We construct the Lemaître-Tolman-Bondi (LTB) dust universe whose distance-redshift relation is equivalent to that in the concordance $Λ$ cold dark matter ($Λ$CDM) cosmological model. In our model, the density distribution and velocity field are not homogeneous, whereas the big-bang time is uniform, which implies that the universe is homogeneous at its beginning. We also study the effects of local clumpiness in the density distribution as well as the effects of large-scale inhomogeneities on the distance-redshift relation, and show that these effects may reduce the amplitude of large-scale inhomogeneities necessary for having a distance-redshift relation that is the same as that of the concordance $Λ$CDM universe. We also study the temporal variation of the cosmological redshift and show that, by the observation of this quantity, we can distinguish our LTB universe model from the concordance $Λ$CDM model, even if their redshift-distance relations are equivalent to each other.
Apparent magnitudes are important for high precision cosmology. It is generally accepted that weak gravitational lensing does not affect the relationship between apparent magnitude and redshift. By considering metric perturbations it is shown that objects observed in an inhomogeneous universe have, on average, higher apparent magnitudes than those observed at the same redshift in a homogeneous universe.
Using a long wavelength iteration scheme to solve Einstein's equations near the Big-Bang singularity of a universe driven by a massive scalar field, we find how big initial quasi-isotropic inhomogeneities can be before they can prevent inflation to set in.
We derive a ``generic'' inhomogeneous ``bridge'' solution for a cosmological model in the presence of a real self-interacting scalar field. This solution connects a Kasner-like regime to an inflationary stage of evolution and therefore provides a dynamical mechanism for the quasi-isotropization of the universe. In the framework of a standard Arnowitt-Deser-Misner Hamiltonian formulation of the dynamics and by adopting Misner-Chitrè-like variables, we integrate the Einstein-Hamilton-Jacobi equation corresponding to a ``generic'' inhomogeneous cosmological model whose evolution is influenced by …
We use the cosmic microwave background temperature anisotropy to place limits on large-scale magnetic fields in an inhomogeneous (perturbed Friedmann) universe. If no assumptions are made about the spacetime geometry, only a weak limit can be deduced directly from the CMB. In the special case where spatial inhomogeneity is neglected to first order, the upper limit is much stronger, i.e. a few nano-G
The gravitational instability of inhomogeneities in the expanding universe is studied by the relativistic second-order approximation. Using the tetrad formalism we consider irrotational dust universes and get equations very similar to those given in the Lagrangian perturbation theory in Newtonian cosmology. Neglecting the cosmological constant and assuming a flat background model we give the solutions of the nonlinear dynamics of cosmological perturbations. We present the complete second-order solutions, which extend and improve earlier works.
Anisotropic stress contributions to the gravitational field can arise from magnetic fields, collisionless relativistic particles, hydrodynamic shear viscosity, gravitational waves, skew axion fields in low-energy string cosmologies, or topological defects. We investigate the effects of such stresses on cosmological evolution, and in particular on the dissipation of shear anisotropy. We generalize some previous results that were given for homogeneous anisotropic universes, by including small inhomogeneity in the universe. This generalization is facilitated by a covariant approach. We find that …
We study the large-scale inhomogeneity of the Universe based on the averaging procedure of Buchert and Ehlers. The generalized Dyer-Roeder equation for the angular diameter distance of the inhomogeneous Universe is derived and solved for different cosmological models. We make a comparison of certain cosmic observables, such as the Hubble function, angular diameter distance,cosmological correction factor of homogeneous and inhomogeneous cosmological models, which are crucial ingredients in galaxy number counts and gravitational lenses.
Exact results stemming directly from Einstein equations imply that inhomogeneous Universes endowed with vanishing pressure density can only decelerate, unless the energy density of the Universe becomes negative. Recent proposals seem to argue that inhomogeneous (but isotropic) space-times, filled only with incoherent matter,may turn into accelerated Universes for sufficiently late times. To scrutinize these scenarios, fully inhomogeneous Einstein equations are discussed in the synchronous system. In a dust-dominated Universe, the inhomogeneous generalization of the deceleration parameter is al…
An exact inhomogeneous solution of Einstein's field equations is shown to be able to inflate in a non-uniform way in the early universe and explain anomalies in the WMAP power spectrum data. It is also possible for the model to explain the accelerated expansion of the universe by late-time inhomogeneous structure.
The dark energy universe equation of state (EOS) with inhomogeneous,Hubble parameter dependent term is considered. The motivation to introduce such a term comes from time-dependent viscosity considerations and modifications of general relativity. For several explicit examples of such EOS it is demonstrated how the type of future singularity changes, how the phantom epoch emerges and how crossing of phantom barrier occurs. Similar cosmological regimes are considered for the universe with two interacting fluids and for universe with implicit EOS. For instance, the crossing of phantom barrier is …
A local void in the globally Friedmann-Robertson-Walker cosmological model with the critical density ($Ω_{0}=1$) is studied. The inhomogeneity is described using a Lema\^ıtre-Tolman-Bondi solution for a spherically symmetric distribution of matter. The scale of the central underdense region is $\sim 150$ Mpc. We investigate the effects this has on the cosmological time scale, the measurement of the Hubble constant and the redshift--luminosity distance for moderately and very distant objects ($z \sim 0.1$ and more). The results indicate that if we happened to live in such a void, but insisted o…
When a gravitational wave (GW) from a distant source propagates through the universe, its amplitude and phase change due to gravitational lensing by the inhomogeneous mass distribution. We derive the amplitude and phase fluctuations, and calculate these variances in the limit of a weak gravitational field of density perturbation. If the scale of the perturbation is smaller than the Fresnel scale $\sim 100 {pc} (f/{mHz})^{-1/2}$ ($f$ is the GW frequency), the GW is not magnified due to the diffraction effect. The rms amplitude fluctuation is $1-10 %$ for $f > 10^{-10}$ Hz, but it is reduced les…
This paper and the others in the series challenge the standard model of the effects of gravitational lensing on observations at large distances. We show that due to the cumulative effect of lensing, areas corresponding to an observed solid angle can be quite different than would be estimated from the corresponding Friedmann-Lema\^ıtre model, even when averaged over large angular scales. This paper concentrates on the specific example of spherically symmetric but spatially inhomogeneous dust universes, the Lema\^ıtre-Tolman-Bondi models, and shows that radial lensing significantly distorts the …
We calculated the entropy of a class of inhomogeneous dust universes. Allowing spherical symmetry, we proposed a holographic principle by reflecting all physical freedoms on the surface of the apparent horizon. In contrast to flat homogeneous counterparts, the principle may break down in some models, though these models are not quite realistic. We refined fractal parabolic solutions to have a reasonable entropy value for the present observable universe and found that the holographic principle always holds in the realistic cases.
We consider a cosmology in which a spherically symmetric large scale inhomogeneous enhancement or a void are described by an inhomogeneous metric and Einstein's gravitational equations. For a flat matter dominated universe the inhomogeneous equations lead to luminosity distance and Hubble constant formulas that depend on the location of the observer. For a general inhomogeneous solution, it is possible for the deceleration parameter to differ significantly from the FLRW result. The deceleration parameter $q_0$ can be interpreted as $q_0 > 0$ ($q_0=1/2$ for a flat matter dominated universe) in …
A possibility that the universe may be strongly inhomogeneous chemically, while very smooth energetically, is considered. A possible mechanism which could lead to such a picture is a large and inhomogeneous lepton asymmetry. The model may explain possibly observed variation of primordial deuterium by an order of magnitude and predicts helium-rich and possibly helium-poor regions where the helium mass fraction differs from the observed 25% by a factor of 2 in either direction. Helium variation can be observed by a different dumping rate of CMB angular spectrum at small angles at different patch…
Recently, Holz & Wald have presented a new method for determining gravitational lensing effects on, e.g., supernova luminosity versus redshift measurements in inhomogeneous universes. In this paper, their method is generalized in several ways: First, the matter content is allowed to consist of several different types of fluids, possibly with non-vanishing pressure. Second, besides lensing by simple point masses and singular isothermal spheres, the more realistic halo dark matter distribution proposed by Navarro, Frenk & White (NFW), based on N-body simulation results, is treated. We discuss va…
Full radiative transfer in 3D space has been solved to pursue the reionization history in an inhomogeneous universe. It has been shown that the reionization of an inhomogeneous universe is not a prompt event, but a fairly slow process. Also, QSO absorption line systems are simulated with using the results of radiative transfer calculations. Ly$α$ continuum depression implies that the metagalactic UV intensity decreases rapidly with $z$ at $z>5$, and the reionization must have taken place between $z=6$ and 10. Finally, it is stressed that H$α$ forest is a more powerful tool to probe the reioniz…
We modify the Press-Schechter formalism to calculate the mass function of gravitationally bounded objects in a local Universe with size $L> 10h^{-1}$Mpc, i.e. separately in voids ($Ω_{m,L}<Ω_m$) and superclusters ($Ω_{m,L}>Ω_m$). The dependence of the abundance of gravitationally bounded objects on local matter density is analyzed.
In this work, I present a generalized linear Hubble law for a barotropic spherically symmetric inhomogeneous spacetime, which is in principle compatible with the acceleration of the cosmic expansion obtained as a result of high redshift Supernovae data. The new Hubble function, defined by this law, has two additional terms besides an expansion one, similar to the usual volume expansion one of the FLRW models, but now due to an angular expansion. The first additional term is dipolar and is a consequence of the existence of a kinematic acceleration of the observer, generated by a negative gradie…
Cosmologies that match in a volume averaged sense need not generally have the same light propagation behaviors. In particular a universe with inhomogeneity may not demonstrate the Friedmann-Robertson-Walker distance-redshift relation even after volume averaging to FRW spacetime. Even the Dyer-Roeder prescription for incorporating inhomogeneity within a universe equivalent to FRW in an angle averaged sense does not guarantee FRW behavior in general. To legitimately use the FRW distance-redshift relation to interpret observations, the physical conditions must match in a line of sight sense (defi…
Although observations point to the neutrality and lack of currents on large scales in the universe, many mechanisms are known that can generate charges or currents during the early universe. We examine the question of survivability of relic charges and currents in a realistic model of the universe. We show that the dynamics of cosmological perturbations drive the universe to become electrically neutral and current-free to a high degree of accuracy on all scales, regardless of initial conditions. We find that charges are efficiently driven away in a time small compared to the Hubble time for te…
Using Monte-Carlo methods, we determine the best-fit value of the homogeneity parameter alpha in the Dyer-Roeder distance-redshift relation for a variety of redshifts, inhomogeneity models and cosmological parameter values. The relation between alpha and the fraction of compact objects, f_p, is found to be approximately linear. This relation can be parametrized with reasonable accuracy for all cases treated in this paper by alpha = a*f_p, where a = 0.6.
Using a multi-plane lensing method that we have developed, we follow the evolution of light beams as they propagate through inhomogeneous universes. We use a P3M code to simulate the formation and evolution of large-scale structure. The resolution of the simulations is increased to sub-Megaparsec scales by using a Monte Carlo method to locate galaxies inside the computational volume according to the underlying particle distribution. We consider cold dark matter models normalized to COBE, and perform a large parameter survey by varying the cosmological parameters Omega_0, lambda_0, H_0, and n (…
The existence of stars and galaxies reqires cosmological models with an inhomogeneous matter and radiation distribution. But in these models the initial singularity surface t_0(r) is in general homogeneous (independent of r). In this second paper of a series devoted to an inhomogeneous Big Bang singularity, we investigate the cosmic microwave background radiation (CMBR) dipole. A special Tolman-Bondi Universe is used to study the effect of a Big-Bang singularity, depending linearly on r, on the CMBR anisotropy. It is shown that, for an observer located off the ``center'' of this Universe (r=0)…
We investigate the influence of primordial perturbations of the energy density and space--time metric on the generation of the lepton and baryon asymmetries. In the weak and strong washout regimes baryon isocurvature perturbations with amplitudes of the same order as those of the CMB perturbations are generated on scales of order of the respective Hubble scale. They are, however, completely washed out by baryon and photon diffusion at the later stages of the universe's evolution.
We discuss the two potentially important effects which should be taken into account in the analysis of the cosmological redshift-space distortion especially at high redshifts; the effect of inhomogeneities in the light propagation and the evolution of bias. Although such inhomogeneities affect significantly the degree of the cosmological redshift distortion, one can determine the density parameter $Ω_0$ from the distortion pattern at $z=0$, and the cosmological constant $λ_0$ from that at $z = (1\sim 2)$. In particular we show that in low-density ($Ω_0\ll 1$) universes one can determine the va…
A new model of the observed universe, using solutions to the full Einstein equations, is developed from the hypothesis that our observable universe is an underdense bubble, with an internally inhomogeneous fractal bubble distribution of bound matter systems, in a spatially flat bulk universe. It is argued on the basis of primordial inflation and resulting structure formation, that the clocks of the isotropic observers in average galaxies coincide with clocks defined by the true surfaces of matter homogeneity of the bulk universe, rather than the comoving clocks at average spatial positions in …
A system of effective Einstein equations for spatially averaged scalar variables of inhomogeneous cosmological models can be solved by providing a `cosmic equation of state'. Recent efforts to explain Dark Energy focus on `backreaction effects' of inhomogeneities on the effective evolution of cosmological parameters in our Hubble volume, avoiding a cosmological constant in the equation of state. In this Letter it is argued that, if kinematical backreaction effects are indeed of the order of the averaged density (or larger as needed for an accelerating domain of the Universe), then the state of…
In this letter, we outline an inhomogeneous model of the Big Bang cosmology. For the inhomogeneous spacetime used here, the universe originates in the infinite past as the one dominated by vacuum energy and ends in the infinite future as the one consisting of "hot and relativistic" matter. The spatial distribution of matter in the considered inhomogeneous spacetime is {\em arbitrary}. Hence, observed structures can arise in this cosmology from suitable "initial" density contrast. Different problems of the standard model of Big Bang cosmology are also resolved in the present inhomogeneous model…
We show that our Universe may be inhomogeneous on large sub-horizon scales without us being able to realise it. We assume that a network of domain walls permeates the universe dividing it in domains with slightly different vacuum energy densities. We require that the energy scale of the phase transition which produced the domain walls is sufficiently low so that the walls have a negligible effect on structure formation. Nevertheless, the different vacuum densities of different domains will lead to different values of the cosmological parameters $Ω_Λ^0$, $Ω_m^0$ and $h$, in each patch thus affe…
The current authors have previously shown that inhomogeneous, but spherically symmetric universe models containing only matter can yield a very good fit to the SNIa data and the position of the first CMB peak. In this work we examine how far away from the center of inhomogeneity the observer can be located in these models and still fit the data well. Furthermore, we investigate whether such an off-center location can explain the observed alignment of the lowest multipoles of the CMB map. We find that the observer has to be located within a radius of 15 Mpc from the center for the induced dipol…
We consider the dimming of photons from high redshift type 1a supernovae by mixing with a pseudoscalar axion field in the intergalactic medium. We model the electron density using a lognormal probability distribution and assume frozen in magnetic fields. Assuming the magnetic fields are produced in the early universe we are unable to obtain sufficient dimming in order to explain the apparent acceleration without violating the bounds on the frequency dependence of the dimming. We also show that any axion mixing leading to a reduction in optical luminosities would also lead to a significant redu…
We suggest to generalize the dark energy equation of state (EoS) by introduction the relaxation equation for pressure which is equivalent to consideration of the inhomogeneous EoS cosmic fluid which often appears as the effective model from strings/brane-worlds. As another, more wide generalization we discuss the inhomogeneous EoS which contains derivatives of pressure. For several explicit examples motivated by the analogy with classical mechanics the accelerating FRW cosmology is constructed. It turns out to be the asymptotically de Sitter or oscillating universe with possible transition fro…
We discuss the general and approximate angular diameter distance in the Friedman-Robertson-Walker cosmological models with nonzero cosmological constant. We modify the equation for the angular diameter distance by taking into account the fact that locally the distribution of matter is non homogeneous. We present exact solutions of this equation in a few special cases. We propose an approximate analytic solution of this equation which is simple enough and sufficiently accurate to be useful in practical applications.
We have previously shown that spherically symmetric, inhomogeneous universe models can explain both the supernova data and the location of the first peak in the CMB spectrum without resorting to dark energy. In this work, we investigate whether it is possible to get an even better fit to the supernova data by allowing the observer to be positioned away from the origin in the spherically symmetric coordinate system. In such a scenario, the observer sees an anisotropic relation between redshifts and the luminosity distances of supernovae. The level of anisotropy allowed by the data will then con…
Using a multiple-lens plane algorithm, we study light propagation in inhomogeneous universes, for 43 different COBE-normalized Cold Dark Matter models, with various values of the density parameter Omega_0, cosmological constant lambda_0, Hubble constant H_0, and rms density fluctuation sigma_8. This is the largest cosmological parameter survey ever done in this field. We performed a total of 3,798 experiments, each experiment consisting of propagating a square beam of angular size 21.9'' x 21.9'' composed of 116,281 light rays from the observer up to redshift z=3. These experiments provide sta…
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.
The assumption that a parametric class of functions fits the data structure sufficiently well is common in fitting curves and surfaces to regression data. One then derives a parameter estimate resulting from a least squares fit, say, and in a second step various kinds of chi^2 goodness of fit measures, to assess whether the deviation between data and estimated surface is due to random noise and not to systematic departures from the model. In this paper we show that commonly-used chi^2-measures are invalid in regression models, particularly when inhomogeneous noise is present. Instead we presen…
We present a new model universe based on the junction of FRW to flat Lemaitre-Tolman-Bondi (LTB) solutions of Einstein equations along our past light cone, bringing structures within the FRW models. The model is assumed globally to be homogeneous, i.e. the cosmological principle is valid. Local inhomogeneities within the past light cone are modeled as a flat LTB, whereas those outside the light cone are assumed to be smoothed out and represented by a FRW model. The model is singularity free, always FRW far from the observer along the past light cone, gives way to a different luminosity distanc…
Astrophysical observations provide a picture of the universe as a 4-dim homogeneous and isotropic flat space-time dominated by an unknown form of dark energy. To achieve such a cosmology one has to consider in the early universe an inflationary era able to overcome problems of standard cosmological models. Here an inhomogeneous model is proposed which allows to obtain a Friedmann-Robertson-Walker behaviour far away from the inhomogeneities and it naturally describes structures formation. We also obtain that the cosmological term does not prevent structure formation, avoiding a fine tuning prob…
We study inhomogeneous cosmological variations in the fine structure 'constant', $α,$ in Friedmann universes. Inhomogeneous motions of the scalar field driving changes in $α$ display spatial oscillations that decrease in amplitude with increasing time. The inhomogeneous evolution quickly approaches that found for exact Friedmann universes. We prove a theorem to show that oscillations of $α$ in time (or redshift) cannot occur in Friedmann universes in the BSBM theories considered here.
Distances play important roles in cosmological observations, especially in gravitational lens systems, but there is a problem in determining distances because they are defined in terms of light propagation, which is influenced gravitationally by the inhomogeneities in the universe. In this paper we first give the basic optical relations and the definitions of different distances in inhomogeneous universes. Next we show how the observational relations depend quantitatively on the distances. Finally, we give results for the frequency distribution of different distances and the shear effect on di…
We use a series of ray-tracing experiments to determine the magnification distribution of high-redshift sources by gravitational lensing. We determine empirically the relation between magnification and redshift, for various cosmological models. We then use this relation to estimate the effect of lensing on the determination of the cosmological parameters from observations of high-z supernovae. We found that, for supernovae at redshifts z<1.8 the effect of lensing is negligible compared to the intrinsic uncertainty in the measurements. Using mock data in the range 1.8<z<8, we show that the effe…
Several models of baryo(lepto)-genesis that give rise to large inhomogeneities in the composition of the universe are presented. In particular, a variation of primordial abundances of light elements by the factor 2-5 at large distances is predicted. A cosmological model of baryonic island is considered. Creation of domains with very large baryon and antibaryon number is described. Such domains mostly collapsed into primordial black holes that could be the dominant part of (non-standard) cosmological cold dark matter with a widely dispersed mass spectrum. A non-collapsed part of these bubbles m…
We investigate a new mechanism for the cosmological QCD phase transition: inhomogeneous nucleation. The primordial temperature fluctuations, measured to be $δT/T \sim 10^{-5}$, are larger than the tiny temperature interval, in which bubbles would form in the standard picture of homogeneous nucleation. Thus the bubbles nucleate at cold spots. We find the typical distance between bubble centers to be a few meters. This exceeds the estimates from homogeneous nucleation by two orders of magnitude. The resulting baryon inhomogeneities may affect primordial nucleosynthesis.
Recently, there have been suggestions that the apparent accelerated expansion of the universe is not caused by repulsive gravitation due to dark energy, but is rather a result of inhomogeneities in the distribution of matter. In this work, we investigate the behaviour of a dust dominated inhomogeneous Lemaitre-Tolman-Bondi universe model, and confront it with various astrophysical observations. We find that such a model can easily explain the observed luminosity distance-redshift relation of supernovae without the need for dark energy, when the inhomogeneity is in the form of an underdense bub…
Using a multi-plane lensing method that we have developed, we follow the evolution of light beams as they propagate through inhomogeneous universes. We use a P3M code to simulate the formation and evolution of large-scale structure. The resolution of the simulations is increased to sub-Megaparsec scales by using a Monte Carlo method to locate galaxies inside the computational volume according to the underlying particle distribution. The galaxies are approximated by isothermal spheres, with each morphological type having its own distribution of masses and core radii. The morphological types are…
