refer to such geometries as teleparallel Robertson–Walker (TRW) geometries, where the corresponding derived metric is of Robertson–Walker form and is characterized by the parameter k=(−1,0,1). The field equations are explicitly presented for the F(T) class of teleparallel TRW spacetimes. We are primarily interested in investigating the k≠0 TRW models. After first studying the k=0 models and, in particular, writing their governing field equations in an appropriate form, we then study their late time stability with respect to perturbations in k in both the cases of a vanishing and non-vanishing effective cosmological constant term. As an illustration, we consider both quadratic F(T) theories and power-law solutions.

Characterizations of GRW spacetimes admitting Ricci–Yamabe solitons

In this paper, we investigate Ricci–Yamabe solitons (RYSs) and gradient Ricci–Yamabe solitons (gradient RYSs) in generalized Robertson–Walker (GRW) spacetimes. At first, we prove that if a GRW spacetime admits a RYS, then it becomes a perfect fluid spacetime (PFS) and the divergence of the Weyl tensor vanishes. Also, a GRW spacetime admitting a RYS is of Petrov type [Formula: see text], [Formula: see text] or [Formula: see text] and in case of four dimension, the spacetime turns into a Robertson–Walker spacetime. Next, we show that if a GRW spacetime of constant scalar curvature admits a gradient RYS, then it becomes a PFS and the divergence of the Weyl tensor vanishes.

On the geometry and dynamics of relativistic particles in generalized Robertson–Walker spacetimes

In this work, we consider geometrical models describing spinning particles in the context of generalized Robertson–Walker spacetimes. We study spacelike and timelike trajectories for massive and massless particles governed by two different Lagrangians: one depending on the torsion and the other on the curvature of the trajectory. For both, we are able to relate the curvature and torsion of such trajectories with the curvature of the spatial fiber of the cosmological model. Moreover, several conserved quantities are described as well as their possible relations with physical parameters of the particle.

Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology

Kaniadakis entropy is a one-parameter deformation of the classical Boltzmann–Gibbs–Shannon entropy, arising from a self-consistent relativistic statistical theory. Assuming a Kaniadakis-type generalization of the entropy associated with the apparent horizon of Friedmann–Robertson–Walker (FRW) Universe and using the gravity-thermodynamics conjecture, a new cosmological scenario is obtained based on the modified Friedmann equations. By employing such modified equations, we analyze the slow-roll inflation, driven by a scalar field with power-law potential, at the early stages of the Universe. We explore the phenomenological consistency of this model by computation of the scalar spectral index and tensor-to-scalar ratio. Comparison with the latest BICEP and Planck data allows us to constrain Kaniadakis parameter to κ≲O(10-12÷10-11)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa \\lesssim \\mathcal {O}(10^{-12}\\div 10^{-11})$$\\end{document}, which is discussed in relation to other observational bounds in the literature. We also disclose the effects of Kaniadakis correction term on the growth of perturbations at the early stages of the Universe by employing the spherically symmetric collapse formalism in the linear regime of density perturbations. We find out that the profile of density contrast is non-trivially affected in this scenario. Interestingly enough, we observe that increasing Kaniadakis parameter κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa $$\\end{document} corresponds to a faster growth of perturbations in a Universe governed by the corrected Friedmann equations. Finally, we comment on the consistency of the primordial power spectrum for scalar perturbations with the best data-fit provided by Planck.

Nonzero spatial curvature in symmetric teleparallel cosmology

We consider the symmetric teleparallel fQ-gravity in Friedmann–Lemaître–Robertson–Walker cosmology with nonzero spatial curvature. For a nonlinear fQ model there exist always the limit of General Relativity with or without the cosmological constant term. The de Sitter solution is always provided by the theory and for the specific models fAQ≃Qαα−1,fBQ≃Q+f1Qαα−1 and fCQ≃Q+f1QlnQ it was found to be the unique attractor. Consequently small deviations from STGR can solve the flatness problem and lead to a de Sitter expansion without introduce a cosmological constant term. This result is different from that given by the power-law theories for the other two scalar of the trinity of General Relativity. What makes the nonlinear symmetric teleparallel theory to stand out are the new degree of freedom provided by the connection defined in the non-coincidence frame which describes the nonzero spatial curvature.

New insights from GW170817 in the dynamical system analysis of Einstein Gauss–Bonnet gravity

In this work, we explore the dynamical system phase space of Einstein–Gauss–Bonnet theory in the cosmological minisuperspace in the light of GW170817. This approach binds the main features of the theory through a system of autonomous differential equations, in the context of a flat Friedmann–Lemaître–Robertson–Walker spacetime. We analyze the critical points that feature in this system to assess their stability criteria. The phase space of this form of scalar-tensor gravity is very rich due to the fourth-order contributions of the Gauss–Bonnet invariant together with the second order contribution of the scalar field together with their coupling dynamics. We find additional critical points as compared with previous works in the literature which may be important for understanding the larger evolution of standard background cosmology within this class of gravitational models.

Holographic description of the dissipative unified dark fluid model with axion field

In this paper, we extend an axion [Formula: see text] gravity model, and apply the holographic principle to describe in a unifying manner the early and the late-time universe when the general equation-of-state (EoS) contains a bulk viscosity. We assume a spatially flat Friedmann–Robertson–Walker (FRW) universe model. We use a description based on the generalized infrared-cutoff holographic dark energy proposed by Nojiri and Odintsov [Eur. Phys. J. C 77 (2017) 528; Gen. Relativ. Gravit. 38 (2006) 1285], and explore the evolution of the universe when the EoS describes the asymptotic behavior between the dust in the early universe and the late universe. We explore various forms of the bulk viscosity, and calculate analytical expressions for the infrared cutoffs in terms of the particle horizon. In this way, we obtain a unifying description of the early and the late-time universe in the presence of axion matter, via a viscous holographic fluid model.

Kaniadakis entropy-based characterization of IceCube PeV neutrino signals

Kaniadakis κ-thermostatistics is by now recognized as an effective paradigm to describe relativistic complex systems obeying power-law tailed distributions, as opposed to the classical (exponential-type) decay. It is founded on a non-extensive one-parameter generalization of the Bekenstein-Hawking entropy, which, in the cosmological framework, gives rise to modified Friedmann equations on the basis of the gravity-thermodynamic conjecture. Assuming the entropy associated with the apparent horizon of the Friedmann–Robertson–Walker (FRW) Universe follows Kaniadakis prescription, in this work we analyze the observed discrepancy between the present bound on the Dark Matter relic abundance and the IceCube high-energy (∼1PeV) neutrinos. We show that this tension can be alleviated in the minimal model of Dark Matter decay with Kaniadakis-governed Universe evolution, while still considering the 4-dimensional Yukawa coupling between Standard Model and Dark Matter particles. This argument phenomenologically supports the need for a Kaniadakis-like generalization of the Boltzmann–Gibbs–Shannon entropy in the relativistic realm, opening new potential scenarios in high-energy astroparticle physics.

Thermodynamics of FLRW apparent horizon in the presence of UV/IR mixing

Generalized uncertainty principle (GUP) and Extended uncertainty principle (EUP) are well-known phenomenological gates to the issue of the so-called Gravitational Quantum Mechanics. Two fundamental impacts of the GUP and EUP are the concepts of minimal measurable length and minimal measurable momentum. The minimal measurable length as the possible smallest uncertainty in position measurement can remove the spacetime singularities arising from the general theory of relativity in UV regime. On the other hand, the minimal measurable momentum as the possible smallest uncertainty in momentum measurement puts an IR cutoff on the late-time (low energy) dynamics of the universe. This minimal momentum essentially arises due to the curvature of the background spacetime manifold. A combination of GUP and EUP gives a UV–IR complete uncertainty principle which is called usually as EGUP in literature. Motivated by these facts, we aim to study the impact of the EGUP with minimal measurable length and minimal measurable momentum on Friedmann equations. We first find the EGUP-modified entropy expression in Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Then, we obtain the EGUP-corrected Friedmann equations by employing the unified first law of thermodynamics. We explore the deceleration parameter in the EGUP setup. We then check whether the generalized second law of thermodynamics is fulfilled and then study some related issues. As a result, we find some constraints on the EGUP parameters.

A tilt instability in the cosmological principle

We show that the Friedmann–Lemaître–Robertson–Walker (FLRW) framework has an instability towards the growth of fluid flow anisotropies, even if the Universe is accelerating. This flow (tilt) instability in the matter sector is invisible to Cosmic No-Hair Theorem-like arguments, which typically only flag shear anisotropies in the metric. We illustrate our claims in the setting of “dipole cosmology”, the maximally Copernican generalization of FLRW that can accommodate a flow. Simple models are sufficient to show that the cosmic flow need not track the shear, even in the presence of a positive cosmological constant. We also emphasize that the growth of the tilt hair is fairly generic if the effective equation of state w rightarrow -1 at late times (as it does in standard cosmology), irrespective of the precise model of dark energy. The generality of our theoretical result puts various recent observational claims about late time anisotropies and cosmic dipoles in a new light.

Transit f(Q,T) Gravity Model: Observational Constraints with Specific Hubble Parameter

The present analysis deals with the study of the f(Q,T) theory of gravity, which was recently considered by many cosmologists. In this theory of gravity, the action is taken as an arbitrary function f(Q,T), where Q is non-metricity and T is the trace of the energy–momentum tensor for matter fluid. In this study, we took two different forms of the function f(Q,T) as f(Q,T)=a1Q+a2T and f(Q,T)=a3Q2+a4T, and discussed the physical properties of the models. Also, we obtained the various cosmological parameters for the Friedmann–Lemaître–Robertson–Walker (FLRW) universe by defining the transit form of a scale factor that yielded the Hubble parameter in redshift form, as H(z)=H0(λ+1)λ+(1+z)δ. We obtained the best-fit values of model parameters using the least squares method for observational constraints on available datasets, like Hubble H(z), Supernova SNe-Ia, etc., by applying the root mean squared error formula (RMSE). For the obtained approximate best-fit values of model parameters, we observed that the deceleration parameter q(z) shows a signature-flipping (transition) point within the range of 0.623≤z0≤1.668. Thus, it shows the decelerated expansion transiting into the accelerated universe expansion with ω→−1 as z→−1 in the extreme future.

Jerk Parameter and Modified Theory

The accelerated expansion of the universe during recent times is well known in cosmology, whereas during early times, there was decelerated expansion. The ΛCDM model is consistent with most observations, but there are some issues with it. In addition, the transition from early deceleration to late-time acceleration cannot be explained by general relativity. Hence, it is worthwhile to examine modified gravity theories to explain this transition and to get a better understanding of dark energy. In this work, dark energy in modified f(R,T) gravity is investigated, where R is the Ricci scalar and T is the trace of the energy momentum tensor. Normally, the simplest form of f(R,T) is used, viz., f(R)=R+λT. In this work, the more complicated form f(R,T)=R+RT is investigated in Friedmann–Lemaître–Robertson–Walker spacetime. This form has not been well studied. Since the jerk parameter in general relativity is constant and j=1, in order to have as small a departure from general relativity as possible, the jerk parameter j=1 is also assumed here. This enables the complete solution for the scale factor to be found. One of these forms is used for a complete analysis and is compared with the usually studied form f(R,T)=R+RT. The solution can also be broken down into a power-law form at early times (deceleration) and an exponential form at late times (acceleration), which makes the analysis simpler. Surprisingly, each of these forms is also a solution to the differential equation j=1 (though they are not solutions to the general solution). The energy conditions are also studied, and plots are provided. It is shown that viable models can be obtained without the need for the introduction of a cosmological constant, which reduces to the ΛCDM at late times.

Phase transitions and critical phenomena for the FRW universe in an effective scalar-tensor theory

We find phase transitions and critical phenomena in cosmic thermodynamics. We derive the thermodynamic pressure (generalized force) P of the FRW (Friedmann–Robertson–Walker) universe in an effective higher order scalar-tensor theory with the work density W of a perfect fluid, which is a natural definition directly read out from the first law of thermodynamics. By this identification, we further construct an equation of state P=P(V,T) for the FRW universe and make a thorough discussion of its P−V phase transitions and critical phenomena. Impressively, we find that the coexistence phases of the phase transitions appear above the critical temperature, which is different from that of van der Waals system and most of black holes system. In the end, we calculate the critical exponents near the criticality of FRW universe and show that they are universal and are independent of the details of the physical system although the thermodynamic quantities depend on the coupling parameters.

A resolution of the monopole problem in the Rh = ct Universe

Spontaneous symmetry breaking in grand unified theories is thought to have produced an exceedingly large number of magnetic monopoles in the early Universe. In the absence of suppression or annihilation, these very massive particles should be dominating the cosmic energy budget today, but none has ever been found. Inflation was invented in part to dilute their number, thereby rendering their density undetectable by current instruments. Should the inflationary paradigm not survive, however, the ensuing disagreement between theory and observation would constitute a cosmological ‘monopole problem’ and create further tension for any extension to the standard model of particle physics. But as is also true for all horizon problems, a monopole overabundance emerges only in cosmologies with an initial period of deceleration. We show that the alternative Friedmann–Lemaître–Robertson–Walker cosmology known as the Rh=ct universe completely eliminates all such anomalies rather trivially and naturally, without the need for an inflated expansion. We find that the monopole energy density today would be completely undetectable in Rh=ct. Evidence continues to grow that the zero active mass condition from general relativity ought to be an essential ingredient in ΛCDM.