Standard FLRW Research Articles

Induced cosmological anisotropies and CMB anomalies by a non-abelian gauge-gravity interaction

We present a non-abelian cousin of the model presented in Lee et al. (2024) which induces cosmological anisotropies on top of standard FLRW geometry. This is in some sense doing a cosmological mean field approximation, where the mean field cosmological model under consideration would be the standard FLRW, and the induced anisotropies are small perturbative corrections on top of it. Here we mostly focus on the non-abelian SU(2) gauge fields coupled to the gravity to generate the anisotropies, which can be a viable model for the axion-like particle (ALP) dark sector. The induced anisotropies are consequences of the non-trivial back-reaction of the gauge fields on the gravity sector, and by a clever choice of the parametrization, one can generate the Bianchi model we have studied in this note. We also show that the anisotropies influence the Sachs–Wolfe effect and we discuss the implications.

Cosmological implications of the Weyl geometric gravity theory

We consider the cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy–momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann–Lemaitre–Robertson–Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. Therefore, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

Dynamical Analysis of the Redshift Drift in FLRW Universes

Redshift drift is the phenomenon whereby the observed redshift between an emitter and observer comoving with the Hubble flow in an expanding FLRW universe will slowly evolve—on a timescale comparable to the Hubble time. In a previous article, three of the current authors performed a cosmographic analysis of the redshift drift in an FLRW universe, temporarily putting aside the issue of dynamics (the Friedmann equations). In the current article, we add dynamics while still remaining within the framework of an exact FLRW universe. We developed a suitable generic matter model and applied it to both standard FLRW and various dark energy models. Furthermore, we present an analysis of the utility of alternative cosmographic variables to describe the redshift drift data.

Induced cosmological anisotropy by a gauge-gravity interaction

We present a simple model which generates cosmological anisotropies on top of standard FLRW geometry. This is in some sense reminiscent of the mean field approximation, where the mean field cosmological model under consideration would be the standard FLRW, and the anisotropy is a small perturbative correction on top of it. Using a supergravity-inspired model, we confirm that the stable fixed point of our model corresponds to standard FLRW cosmology. We use a Bianchi VII0-type model supplemented with a scalar and U(1) gauge fields, and we show that the anisotropies of the geometry are generated by the non-trivial interaction between the gravity sector and the U(1) gauge sector. Studying the attractor flow, we show that the anisotropies are present at early times (high redshift) and decay asymptotically to an FLRW attractor fixed point. With such a mechanism, observations of non-isotropy are not contradictory to FLRW geometry or indeed the ΛCDM model. Such models could in principle shed some insights on the present cosmological tensions.

The Evolution of a Higher-Dimensional FRW Universe with Variable G and Λ and Particle Creation

Using an open thermodynamic systems theory, the effect of particle creation on the evolution and dynamics of the standard cosmological FLRW model in a higher-dimensional spacetime with functionally dependent cosmological and gravitational constants Λ and G is investigated. The gravitational field equations have been transformed into a dimensionless system of non-linear, first-order, coupled differential equations (DEs) as functions of the universe’s density parameters Ωi and rate of particle creation Ψ in redshift space, which can be numerically casted. Two cosmological models are obtained, depending on the choice of particle creation rate—Ψ∼H2 and Ψ∼n2 for dust-, radiation- and dark-energy-dominated universes, respectively. The dynamic behaviour of each model is discussed.

Gravitational orbits in the expanding Universe revisited

Modified Newtonian equations for gravitational orbits in the expanding Universe indicate that local gravitationally bounded systems like galaxies and planetary systems are unaffected by the expansion of the Universe. This result is derived for the space expansion described by the standard FLRW metric. In this paper, the modified Newtonian equations are derived for the space expansion described by the conformal cosmology (CC) metric. In this metric, the comoving and proper times are different similarly as the comoving and proper distances. As shown by Vavryčuk (Front. Phys. 2022), this metric is advantageous, because it properly predicts the cosmic time dilation, and fits the Type Ia supernova luminosity observations with no need to introduce dark energy. Surprisingly, the solution of the equations for gravitational orbits based on the CC metric behaves quite differently than that based on the FLRW metric. In contrast to the common opinion that local systems resist the space expansion, they expand according to the Hubble flow in the CC metric. The evolution of the local systems with cosmic time is exemplified on numerical modelling of spiral galaxies. The size of the spiral galaxies grows consistently with observations and a typical spiral pattern is well reproduced. The theory predicts flat rotation curves without an assumption of dark matter surrounding the galaxy. The theory resolves challenges to the ΛCDM model such as the problem of faint satellite galaxies, baryonic Tully-Fisher relation or the radial acceleration relation. Furthermore, puzzles in the solar system are successfully explained such as the Faint young Sun paradox or the Moon’s and Titan’s orbit anomalies.

Equation of state of the running vacuum

Recent studies of quantum field theory in FLRW spacetime suggest that the cause of the speeding up of the universe is the running vacuum (RV), see Moreno-Pulido and Solà Peracaula (Eur Phys J C 82(6):551, 2022; Eur Phys J C 80(8):692, 2020). Appropriate renormalization of the energy-momentum tensor shows that the vacuum energy density is a smooth function of the Hubble rate and its derivatives: rho _textrm{vac}=rho _textrm{vac}(H, {dot{H}},ddot{H},ldots ). This is because in QFT the quantum scaling of rho _textrm{vac} with the renormalization point turns into cosmic evolution with H. As a result, any two nearby points of the cosmic expansion during the standard FLRW epoch are smoothly related through delta rho _textrm{vac}sim mathcal{O}(H^2). In our approach, what we call the ‘cosmological constant’ Lambda is just the nearly sustained value of 8pi G(H)rho _textrm{vac}(H) around (any) given epoch, where G(H) is the running gravitational coupling. In the present study, after summarizing the main QFT calculations supporting the RV approach, we focus on the calculation of the equation of state (EoS) of the RV for the entire cosmic history within such a QFT framework. In particular, in the very early universe, where higher (even) powers rho _textrm{vac}sim mathcal{O}(H^N) (N=4,6,dots ) triggered inflation during a short period in which H=const, the vacuum EoS is very close to w_textrm{vac}=-1. This ceases to be true during the FLRW era, where it adopts the EoS of matter during the relativistic (w_textrm{vac}=1/3) and non-relativistic (w_textrm{vac}=0) epochs. Interestingly enough, we find that in the late universe the EoS becomes mildly dynamical and mimics quintessence, w_textrm{vac}gtrsim -1. It finally asymptotes to -1 in the remote future, but in the transit the RV helps alleviating the H_0 and sigma _8 tensions.

Considering light–matter interactions in the Friedmann equations

Recent observations indicate that the Universe is not transparent but partially opaque due to absorption of light by ambient cosmic dust. This implies that the Friedmann equations valid for the transparent universe must be modified for the opaque universe. This paper studies a scenario in which the opacity rises with redshift. In this case, the light–matter interactions become important, because cosmic opacity produces radiation pressure that counterbalances gravitational forces. The presented theoretical model assumes the Universe is expanding according to the standard FLRW metric but with the scale factor depending on both types of forces: gravity as well as radiation pressure. The modified Friedmann equations predict a cyclic expansion/contraction evolution of the Universe within a limited range of scale factors with no initial singularity. The model avoids dark energy and removes some other tensions of the standard cosmological model. The paper demonstrates that considering light–matter interactions in cosmic dynamics is crucial and can lead to new cosmological models essentially different from the standard CDM model. This emphasizes the necessity of new observations and studies of cosmic opacity and cosmic dust at high redshifts for more realistic modelling of the evolution of the Universe.

Quasi-topological electromagnetism: Dark energy, dyonic black holes, stable photon spheres and hidden electromagnetic duality

We introduce the quasi-topological electromagnetism which is defined to be the squared norm of the topological 4-form F ∧ F. A salient property is that its energy-momentum tensor is of the isotropic perfect fluid with the pressure being precisely the opposite to its energy density. It can thus provide a model for dark energy. We study its application in both black hole physics and cosmology. The quasi-topological term has no effect on the purely electric or magnetic Reissner-Nordstrom black holes, the dyonic solution is however completely modified. We find that the dyonic black holes can have four real horizons. For suitable parameters, the black hole can admit as many as three photon spheres, with one being stable. Another intriguing property is that although the quasi-topological term breaks the electromagnetic duality, the symmetry emerges in the on-shell action in the Wheeler-DeWitt patch. In cosmology, we demonstrate that the quasi-topological term alone is equivalent to a cosmological constant, but the model provides a mechanism for the dark energy to couple with other types of matter. We present a concrete example of the quasi-topological electromagnetism coupled to a scalar field that admits the standard FLRW cosmological solutions.

Environment dependence of the growth of the most massive objects in the Universe

This paper investigates the growth of the most massive cosmological objects. We utilize the Simsilun simulation, which is based on the approximation of the silent universe. In the limit of spatial homogeneity and isotropy the silent universes reduce to the standard FLRW models. We show that within the approximation of the silent universe the formation of the most massive cosmological objects differs from the standard background-dependent approaches. For objects with masses above $10^{15} M_\odot$ the effect of spatial curvature (overdense regions are characterized by positive spatial curvature) leads to measurable effects. The effect is analogous to the effect that the background cosmological model has on the formation of these objects (i.e. the higher matter density and spatial curvature the faster the growth of cosmic structures). We measure this by the means of the mass function and show that the mass function obtained from the Simsilun simulation has a higher amplitude at the high-mass end compared to standard mass function such as the Press-Schechter or the Tinker mass function. For comparison, we find that the expected mass of most massive objects using the Tinker mass function is $4.4^{+0.8}_{-0.6} \, \times 10^{15} M_\odot$, whereas for the Simsilun simulation is $6.3^{+1.0}_{-0.8} \, \times 10^{15} M_\odot$. We conclude that the nonlinear relativistic effects could affect the formation of the most massive cosmological objects, leading to a relativistic environment-dependence of the growth rate of the most massive clusters.

Strength of singularities in varying constants theories

In this paper we consider a specific type of the bimetric theory of gravitation with the two different metrics introduced in the cosmological frame. Both metrics respect all the symmetries of the standard FLRW solution and contain conformally related spatial parts. One of the metric is assumed to describe the causal structure for the matter. Another metric defines the causal structure for the gravitational interactions. A crucial point is that the spatial part of the metric describing gravity is given by the spatial part of the matter metric conformally rescaled by a time-dependent factor alpha which, as it turns out, can be linked to the effective gravitational constant and the effective speed of light. In the context of such a bimetric framework we examine the strength of some singular cosmological scenarios in the sense of the criteria introduced by Tipler and Królak. In particular, we show that for the nonsingular scale factor associated with the matter metric, both the vanishing or blowing up of the factor alpha for some particular moment of the cosmic expansion may lead to a strong singularity with infinite value of the energy density and infinite value of the pressure.

How Problematic is the Near-Euclidean Spatial Geometry of the Large-Scale Universe?

Modern observations based on general relativity indicate that the spatial geometry of the expanding, large-scale Universe is very nearly Euclidean. This basic empirical fact is at the core of the so-called "flatness problem", which is widely perceived to be a major outstanding problem of modern cosmology and as such forms one of the prime motivations behind inflationary models. An inspection of the literature and some further critical reflection however quickly reveals that the typical formulation of this putative problem is fraught with questionable arguments and misconceptions and that it is moreover imperative to distinguish between different varieties of problem. It is shown that the observational fact that the large-scale Universe is so nearly flat is ultimately no more puzzling than similar "anthropic coincidences", such as the specific (orders of magnitude of the) values of the gravitational and electromagnetic coupling constants. In particular, there is no fine-tuning problem in connection to flatness of the kind usually argued for. The arguments regarding flatness and particle horizons typically found in cosmological discourses in fact address a mere $single$ issue underlying the standard FLRW cosmologies, namely the $extreme$ improbability of these models with respect to any "reasonable measure" on the "space of all spacetimes". This issue may be expressed in different ways and a phase space formulation, due to Penrose, is presented here. A horizon problem only arises when additional assumptions - which are usually kept implicit and at any rate seem rather speculative - are made.

Balancing anisotropic curvature with gauge fields in a class of shear-free cosmological models

We present a complete list of general relativistic shear-free solutions in a class of anisotropic, spatially homogeneous and orthogonal cosmological models containing a collection of n independent p-form gauge fields, where , in addition to standard ΛCDM matter fields modelled as perfect fluids. Here a (collection of) gauge field(s) balances anisotropic spatial curvature on the right-hand side of the shear propagation equation. The result is a class of solutions dynamically equivalent to standard FLRW cosmologies, with an effective curvature constant that depends both on spatial curvature and the energy density of the gauge field(s). In the case of a single gauge field (n = 1) we show that the only spacetimes that admit such solutions are the LRS Bianchi type III, Bianchi type VI0 and Kantowski–Sachs metric, which are dynamically equivalent to open (), flat () and closed () FLRW models, respectively. With a collection of gauge fields (n > 1) also Bianchi type II admits a shear-free solution (). We identify the LRS Bianchi type III solution to be the unique shear-free solution with a gauge field Hamiltonian bounded from below in the entire class of models.

Testing backreaction effects with observational Hubble parameter data

The spatially averaged inhomogeneous Universe includes a kinematical backreaction term {mathcal {Q}}_{mathcal {D}} that is relate to the averaged spatial Ricci scalar {langle mathcal {R}} rangle _{mathcal {D}} in the framework of general relativity. Under the assumption that {mathcal {Q}}_{mathcal {D}} and {langle mathcal {R}} rangle _{mathcal {D}} obey the scaling laws of the volume scale factor a_{mathcal {D}}, a direct coupling between them with a scaling index n is remarkable. In order to explore the generic properties of a backreaction model for explaining the accelerated expansion of the Universe, we exploit two metrics to describe the late time Universe. Since the standard FLRW metric cannot precisely describe the late time Universe on small scales, the template metric with an evolving curvature parameter kappa _{mathcal {D}}(t) is employed. However, we doubt the validity of the prescription for kappa _{mathcal {D}}, which motivates us apply observational Hubble parameter data (OHD) to constrain parameters in dust cosmology. First, for FLRW metric, by getting best-fit constraints of varOmega ^{{mathcal {D}}_0}_m = 0.25^{+0.03}_{-0.03}, n = 0.02^{+0.69}_{-0.66}, and H_{mathcal {D}_0} = 70.54^{+4.24}_{-3.97} mathrm{km s^{-1} Mpc^{-1}}, the evolutions of parameters are explored. Second, in template metric context, by marginalizing over H_{mathcal {D}_0} as a prior of uniform distribution, we obtain the best-fit values of n=-1.22^{+0.68}_{-0.41} and {{varOmega }_{m}^{mathcal {D}_{0}}}=0.12^{+0.04}_{-0.02}. Moreover, we utilize three different Gaussian priors of H_{mathcal {D}_0}, which result in different best-fits of n, but almost the same best-fit value of {{varOmega }_{m}^{mathcal {D}_{0}}}sim 0.12. Also, the absolute constraints without marginalization of parameter are obtained: n=-1.1^{+0.58}_{-0.50} and {{varOmega }_{m}^{mathcal {D}_{0}}}=0.13pm 0.03. With these constraints, the evolutions of the effective deceleration parameter q^{mathcal {D}} indicate that the backreaction can account for the accelerated expansion of the Universe without involving extra dark energy component in the scaling solution context. Nevertheless, the results also verify that the prescription of kappa _{mathcal {D}} is insufficient and should be improved.

Perturbative instability of inflationary cosmology from quantum potentials

It was argued that the Raychaudhuri equation with a quantum correction term seems to avoid the Big Bang singularity and to characterize an everlasting Universe [PLB741,276(2015)]. Critical comments on both conclusions and on the correctness of the key expressions of this work were discussed in literature [MPLA31(2016)1650044]. In the present work, we have analyzed the perturbative (in)stability conditions in the inflationary era of the early Universe. We conclude that both unstable and stable modes are incompatible with the corresponding ones obtained in the standard FLRW Universe. We have shown that unstable modes do exist at small (an)isotropic perturbation and for different equations of state. Inequalities for both unstable and stable solutions with the standard FLRW space were derived. They reveal that in the FLRW flat Universe both perturbative instability and stability are likely. While negative stability modes have been obtained for radiation- and matter-dominated eras, merely, instability modes exist in case of a finite cosmological constant and also if the vacuum energy dominates the cosmic background geometry.

Gedanken Experiment for Degree of Flatness, or Lack of, in Early Universe Conditions

This document will from first principles delineate the degree of flatness, or deviations from, in early universe models. We will, afterwards, make comparison with recent results we have looked at concerning metric tensor fluctuations and comment upon the role of what early universe gravitational energy may play a role in the presumed deviation from flat space results. Note that N~Sinitial(graviton)~1037 will be tied into the presumed results for initial state density, in ways we will comment upon, leading to observations which are supporting the physics given by Equation (26) of this document as with regards to Gravitational waves, from relic conditions. The deviations from flat space may help confirm the conclusions given by Buchert, Carfora, Kolb, and Wiltshire allegedly refuting the claim by Green and Wald that “the standard FLRW model approximates our Universe extremely well on all scales, except close to strong field astrophysical objects”, as well as give additional analysis appropriate for adding detail to expanding experimental procedures for investigating non FLRW models such as the Polynomial Inflation models as given by Kobayashi, and Seto, as well as other nonstandard cosmologies, as brought up by Corda, and other researchers. As well as improve upon post Bicep 2 measurements which will avoid GW signatures from interstellar dust, as opposed to relic GW. We hope that our approach may help in the differentiation between different cosmology models. Most importantly, our procedure may help, with refinement of admissible frequency range, avoid the problem of BICEP 2, which had its presumed GW signals from presumed relic conditions identical to dust induced frequencies, as so identified by the Planck collaboration in reference [25] which we comment upon in the conclusion.

Is there proof that backreaction of inhomogeneities is irrelevant in cosmology?

No. In a number of papers, Green and Wald argue that the standard FLRW model approximates our Universe extremely well on all scales, except close to strong-field astrophysical objects. In particular, they argue that the effect of inhomogeneities on average properties of the Universe (backreaction) is irrelevant. We show that this latter claim is not valid. Specifically, we demonstrate, referring to their recent review paper, that (i) their two-dimensional example used to illustrate the fitting problem differs from the actual problem in important respects, and it assumes what is to be proven; (ii) the proof of the trace-free property of backreaction is unphysical and the theorem about it fails to be a mathematically general statement; (iii) the scheme that underlies the trace-free theorem does not involve averaging and therefore does not capture crucial non-local effects; (iv) their arguments are to a large extent coordinate-dependent, and (v) many of their criticisms of backreaction frameworks do not apply to the published definitions of these frameworks. It is therefore incorrect to infer that Green and Wald have proven a general result that addresses the essential physical questions of backreaction in cosmology.

Canonical D = 1 supergravity framework for FLRW cosmology

We construct an extension of standard flat FLRW cosmology with matter, possessing local D = 1, N=1 proper-time supersymmetry. The fundamental equation for the resulting mini-superspace models of quantum universes is a Dirac-like analogue of the Friedmann and Wheeler-DeWitt equations. We provide solutions of this equation for specific matter configurations based on the supersymmetric O(3) and O(2,1) σ-models. It turns out that in the compact model the volume rate of growth of the universe is quantized and non-vanishing due to the zero-point energy of the scalar fields. In the non-compact model the spectrum of the growth rates is continuous but subject to an uncertainty relation involving the scale and the growth factor.

Constraints on cosmokinetics of smooth deformations

We study the possibility that the universe is subjected to a deformation, besides its expansion described by Friedmann's equations. The concept of smooth deformation of a riemannian manifolds associated with the extrinsic curvature is applied the standard FLRW cosmology. Starting from the resulting modified Friedman's equation we study two possible solutions with six models for each one in low redshift. In other to constrain the models, we calculate deceleration, jerk and Hubble parameters and compare with different data as the latest BAO/CMB + SNIa constraints, SNLS SNIa, x-ray galaxy clusters and the gold sample (SNIa). As a result, we obtain a set of proper models compatible with the current observational data.

Inhomogeneity implies accelerated expansion

The Einstein equations for an inhomogeneous irrotational dust universe are analysed. A set of mild assumptions, all of which are shared by the standard FLRW type scenarios, results in a model that depends only on the distribution of scalar spatial curvature. If the shape of this distribution is made to fit the structure of the present universe, with most of the matter in galaxy clusters and very little in the voids that will eventually dominate the volume, then there is a period of accelerated expansion after cluster formation, even in the absence of a cosmological constant.