Fluctuation terms and higher moments of a quantum state imply corrections to the classical equations of motion that may have implications in early-universe cosmology, for instance in the state-dependent form of effective potentials. In addition, space-time properties are relevant in cosmology, in particular when combined with quantum corrections required to maintain general covariance in a consistent way. Here, an extension of previous investigations of static quasiclassical space-time models to dynamical ones is presented, describing the evolution of 1-dimensional space as in the classical Lemaitre--Tolman--Bondi models. The corresponding spatial metric has two independent components, both of which are in general subject to quantum fluctuations. The main result is that individual moments from both components are indeed required for general covariance to be maintained at a semiclassical level, while quantum correlations between the components are less relevant.
We sketch a quantum mechanical framework for the universe as a whole. Within that framework we propose a program for describing the ultimate origin in quantum cosmology of the quasiclassical domain of familiar experience and for characterizing the process of measurement. Predictions in quantum mechanics are made from probabilities for sets of alternative histories. Probabilities can be assigned only to sets of histories that approximately decohere. Decoherence is defined and the mechanism of decoherence is reviewed. Decoherence requires a sufficiently coarse-grained description of alternative …
Astronomical observations reveal hierarchical structures in the Universe, from galaxies, groups of galaxies, clusters and superclusters, to filaments and voids. On the largest scales it seems that some kind of statistical homogeneity can be observed. As a result, modern cosmological models are based on spatially homogeneous and isotropic solutions of the Einstein equations, and the evolution of the universe is approximated by the Friedmann equations. In parallel to standard homogeneous cosmology, the field of inhomogeneous cosmology and backreaction is being developed. This field investigates …
We consider Gell-Mann and Hartle's consistent histories formulation of quantum cosmology in the interpretation in which one history, chosen randomly according to the decoherence functional probabilities, is realised from each consistent set. We show that in this interpretation, if one assumes that an observed quasiclassical structure will continue to be quasiclassical, one cannot infer that it will obey the predictions of classical or Copenhagen quantum mechanics.
We obtain a scaling relation for spherically symmetric k-essence scalar fields $ϕ(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $ϕ(r,t)=ϕ_{1}(r) + ϕ_{2}(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhom…
Saulder et al [2019, A&A, 622, A83; arXiv:1811.11976] have performed a novel observational test of the local expansion of the Universe for the standard cosmology as compared to an alternative model with differential cosmic expansion. Their analysis employs mock galaxy samples from the Millennium Simulation, a Newtonian $N$-body simulation on a $Λ$CDM background. For the differential expansion case the simulation has been deformed in an attempt to incorporate features of a particular inhomogeneous cosmology: the timescape model. It is shown that key geometrical features of the timescape cosmolo…
The spectral distortion of the cosmic microwave background blackbody spectrum in a radially inhomogeneous spacetime, designed to exactly reproduce a LambdaCDM expansion history along the past light cone, is shown to exceed the upper bound established by COBE-FIRAS by a factor of approximately 3700. This simple observational test helps uncover a slew of pathological features that lie hidden inside the past light cone, including a radially contracting phase at decoupling and, if followed to its logical extreme, a naked singularity at the radially inhomogeneous Big Bang.
We perform three-dimensional numerical relativity simulations of homogeneous and inhomogeneous expanding spacetimes, with a view towards quantifying non-linear effects from cosmological inhomogeneities. We demonstrate fourth-order convergence with errors less than one part in 10^6 in evolving a flat, dust Friedmann-Lemaitre-Roberston-Walker (FLRW) spacetime using the Einstein Toolkit within the Cactus framework. We also demonstrate agreement to within one part in 10^3 between the numerical relativity solution and the linear solution for density, velocity and metric perturbations in the Hubble …
Soliton solutions are recovered as scale-invariant asymptotic states of vacuum inhomogeneous cosmologies using renormalization group method. The stability analysis of these states is also given.
Specific dark energy models with linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that the choice of such 4d inhomogeneous fluid models may lead to a brane FRW cosmology without any explicit account of higher dimensions at all. Effectively, we thus obtain a brane dark energy universe without introducing the brane concept explicitly. Several examples of brane Rip cosmology arising from 4d inhomogeneous dark fluid models are given.
We present a new exact solution in Brans-Dicke theory. The solution describes inhomogeneous plane-symmetric perfect fluid cosmological model with an equation of state $p=γρ$. Some main properties of the solution are discussed.
This brief article sums up results obtained in arXiv:0911.2653, which develops a constrained SU(2) lattice gauge theory in the "dipole" approximation. This is a further step toward the issue of a (inhomogeneous) loop quantum cosmology and its merging into loop quantum gravity.
One possibility for explaining the apparent accelerating expansion of the universe is that we live in the center of a spherically inhomogeneous universe. Although current observations cannot fully distinguish $Λ$CDM and these inhomogeneous models, direct measurement of the acceleration of the universe can be a powerful tool in probing them. We have shown that, if $Λ$CDM is the correct model, DECIGO/BBO would be able to detect the positive redshift drift (which is the time evolution of the source redshift $z$) in 3--5 year gravitational wave (GW) observations from neutron-star binaries, which e…
An alternative to the postulate of dark energy required to explain the accelerated expansion of the universe is to adopt an inhomogeneous cosmological model to explain the supernovae data without dark energy. We adopt a void cosmology model, based on the inhomogeneous Lemaître-Tolman-Bondi solution of Einstein's field equations. The model can resolve observational anomalies in the $ΛCDM$ model, such as the discrepancy between the locally measured value of the Hubble constant, $H_0=73.24\pm 1.74\,{\rm km}\,{\rm s}^{-1}\,{\rm Mpc}^{-1}$, and the $H_0=66.93\pm 0.62\,{\rm km}\,{\rm s}^{-1}\,{\rm M…
The conditions for the appearance of the Little Rip, Pseudo Rip and Quasi Rip universes in the terms of the parameters in the equation of state of some dark fluid are investigated. Several examples of the Rip cosmologies are investigated.
The Einstein-Klein-Gordon field equations are solved in a inhomogeneous shear-free universe containing a material fluid, a self-interacting scalar field, a variable cosmological term, and a heat flux. A quintessence-dominated scenario arises with a power-law accelerated expansion compatible with the currently observed homogeneous universe.
The current cosmological model ($Λ$CDM) with the underlying FLRW metric relies on the assumption of local isotropy, hence homogeneity of the Universe. Difficulties arise when one attempts to justify this model as an average description of the Universe from first principles of general relativity, since in general, the Einstein tensor built from the averaged metric is not equal to the averaged stress--energy tensor. In this context, the discrepancy between these quantities is called "cosmological backreaction" and has been the subject of scientific debate among cosmologists and relativists for m…
An inhomogeneous version of pre--Big Bang cosmology emerges, within string theory, from quite generic initial conditions, provided they lie deeply inside the weak-coupling, low-curvature regime. Large-scale homogeneity, flatness, and isotropy appear naturally as late-time outcomes of such an evolution.
If we assume that we live in the center of a spherical inhomogeneous universe, we can explain the apparent accelerating expansion of the universe without introducing the unknown dark energy or modifying gravitational theory. Direct measurement of the cosmic acceleration can be a powerful tool in distinguishing $Λ$CDM and the inhomogeneous models. If $Λ$CDM is the correct model, we have shown that DECIGO/BBO has sufficient ability to detect the positive redshift drift of the source by observing gravitational waves from neutron star binaries for 5-10 years. This enables us to rule out any Lemaît…
In this work cosmological models are considered for the low energy string cosmological effective action (tree level) in the absence of dilaton potential. A two parametric non-diagonal family of analytic solutions is found. The curvature is non singular, however the string coupling diverges exponentially.
The past lightcone of an observer in a cosmological spacetime is the unique geometric structure directly linked to observations. After general properties of the Hawking energy along slices of the past lightcone have previously been studied, the present work continues along this path by providing explicit cosmological applications of the Hawking energy associated with a lightcone. Firstly, it is shown that amongst all two-dimensional non-trapped spheres with equal area and average matter density, a shear-free matter distribution maximizes the Hawking energy for sufficiently high densities. Seco…
Specific dark energy models with a linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that such 4d inhomogeneous fluid models may lead to a turbulence FRW cosmology. Both one-component and two-component models from 4d inhomogeneous dark fluid models are considered. In the one-component model the universe may develop from a viscous era with, for instance, a constant bulk viscosity, into a turbulent era. In the two-component model the fluid can be decomposed into two components, one non…
In this paper, we investigate $f(T)$ cosmology and find an exact solution for $f$ which gives a Little Rip cosmology. Also, considering accelerating cosmology with dark matter, the time-dependent solution is found. For these cases, by using solutions obtained from $f(T)$ gravity we find expressions for $ω$ and $Λ$ defined as time functions via equivalent description in terms of inhomogeneous fluid. This puts the question: which theoretical model describes the observational cosmology?
We study how the initial inhomogeneities of the universe affect the onset of inflation in the closed universe. We consider the model of a chaotic inflation which is driven by a massive scalar field. In order to construct an inhomogeneous universe model, we use the long wavelength approximation ( the gradient expansion method ). We show the condition of the inhomogeneities for the universe to enter the inflationary phase.
This article looks at how inhomogeneous spacetime models may be significant for cosmology. First it looks at how the averaging process may affect large scale dynamics, with backreaction effects leading to effective contributions to the averaged energy-momentum tensor. Secondly it considers how local inhomogeneities may affect cosmological observations in cosmology, possibly significantly affecting the concordance model parameters. Thirdly it presents the possibility that the universe is spatially inhomogeneous on Hubble scales, with a violation of the Copernican principle leading to an apparen…
We analyze the existence of inflationary solutions in an inhomogeneous Kaluza-Klein cosmological model in 4+n dimensions. It is shown that the 5-dimensional case is the exception rather than the rule, in the sense that the system is integrable (under the assumption of the equation of state $ρ= kp$) for any value of k. It is also shown that the cases k=0 and k=1/3 are integrable if and only if n=1.
Purely time dependent solutions in four-dimensional Einstein-Cartan-Kalb-Ramond (ECKR) theory of gravity are shown not to be possible leading to a trivial vanishing of all Kalb-Ramond fields. This result seems to contradict previously results obtained by SenGupta et al. (Class. and Quantum Gravity 19(2002)677) where de Sitter spacetime solution is found as an example of opticaly active spacetime. It seems that only inhomogeneous KR fields are possible in four-dimensional torsioned spacetimes.
Recently a new no-global-recollapse argument was given for some inhomogeneous and anisotropic cosmologies that utilizes surface deformation by the mean curvature flow. In this paper we discuss important properties of the mean curvature flow of spacelike surfaces in Lorentzian manifolds. We show that singularities may form during cosmic evolution and the theorems forbidding the global recollapse lose their validity. The time evolution of the spatial scalar curvature that may kinematically prevent the recollapse is determined in normal coordinates, which shows the impact of inhomogeneities expli…
We obtain a scaling relation for spherically symmetric k-essence scalar fields $ϕ(r,t)$ for an inhomogeneous cosmology with the Lemaitre-Tolman- Bondi (LTB) metric. We show that this scaling relation reduces to the known relation for a homogeneous cosmology when the LTB metric reduces to the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric under certain identifications of the metric functions. A k-essence lagrangian is set up and the Euler-Lagrangian equations solved assuming $ϕ(r,t)=ϕ_{1}(r) + ϕ_{2}(t)$. The solutions enable the LBT metric functions to be related to the fields. The LTB inhom…
We consider the possibility to solve the issues of the phantom field cosmology by means of the PT-symmetric quantum theory. The Born-Oppenheimer approximation is applied to the Wheeler-DeWitt equation to study the inhomogeneous fluctuations over the homogeneous minisuperspace. The evolution of the longitudinal inhomogeneous modes in WKB-time is described using a time-dependent pseudo-Hermitian effective Hamiltonian.
We propose a scale-dependent cosmology in which the Robertson--Walker metric and the Einstein equation are modified in such a way that $Ω_0$, $H_0$ and the age of the Universe all become scale-dependent. Its implications on the observational cosmology and possible modifications of the standard Friedmann cosmology are discussed. For example, the age of the Universe in this model is longer than that of the standard model.
Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VI_h cosmology. The asymptotic behaviour of the solutions is investigated and further applications are briefly discussed.
In this talk we show a stiff fluid solution of the Einstein equations for a cylindrically symmetric spacetime. The main features of this metric are that it is non-separable in comoving coordinates for the congruence of the worldlineS of the fluid and that it yields regular curvature invariants.
We outline the key-steps toward the construction of a physical, fully relativistic cosmology. The influence of inhomogeneities on the effective evolution history of the Universe is encoded in backreaction terms and expressed through spatially averaged geometrical invariants. These are absent and potential candidates for the missing dark sources in the standard model. Since they can be interpreted as energies of an emerging scalar field (the morphon), we are in the position to propose a strategy of how phenomenological scalar field models for Dark Energy, Dark Matter and Inflation, that are usu…
We investigate the existence of inhomogeneous Szekeres spacetimes in Einstein-æther theory. We show that inhomogeneous solutions which can be seen as extension of the Szekeres solutions existing in Einstein-æther gravity only for a specific relation between the dimensionless coefficients which defines the coupling between the æther filed with gravity. The two Szekeres classes of solutions are derived. Also a class of inhomogeneous FLRW-like spacetimes is allowed by the theory for arbitrary values of the dimensionless coefficients of the æther field. The stability of the solutions obtained is p…
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 …
We present a special case of the Stephani solution with spherical symmetry while considering different values of spatial curvature. We investigate the dynamics of the universe evolution in our model, build the R--T-regions for the resulting spacetime and analyze the behavior of the deceleration parameter. The singularities of the model are also discussed. The geometry of the spatial part of the obtained solution is explored.
Most of current cosmological theories are built combining an isotropic and homogeneous manifold with a scale factor that depends on time. If one supposes a hyperconical universe with linear expansion, an inhomogeneous metric can be obtained by an appropriate transformation that preserves the proper time. This model locally tends to a flat Friedman-Robertson-Walker metric with linear expansion. The objective of this work is to analyse the observational compatibility of the inhomogeneous metric considered. For this purpose, the corresponding luminosity distance was obtained and was compared with…
After recalling a general non-perturbative expression for the luminosity-redshift relation holding in a recently proposed "geodesic light-cone" gauge, we show how it can be transformed to phenomenologically more convenient gauges in which cosmological perturbation theory is better understood. We present, in particular, the complete result on the luminosity-redshift relation in the Poisson gauge up to second order for a fairly generic perturbed cosmology, assuming that appreciable vector and tensor perturbations are only generated at second order. This relation provides a basic ingredient for t…
The plane-symmetric inhomogeneous cosmological models of perfect fluid distribution with electro-magnetic field is obtained in the framework of Lyra's geometry. To get the deterministic solution, I have considered $ A=f(x)ν(t) $, $ B=g(x)μ(t) $ and $ C=h(x)μ(t) $, where A, B and C are metric coefficients. It has been found that the solutions generalize the solution obtained by Pradhan, Yadav and Singh (2007) and are consistent with the recent observations of type Ia supernovae. A detailed study of physical and kinematical properties of the models have been carried out.
Examples are presented of applications of the Lemaître - Tolman model to problems of astrophysics and gravitation theory. They are: 1. Inferring the spatial distribution of matter by interpretation of observations; 2. Interaction of inhomogeneities in matter distribution with the CMB radiation; 3. Evolution of voids; 4. Singularities; 5. Influence of electromagnetic field on gravitational collapse. This review is meant to demonstrate that the theory is already well-prepared to meet the challenges posed by an inhomogeneous Universe.
Vacuum energy is a simple model for dark energy driving an accelerated expansion of the universe. If the vacuum energy is inhomogeneous in spacetime then it must be interacting. We present the general equations for a spacetime-dependent vacuum energy in cosmology, including inhomogeneous perturbations. We show how any dark energy cosmology can be described by an interacting vacuum+matter. Different models for the interaction can lead to different behaviour (e.g., sound speed for dark energy perturbations) and hence could be distinguished by cosmological observations. As an example we present t…
A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on the minimum volume section, and from this we construct the physical Hilbert space. Moreover, a perturbative study allows us to introduce small inhomogeneities. After gauge fixing, the inhomogeneous part of the system is reduced to a linear field theory. We then adopt a standard Fock representation to quantize these degrees of freedom. For the considered case o…
We introduce the concept of back-reaction in relativistic cosmological modeling. Roughly speaking, this can be thought of as the difference between the large-scale behaviour of an inhomogeneous cosmological solution of Einstein's equations, and a homogeneous and isotropic solution that is a best-fit to either the average of observables or dynamics in the inhomogeneous solution. This is sometimes paraphrased as `the effect that structure has of the large-scale evolution of the universe'. Various different approaches have been taken in the literature in order to try and understand back-reaction …
Exact cosmological solutions are obtained for a five dimensional inhomogeneous fluid distribution along with a Brans-Dicke type of scalar field. The set includes varied forms of matter field including $ρ+p=0$, where p is the 3D isotropic pressure. Depending on the signature of 4-space curvature our solutions admit of indefinite expansion in the usual 3-space and dimensional reduction of the fifth dimension. Due to the presence of the scalar field the case $p=-ρ$ does not yield an exponential expansion of the scale factor, which strikingly differs from our earlier investigations without scalar …
The purpose of this short review is to describe cosmological models with a linear inhomogeneous time-dependent equation of state (EoS) for the dark energy, when the dark fluid is coupled with dark matter. This may lead to a bounce cosmology. We consider equivalent descriptions in terms of the EoS parameters for an exponential, a power-law, or a double-exponential law for the scale factor $a$. Stability issues are discussed by considering small perturbations around the critical points for the bounce, in the early as well as in the late, universe. The latter part of the paper is concerned with d…
We briefly report on a previously found new, approximate, solution to Einstein field equations, describing a cubic lattice of spherical masses. This model mimics in a satisfactory way a Universe which can be strongly inhomogeneous at small scales, but quite homogeneous at large ones. As a consequence of field equations, the lattice Universe is found to expand or contract in the same way as the solution of a Friedmann Universe filled with dust having the same average density. The study of observables indicates however the possible existence of a fitting problem, i.e. the fact that the Friedmann…
The basic concepts and equations of Newtonian Cosmology are presented in the form necessary for the derivation and analysis of the averaged Navier-Stokes-Poisson equations. A particular attention is paid to the physical and cosmological hypotheses about the structure of Newtonian universes. The system of the Navier-Stokes-Poisson equations governing the cosmological dynamics of Newtonian universes is presented and discussed. A reformulation of the Navier-Stokes-Poisson equations in terms of the fluid kinematic quantities is given and the structure of this system of equations is analyzed.
With the era of precision cosmology upon us, and upcoming surveys expected to further improve the precision of our observations below the percent level, ensuring the accuracy of our theoretical cosmological model is of the utmost importance. Current tensions between our observations and predictions from the standard cosmological model have sparked curiosity in extending the model to include new physics. Although, some suggestions include simply accounting for aspects of our Universe that are ignored in the standard model. One example acknowledges the fact that our Universe contains significant…
We consider notions of physical equivalence of sets of histories in the quantum mechanics of a closed system. We show first how the same set of histories can be relabeled in various ways, including the use of the Heisenberg equations of motion and of passive transformations of field variables. In the the usual approximate quantum mechanics of a measured subsystem, two observables re- presented by different Hermitian operators are physically distinguished by the different apparatus used to measure them. In the quantum mechanics of a closed system, however, any apparatus is part of the system an…
We study numerically the inhomogeneous pre-big-bang inflation in a spherically symmetric space-time. We find that a large initial inhomogeneity suppresses the onset of the pre-big-bang inflation. We also find that even if the pre-big-bang inflationary stage is realized, the initial inhomogeneities are not homogenized. Namely, during the pre-big-bang inflation ``hairs''(irregularities) do not fall, in sharp contrast to the usual (potential energy dominated) inflation where initial inhomogeneity and anisotropy are damped and thus the resulting universe is less sensitive to initial conditions.
Interest in cosmological singularities has remarkably grown in recent times, particularly on future singularities with the discovery of late-time acceleration of the universe and dark energy. Recent work has seen a proper classification of such singularities into strong and weak based on their strength, with weak singularities being the likes of sudden, w and big freeze singularities and strong singularities like the big rip. This has led to a classification of such singularities in various types like Big rip is Type 1, w-singularity is type V etc. While singularities of type I-type IV have be…
This is an introduction to loop quantum cosmology (LQC) reviewing mini- and midisuperspace models as well as homogeneous and inhomogeneous effective dynamics.
We model the large scale late time universe as a Lambda-CDM cosmology driven by cosmological constant and perfect dust fluid. Our aim is to find new solutions in the matter and Lambda epoch consistent with inflationary initial conditions, namely that to the far past in the matter era the cosmology tends to a flat FLRW solution. We identify the moduli degrees of freedom that parametrize the flat Lambda-dust FLRW solution and then promote these moduli to slowly varying functions of the spatial coordinates and show how to solve the Einstein equations in a comoving gradient expansion, controlled b…
The Gowdy cosmologies provide a suitable arena to further develop Loop Quantum Cosmology, allowing the presence of inhomogeneities. For the particular case of Gowdy spacetimes with the spatial topology of a three-torus and a content of linearly polarized gravitational waves, we detail a hybrid quantum theory in which we combine a loop quantization of the degrees of freedom that parametrize the subfamily of homogeneous solutions, which represent Bianchi I spacetimes, and a Fock quantization of the inhomogeneities. Two different theories are constructed and compared, corresponding to two differe…
The hypothesis that dark matter and dark energy are unified through the Chaplygin gas is reexamined. Using a generalization of the spherical model which incorporates effects of the acoustic horizon we show that an initially perturbative Chaplygin gas evolves into a mixed system containing cold dark matter in the form of gravitational condensate. Furthermore, we demonstrate that the observed CMB angular and baryonic power spectra are reproduced.
We apply a hybrid approach which combines loop and Fock quantizations to fully quantize the linearly polarized Gowdy $T^3$ model in the presence of a massless scalar field with the same symmetries as the metric. Like in the absence of matter content, the application of loop techniques leads to a quantum resolution of the classical cosmological singularity. Most importantly, thanks to the inclusion of matter, the homogeneous sector of the model contains flat Friedmann-Robertson-Walker (FRW) solutions, which are not allowed in vacuo. Therefore, this model provides a simple setting to study at th…
