The Hubble tension cast a blight on the standard cosmology. As a possible attitude to the problem, the local variation of the expansion rate in an inhomogeneous cosmology has been proposed where the spatial averaging over a finite domain was introduced in order to construct local Friedmann spacetime. However, it is not clear that the concept of the spatial averaging itself is gauge invariant or not. Namely the conclusion obtained by the averaging in a particular gauge is physically meaningful or not. In this paper we address this question, namely the gauge invariance of the spatial averaging in cosmology . We show that the answer is positive by studying the spatial average in the gauge-invariant cosmological perturbation theory.
We introduce brane-worlds with non-constant tension, strenghtening the analogy with fluid membranes, which exhibit a temperature-dependence according to the empirical law established by Eötvös. This new degree of freedom allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We establish the covariant dynamics on a brane with variable tension in full generality, by considering asymmetrically embedded branes and allowing for non-standard model fields in the 5-dimensional space-time. Then we apply the formalism for a perfect fluid on a…
We study the distance-redshift relation in a universe filled with point particles, and discuss what the universe looks like when we make the number of particles N very large, while fixing the averaged mass density. Using the Raychaudhuri equation and a simple analysis of the probability of strong lensing effects, we show that the statistical nature of the amplification is independent of N, and clarify the appearance of the point particle universe.
In recent years the discrepancy in the value of the Hubble parameter has been growing. Recently, there are works supporting the proposal that the uncertainty principles can solve the Hubble tension. Motivated by this proposal, we work with an isotropic and homogeneous FRW universe, obtain its Hamiltonian equations, and thus, the Hubble parameter through the first Friedmann equation. In the context of GUP and EUP models, the Hubble parameter is modified. Since the fingerprints of quantum gravity are imprinted on the CMB, we consider the GUP/EUP-modified Hubble parameter in the first Friedmann e…
We show how a modified Friedmann equation, originating from a model of the universe built from a certain $W_3$ algebra, has the potential to explain the difference between the Hubble constants extracted from CMB data and from supernova data.
Scalar field cosmologies with a generalized harmonic potential and matter with energy density $ρ_m$, pressure $p_m$, and barotropic equation of state (EoS) $p_m=(γ-1)ρ_m, \; γ\in[0,2]$ in Kantowski-Sachs (KS) and closed Friedmann--Lemaître--Robertson--Walker (FLRW) metrics are investigated. We use methods from non--linear dynamical systems theory and averaging theory considering a time--dependent perturbation function $D$. We define a regular dynamical system over a compact phase space, obtaining global results. That is, for KS metric the global late--time attractors of full and time--averaged…
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lemaître-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $γ$, th…
A brane universe derived from the Randall-Sundrum models is considered in which an additional Misner-like periodicity is introduced in the extra direction. This model solves the ambiguity in the choice of the brane world by identifying the branes with opposite tensions, in such a way that if one enters the brane with positive tension, one finds oneself emerging from the brane with negative tension, without having experienced any tension. We show that the cosmological evolution resulting from this model matches that of the standard Friedmann scenario, at least in the radiation dominated era, an…
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic in…
We study cosmological solutions in the dilatonic brane world models. The effective four-dimensional equations on the brane are analyzed for the models with one positive tension brane and two branes with tensions of opposite signs. Just as in the non-dilatonic brane case, the conventional Friedmann equations of the four-dimensional universe are reproduced to the leading order in matter energy density for the model with one brane and the introduction of a radion potential is required in order to reproduce the Friedmann equations with the correct sign for the model with two branes.
We show that derivation of Friedmann's equations from the Einstein-Hilbert action, paying attention to the requirements of isotropy and homogeneity during the variation, leads to a different interpretation of pressure than what is typically adopted. Our derivation follows if we assume that the unapproximated metric and Einstein tensor have convergent perturbation series representations on a sufficiently large Robertson-Walker coordinate patch. We find the source necessarily averages all pressures, everywhere, including the interiors of compact objects. We demonstrate that our considerations ap…
The relation between angular diameter distance and redshift in a spherically symmetric dust-shell universe is studied. This model has large inhomogeneities of matter distribution on small scales. We have discovered that the relation agrees with that of an appropriate Friedmann-Lemaitre(FL) model if we set a ``homogeneous'' expansion law and a ``homogeneous'' averaged density field. This will support the averaging hypothesis that a universe looks like a FL model in spite of small-scale fluctuations of density field, if its averaged density field is homogeneous on large scales.
We investigate the backreaction of cosmological long wavelength perturbations on the evolution of the Universe. By applying the renormalization group method to a Friedmann-Robertson-Walker universe with long wavelength fluctuations, we demonstrate that the renormalized solution with the backreaction effect is equivalent to that of the separate universe. Then, using the effective Friedmann equation, we show that only non-adiabatic mode of long wavelength fluctuations affects the expansion law of the spatially averaged universe.
It is shown, from the two independent approaches of McCrea-Milne and of Zeldovich, that one can fully recover the set equations corresponding to the relativistic equations of the expanding universe of Friedmann-Lemaitre-Robertson-Walker geometry. Although similar, the Newtonian and relativistic set of equations have a principal difference in the content and hence define two flows, local and global ones, thus naturally exposing the Hubble tension at the presence of the cosmological constant Λ. From this, we obtain absolute constraints on the lower and upper values for the local Hubble parameter…
The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaitre-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H_0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definition…
A static Friedmann brane in a 5-dimensional bulk (Randall-Sundrum type scenario) can have a very different relation between the density, pressure, curvature and cosmological constant than in the case of the general relativistic Einstein static universe. In particular, static Friedmann branes with zero cosmological constant and 3-curvature, but satisfying rho>0 and rho+3p>0, are possible. Furthermore, we find static Friedmann branes in a bulk that satisfies the Einstein equations but is not Schwarzschild-anti de Sitter or its specializations. In the models with negative bulk cosmological consta…
The current cosmic time evolution of the Universe is described by the General Relativity theory when a cosmological principle is considered under a flat space time landscape. The set of known as Friedmann equations, contain the principles that lead to the construction of the standard $Λ$CDM model. However, the current state-of-art regarding these equations, even if it is a fundamental method, is based in solving analytically the differential equations by considering several forms of matter/energy components or evaluating them in specific cosmic times where two or more components contribute at …
We study the averaging problem from a point of view of variation of spatial volume $V$. We show that in the space of spherically symmetric dust solutions which are regular on the spatial manifold $S^3$ the variation $δV$ vanishes at the Friedmann-Lemaitre-Robertson-Walker (FLRW) solution in an appropriate sense, which supports the validity of the FLRW solution as the averaged solution. We also present the second variation $δ^2 V$, giving the leading effect of the deviation from the FLRW solution.
The description of spacetime is an fundamental problem of cosmology. We explain why the current assignments of spacetime geometries for $Ω_k$ of the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) model are probably incorrect and suggest more useful descriptions. We show that $Ω_k$ represents not only curvature but the influence of matter density on the extent of spacetime between massive objects. Recent analyses of supernovae type Ia (SNe Ia) and HII/GEHR data with the FLRW model present the best fits with a small value for $Ω_m$ and a large $Ω_k$. These results are consistent with our Universe …
We perform a Markov Chain Monte Carlo analysis of the self-accelerating and normal branch of Dvali-Gabadadze-Porrati braneworld gravity. By adopting a parameterized post-Friedmann description of gravity, we utilize all of the cosmic microwave background data, including the largest scales, and its correlation with galaxies in addition to the geometrical constraints from supernovae distances and the Hubble constant. We find that on both branches brane tension or a cosmological constant is required at high significance with no evidence for the unique Dvali-Gabadadze-Porrati modifications. The cro…
The present matter density of the Universe, while highly inhomogeneous on small scales, displays approximate homogeneity on large scales. We propose that whereas it is justified to use the Friedmann-Lemaitre-Robertson-Walker (FLRW) line element (which describes an exactly homogeneous and isotropic universe) as a template to construct luminosity distances in order to compare observations with theory, the evolution of the scale factor in such a construction must be governed not by the standard Einstein equations for the FLRW metric, but by the modified Friedmann equations derived by Buchert [7, …
Averaging in general relativity is a complicated operation, due to the general covariance of the theory and the non-linearity of Einstein's equations. The latter of these ensures that smoothing spacetime over cosmological scales does not yield the same result as solving Einstein's equations with a smooth matter distribution, and that the smooth models we fit to observations need not be simply related to the actual geometry of spacetime. One specific consequence of this is a decoupling of the geometrical spatial curvature term in the metric from the dynamical spatial curvature in the Friedmann …
Braneworld models have been proposed as a possible solution to the problem of the accelerated expansion of the Universe. The idea is to dispense the dark energy (DE) and drive the late-time cosmic acceleration with a five-dimensional geometry. Here, we investigate a brane model with variable brane tension as a function of redshift called chrono-brane. We propose the polynomial $λ=(1+z)^{n}$ function inspired in tracker-scalar-field potentials. To constrain the $n$ exponent we use the latest observational Hubble data from cosmic chronometers, Type Ia Supernovae from the full JLA sample, baryon …
In relativistic inhomogeneous cosmology, structure formation couples to average cosmological expansion. A conservative approach to modelling this assumes an Einstein--de Sitter model (EdS) at early times and extrapolates this forward in cosmological time as a "background model" against which average properties of today's Universe can be measured. This requires adopting an early-epoch--normalised background Hubble constant $H_1^{bg}$. Here, we show that the $Λ$CDM model can be used as an observational proxy to estimate $H_1^{bg}$ rather than choose it arbitrarily. We assume (i) an EdS model at …
A late epoch cosmic acceleration may be naturally entangled with cosmic coincidence -- the observation that at the onset of acceleration the vacuum energy density fraction nearly coincides with the matter density fraction. In this Letter we show that this is indeed the case with the cosmology of a Friedmann-Lamaître-Robertson-Walker (FLRW) 3-brane in a five-dimensional anti-de Sitter spacetime. We derive the four-dimensional effective action on a FLRW 3-brane, which helps define a general reduction formula, namely, $M_P^{2}=ρ_{b}/|Λ_5|$, where $M_{P}$ is the effective Planck mass, $Λ_5$ is the…
Hubble Tension and Dark Energy in Teleparallel Gauss-Bonnet Gravity: New Constraints from DESI BAO, Pantheon$^+$ and Hubble Data
Vellore Institute of Technology（维洛尔理工学院）；University of Nizwa（尼兹瓦大学）；Khazar University（哈扎尔大学）；Birla Institute of Technology and Science-Pilani, Hyderabad Campus（比拉理工科学学院-皮拉尼校区，海得拉巴校区）
Regular black strings solutions associated to a dynamical Friedmann-Robertson-Walker braneworld are obtained as a particular case of a regular bulk metric, in the context of a variable brane tension. By analyzing the 5D Kretschmann invariants, we show that the variable brane tension is capable to remove bulk singularities, along some eras of the evolution of the Universe. In particular, the black string time-dependent profile in the bulk is analyzed in the context of the McVittie metric on an Eötvös fluid braneworld, wherein the fluid dynamical brane tension depends on the brane temperature. T…
Partial reduction is a Randall-Sundrum reduction for only part of the AdS region between finite tension brane and zero tension brane. This is interesting in AdS/BCFT where the AdS bulk contains a defect brane. We employ partial reduction for a AdS bulk with a brane evolving as a $2d$ Friedmann-Robertson-Walker (FRW) cosmology and demonstrate the equivalence between defect extremal surface and island formula for a large subregion fine grained entropy in boundary CFT. We then move to higher dimensions and demonstrate the existence of $4d$ massless graviton on AdS$_4$ brane in partial reduction. …
We show that the gravitational magnification factor averaged over all configurations of lenses in a locally inhomogeneous universe satisfy a second order differential equation with redshift $z$ by taking the continuous limit of multi-plane gravitational lens equation (the number $N$ of lenses $\to\infty$) and that the gravitationally magnified Dyer-Roeder distance in a clumpy universe becomes to that of the Friedmann-Lema\^ıtre universe for arbitrary values of the density parameter $Ω_{0}$ and of a mass fraction $\barα$ (smoothness parameter).
Towards a Machine Learning Solution for Hubble Tension: Physics-Informed Neural Network (PINN) Analysis of Tsallis Holographic Dark Energy in Presence of Neutrinos
We propose comparing cosmological solutions in terms of their total spatial volumes $V(τ)$ as functions of proper time $τ$, assuming synchronous gauge, and with this intention evaluate the variations of $V(τ)$ about the Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) solutions for dust. This can be done successfully in a simple manner without solving perturbation equations. In particular, we find that first variations vanish with respect to all directions which do not possess homogeneity and isotropy preserving components; in other words, every FLRW solution is a {\it critical point} for $V(τ)$ i…
The recent analysis of the Planck results reveals a tension between the best fits for (Ωm0, H0) derived from the cosmic microwave background or baryonic acoustic oscillations on the one hand, and the Hubble diagram on the other hand. These observations probe the universe on very different scales since they involve light beams of very different angular sizes; hence the tension between them may indicate that they should not be interpreted the same way. More precisely, this Letter questions the accuracy of using only the (perturbed) Friedmann-Lemaître geometry to interpret all the cosmological ob…
The Hubble tension casts a blight on the standard cosmology. As a possible solution to the problem, the local variation of the expansion rate has been proposed where the spatial averaging over a finite domain was introduced in order to restore the local Friedmannian behavior in an inhomogeneous cosmology. So far, however, the approaches are limited to the particular choices of the gauges, and it has been unclear whether the results are gauge-invariant. In this paper, we present the gauge-invariant formulation of the local expansion rate which is driven by the spatial average of the gauge-invar…
One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root of the problem is that averaging does not commute with the Einstein equations that govern the dynamics of the model. This leads to the well-know question of backreaction in cosmology. In this work, we approach the problem using the covariant framework of Macroscopic Gravity (MG). We use its cosmological solution with a flat FLRW macroscopic background where …
The properties of geodesics flow are studied in a Friedmann-Robertson-Walker metric perturbed due to the inhomogeneities of matter. The basic, averaged Jacobi equation is derived, which reveals that the low density regions (voids) are able to induce hyperbolicity, even if the global curvature of the Universe is zero or slightly positive. It is shown that the energy independence is a characteristic property of these geometric effects. The importance of these conclusions is determined by the temperature independent ellipticity of excursion sets and regions of different randomness found in Kolmog…
The $H_0$-tension problem poses a confrontation of dark energy driving late-time cosmological expansion measured by the Hubble parameter $H(z)$ over an extended range of redshifts $z$. Distinct values $H_0\simeq 73$ km\,s$^{-1}$Mpc$^{-1}$ and $H_0\simeq 68$ km\,s$^{-1}$Mpc$^{-1}$ obtain from surveys of the Local Universe and, respectively, $Λ$CBM analysis of the CMB. These are representative of accelerated expansion with $H^\prime(0)\simeq0$ by $Λ=ω_0^2$ and, respectively, $H^\prime(0)>0$ in $Λ$CDM, where $ω_0=\sqrt{1-q}H$ is a fundamental frequency of the cosmological horizon in a Friedmann-R…
Recent low-redshift observations give value of the present-time Hubble parameter $H_{0}\simeq 74~\rm{km s}^{-1}\rm{Mpc}^{-1}$, roughly 10\% higher than the predicted value $H_{0}=67.4~\rm{km s}^{-1}\rm{Mpc}^{-1}$ from Planck's observations of the Cosmic Microwave Background radiation~(CMB) and the $Λ$CDM model. Phenomenologically, we show that by adding an extra component X with negative density in the Friedmann equation, it can relieve the Hubble tension without changing the Planck's constraint on the matter and dark energy densities. For the extra negative density to be sufficiently small, i…
The curvature of a spacetime, either in a topological sense, or averaged over super-horizon-sized patches, is often equated with the global curvature term that appears in Friedmann's equation. In general, however, the Universe is inhomogeneous, and gravity is a nonlinear theory, thus any curvature perturbations violate the assumptions of the FLRW model; it is not necessarily true that local curvature, averaged over patches of constant-time surfaces, will reproduce the observational effects of global symmetry. Further, the curvature of a constant-time hypersurface is not an observable quantity,…
This paper presents numerical solutions of particular Lemaitre-Tolman models approximating a fractal behaviour along the past light cone, as discussed in paper I (0807.0866) of this series. The initial conditions of the numerical problem are discussed and the algorithm used to carry out the numerical integrations is presented. It was found that the numerical solutions are stiff across the flat-curved interface necessary to obtain the initial conditions of the problem. The spatially homogeneous Friedmann models are treated as special cases of the Lemaitre-Tolman solution and solved numerically.…
The gravitational field equations on cosmological scales are obtained by averaging the Einstein field equations of general relativity. By assuming spatial homogeneity and isotropy on the largest scales, the local inhomogeneities affect the dynamics though correction (backreaction) terms, which can lead to behaviour qualitatively and quantitatively different from the Friedmann-Lemaître-Robertson-Walker models. The effects of averaging on cosmological observations are discussed. It is argued that, based on estimates from observational data, the backreaction (and, in particular, the averaged spat…
How do we appropriately fit a model based on an idealised Friedmann-Lema\^{}tre Robertson-Walker spacetime to observations made from a single location in a lumpy Universe? We address this question for surveys that measure the imprints of the baryon acoustic oscillation in galaxy distribution and the peak apparent magnitude of the Type Ia supernova. These observables are related to the cosmological model through the Alcock-Paczyński parameters and the distance-redshift relation. Using the corresponding inhomogeneous spacetime expressions of these as observed data, we perform a parameter inferen…
Comparing measures of the Hubble and BAO tensions in $Λ$CDM and possible solutions in $f(Q)$ gravity
Institute of Cosmology & Gravitation, University of Portsmouth（朴茨茅斯大学宇宙学与引力研究所）；Scottish Universities Physics Alliance, University of Saint Andrews（圣安德鲁斯大学苏格兰大学物理联盟）
We discuss cosmology based on a Cuscuta-Galileon gravity theory, which preserves just two degrees of freedom. Although there exists no additional degrees of freedom, introduction of a potential of a scalar field changes the dynamics. The scalar field is completely determined by matter fields. Giving an exponential potential as an example, we discuss the cosmological dynamics. The gravitational "constant" $G_{\rm F}$ appeared in the effective Friedmann equation becomes time dependent. We also present how to construct a potential when we know the evolution of the Hubble parameter. When we assume…
A Bianchi IX Mixmaster spacetime is the most general spatially homogeneous solution of Einstein's equations and it can represent the space-averaged Universe. We introduce two novel mechanisms resulting in a Mixmaster Universe with non-singular bounces which are quasi-isotropic. A fluid with a non-linear equation of state allows non-singular bounces. Using negative anisotropic stresses successfully isotropises this Universe and mitigates the well known Mixmaster chaotic behaviour. Thus the Universe can be an eternal Mixmaster, going through an infinite series of different cycles separated by bo…
Idealizing matter as a pressureless fluid and representing its motion by a peculiar--velocity field superimposed on a homogeneous and isotropic Hubble expansion, we apply (Lagrangian) spatial averaging on an arbitrary domain $\cal D$ to the (nonlinear) equations of Newtonian cosmology and derive an exact, general equation for the evolution of the (domain dependent) scale factor $a_{\cal D}(t)$. We consider the effect of inhomogeneities on the average expansion and discuss under which circumstances the standard description of the average motion in terms of Friedmann's equation holds. We find th…
