We present an analytical approximation formula for the growth function in a spatially flat cosmology with dust and a cosmological constant. Our approximate formula is written simply in terms of a rational function. We also show the approximate formula in a dust cosmology without a cosmological constant, directly as a function of the scale factor in terms of a rational function. The single rational function applies for all, open, closed and flat universes.
Our results involve no elliptic functions, and have very small relative error of less than 0.2 per cent over the range of the scale factor $1/1000 \la a \lid 1$ and the density parameter $0.2 \la Ω_{\rmn{m}} \lid 1$ for a flat cosmology, and less than $0.4$ per cent over the range $0.2 \la Ω_{\rmn{m}} \la 4$ for a cosmology without a cosmological constant.
Friedmann-Lemaître-Robertson-Walker cosmology is examined from the point of view of gravitoelectromagnetism, in the approximation of spacetime regions small in comparison with the Hubble radius. The usual Lorentz gauge is not appropriate for this situation, while the Painlevé-Gullstrand gauge is rather natural. Several non-trivial features and differences with respect to "standard" asymptotically flat gravitoelectromagnetism are discussed.
We build a simple cosmological model by means of a parabolic Lemaître-Tolman-Bondi (LTB) metric up to a redshift $z\simeq 0.4$, an hyperbolic Friedmann metric for $z\sim 0.4$ up to the scale where dimming galaxies are observed ($z\sim 1.4$) and a bulk spatially flat metric up to the last scattering surface. Following Wiltshire, by taking into account the different rate of clocks for an observer at the centre of a parabolic LTB spacetime with respect to a one in the hyperbolic Friedmann metric, an "apparent" negative deceleration parameter is perceived by the observer at the centre of LTB, prov…
We completely classify the Friedmann-Lemaître-Robertson-Walker solutions with spatial curvature $K=0,\pm 1$ for perfect fluids with linear equation of state $p=wρ$, where $ρ$ and $p$ are the energy density and pressure, without assuming any energy conditions. We extend our previous work to include all geodesics and parallelly propagated curvature singularities, showing that no non-null geodesic emanates from or terminates at the null portion of conformal infinity and that the initial singularity for $K=0,-1$ and $-5/3<w<-1$ is a null non-scalar polynomial curvature singularity. We thus obtain …
We present a new idea of testing the validity of the Friedman-Lema\^ıtre-Robertson-Walker metric, through the multiple measurements of galactic-scale strong gravitational lensing systems with type Ia supernovae in the role of sources. Each individual lensing system will provide a model-independent measurement of the spatial curvature parameter referring only to geometrical optics independently of the matter content of the universe. This will create a valuable opportunity to test the FLRW metric directly. Our results show that with hundreds of strongly lensed SNe Ia observed by LSST, one would …
In a universe where, according to the standard cosmological models, some 97% of the total mass-energy is still "missing in action" it behooves us to spend at least a little effort critically assessing and exploring radical alternatives. Among possible, (dare we say plausible), nonstandard but superficially viable models, those spacetimes conformal to the standard Friedmann-Lemaitre-Robertson-Walker class of cosmological models play a very special role --- these models have the unique and important property of permitting large non-perturbative geometric deviations from Friedmann-Lemaitre-Robert…
Compact, flat Friedmann-Lemaitre-Robertson-Walker (FLRW) models have recently regained interest as a good fit to the observed cosmic microwave background temperature fluctuations. However, it is generally thought that a globally, exactly-flat FLRW model is theoretically improbable. Here, in order to obtain a probability space on the set F of compact, comoving, 3-spatial sections of FLRW models, a physically motivated hypothesis is proposed, using the density parameter Omega as a derived rather than fundamental parameter. We assume that the processes that select the 3-manifold also select a glo…
Recent updated results of quasar spectra suggested a 3.9$σ$ significance of spatial variation of the fine-structure constant. Theoretically, it is important to examine whether the fine-structure constant, as a fundamental constant in quantum theory, is possible varying with space and time. In this paper, we explore the possibility that spatial variation of the fine-structure constant could be compatible with Einstein's general relativity. Namely, the spatially dependent fine-structure constant in the Universe could be originated in different values of the speed of light in separate local frame…
We consider the wave equation, $\square_gψ=0$, in fixed flat Friedmann-Lemaître-Robertson-Walker and Kasner spacetimes with topology $\mathbb{R}_+\times\mathbb{T}^3$. We obtain generic blow up results for solutions to the wave equation towards the Big Bang singularity in both backgrounds. In particular, we characterize open sets of initial data prescribed at a spacelike hypersurface close to the singularity, which give rise to solutions that blow up in an open set of the Big Bang hypersurface $\{t=0\}$. The initial data sets are characterized by the condition that the Neumann data should domin…
Recently, some Lema{\^ı}tre-Tolman-Bondi metrics have been considered as models alternative to the dark energy within the Friedmann-Lema{\^ı}tre-Robertson-Walker universes. The vanishing of the intrinsic energy of these metrics is examined since such a vanishing, in the present case and in general, could be interpreted as a necessary condition to consider the possibility of the quantum creation of a metric. More specifically, this vanishing is examined in the particular case where the Lema{\^ı}tre-Tolman-Bondi metrics behave asymptotically like a Friedmann-Lema{\^ı}tre-Robertson-Walker univers…
The present thesis is focused on the study of FLRW cosmology in modified gravities and with scalar fields. The mystery of dark energy has made that the last decade, many efforts in theoretical physics have been focused on the explanation of the current acceleration of the Universe expansion. On the other hand, an early accelerated epoch, known as inflation, is also required in the standard cosmological model in order to fit the observational data. Here, we study the possibility to explain both effects under the same mechanism, by means of scalar fields or modified gravity. In this sense, F(R) …
We propose physically motivated spacetime uncertainty relations (STUR) for flat Friedmann-Lemaître cosmologies. We show that the physical features of these STUR crucially depend on whether a particle horizon is present or not. In particular, when this is the case we deduce the existence of a maximal value for the Hubble rate (or equivalently for the matter density), thus providing an indication that quantum effects may rule out a pointlike big bang singularity. Finally, we costruct a concrete realisation of the corresponding quantum Friedmann spacetime in terms of operators on a Hilbert space.
We study linear perturbations to a Lema{\^ı}tre-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities. We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, ζ_{SMTP}, which is conserved on all scales. We then briefly extend our discussion to the Lema{\^ı}tre spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime.
The Big Bang predicted theoretically by Friedmann could not be discovered in the 1920th, since global cosmological distances (more than 300-1000 Mpc) were not available for observations at that time. In 1927-29, Lemaître and Hubble studied receding motions of galaxies at local distances of less than 20-30 Mpc and found that the motions followed the (nearly) linear velocity-distance relation, known now as Hubble's law. For decades, the real nature of this phenomenon has remained a mystery, in Sandage's words. After the discovery of dark energy, it was suggested that the dynamics of local expans…
We study the evolution of linear perturbations in a Lemaître-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard Friedmann universes as the inhomogeneous background causes gauge-invariant perturbations to couple at first order. As shown by Clarkson et al. (2009), the evolution is constrained by a system of linear partial differential equations which need to be integrated numerically. We present a new numerical scheme using finite element methods to solve this equation system an…
A version of the Swiss-cheese model is investigated. The flat Friedmann-Robertson-Walker (FRW) universe is modified by the addition of several spherical regions with Lemaitre-Tolman-Bondi metric. We discuss light propagation in this model in detail to pave the way for a detailed numerical study of the Hubble diagram.
Massive bigravity models are interesting alternatives to standard cosmology. In most cases, however, these models have been studied for a simplified scenario in which both metrics take homogeneous and isotropic forms [Friedmann-Lemaître-Robertson-Walker (FLRW)] with the same spatial curvatures. The interest to consider more general geometries arises, in particular, in view of the difficulty so far encountered in building stable cosmological solutions with homogeneous and isotropic metrics. Here we consider a number of cases in which the two metrics take more general forms, namely FLRW with dif…
Recently, the present authors studied perturbations in the Lemaitre-Tolman-Bondi cosmological model by applying the second-order perturbation theory in the dust Friedmann-Lemaitre-Robertson-Walker universe model. Before this work, the same subject was studied in some papers by analyzing linear perturbations in the Lemaitre-Tolman-Bondi cosmological model under the assumption proposed by Clarkson, Clifton and February, in which two of perturbation variables are negligible. However, it is a non-trivial issue in what situation the Clarkson-Clifton-February assumption is valid. In this paper, we i…
In this paper, we exploit the fact that the dynamics of homogeneous and isotropic Friedmann-Lemaitre universes is a special case of generalized Lotka-Volterra system where the competitive species are the barotropic fluids filling the Universe. Without coupling between those fluids, Lotka-Volterra formulation offers a pedagogical and simple way to interpret usual Friedmann-Lemaitre cosmological dynamics. A natural and physical coupling between cosmological fluids is proposed which preserve the structure of the dynamical equations. Using the standard tools of Lotka-Volterra dynamics, we obtain t…
We find new, simple cosmological solutions with flat, open, and closed spatial geometries, contrary to the previous wisdom that only the open model is allowed. The metric and the Stückelberg fields are given explicitly, showing nontrivial configurations of the Stückelberg in the usual Friedmann-Lemaître-Robertson-Walker coordinates. The solutions exhibit self-acceleration, while being free from ghost instabilities. Our solutions can accommodate inhomogeneous dust collapse represented by the Lemaître-Tolman-Bondi metric as well. Thus, our results can be used not only to describe homogeneous and…
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…
We investigate the cosmological aspects of the most general parity preserving Metric-Affine Gravity theory quadratic in torsion and non-metricity in the presence of a cosmological hyperfluid. The equations of motion are obtained by varying the action with respect to the metric and the independent affine connection. Subsequently, considering a Friedmann-Lemaître-Robertson-Walker background, we derive the most general form of the modified Friedmann equations for the full quadratic theory. We then focus on a characteristic sub-case involving only two quadratic contributions given in terms of tors…
