A class of inhomogeneous cosmological models

Classical and Quantum Gravity, 1997

We consider the problem of an isolated, self-gravitating system embedded in an inhomogeneous universe within the framework of scalar-tensor gravity. The cosmological inhomogeneities are calculated using the long-wavelength iteration scheme. In this scheme the gravitational and matter fields are obtained as expansions in ever-increasing spatial gradients of a 'seed' metric. On the other hand, the gravitational and matter fields for the isolated system are obtained to so-called post-Newtonian order. In this paper we write down and analyse the long-wavelength iteration scheme corrections to the PPN parameters β and γ , as well aṡ G/G, where G is the Newton gravitational coupling. Three different scalar-tensor couplings are considered: (i) the Brans-Dicke constant coupling; (ii) a power-law coupling; and (iii) a logarithmic coupling. It will be shown for all three couplings (with a dust-filled universe) thaṫ G/G decays to the general relativity value of zero. However, the PPN parameters decay to general relativity values only if the scalar-tensor coupling diverges at a fast enough rate.

Communications in Theoretical Physics, 2008

Cylindrically symmetric inhomogeneous cosmological model for bulk viscous fluid distribution with electromagnetic field is obtained. The source of the magnetic field is due to an electric current produced along the z-axis. F12 is the non-vanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansion θ in the model is proportional to the shear σ. The values of cosmological constant for these models are found to be small and positive at late time which are consistent with the results from recent supernovae Ia observations. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.

International Journal of Modern Physics D, 2002

We consider a magnetic cylindrically symmetric universe with a plane-symmetric inhomogeneous viscous fluid cosmological model with electromagnetic field. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. To get a determinate solution, we assume the free gravitational field to be Petrov type-II non-degenerate. Without assuming any ad hoc law, we obtain a cosmological constant as a decreasing function of time. The behaviour of the electromagnetic field tensor together with some physical aspects of the model are also discussed.

International Journal of Modern Physics D, 2003

A plane-symmetric non-static cosmological model representing a bulk viscous fluid distribution has been obtained which is inhomogeneous and anisotropic and a particular case of which is gravitationally radiative. Without assuming any adhoc law, we obtain a cosmological constant as a decreasing function of time. The physical and geometric features of the models are also discussed. *

Physical Review D, 1993

2013

We characterize the radial and angular variance of the Hubble flow in the COMPOSITE sample of 4534 galaxies, on scales in which much of the flow is in the nonlinear regime. With no cosmological assumptions other than the existence of a suitably averaged linear Hubble law, we find with decisive Bayesian evidence (ln B >> 5) that the Hubble constant averaged in independent spherical radial shells is closer to its asymptotic value when referred to the rest frame of the Local Group, rather than the standard rest frame of the Cosmic Microwave Background. An exception occurs for radial shells in the range 40/h-60/h Mpc. Angular averages reveal a dipole structure in the Hubble flow, whose amplitude changes markedly over the range 32/h-62/h Mpc. Whereas the LG frame dipole is initially constant and then decreases significantly, the CMB frame dipole initially decreases but then increases. The map of angular Hubble flow variation in the LG rest frame is found to coincide with that of the residual CMB temperature dipole, with correlation coefficient -0.92. These results are difficult to reconcile with the standard kinematic interpretation of the motion of the Local Group in response to the clustering dipole, but are consistent with a foreground non-kinematic anisotropy in the distance-redshift relation of 0.5% on scales up to 65/h Mpc. Effectively, the differential expansion of space produced by nearby nonlinear structures of local voids and denser walls and filaments cannot be reduced to a local boost. This hypothesis suggests a reinterpretation of bulk flows, which may potentially impact on calibration of supernovae distances, anomalies associated with large angles in the CMB anisotropy spectrum, and the dark flow inferred from the kinematic Sunyaev-Zel'dovich effect. It is consistent with recent studies that find evidence for a non-kinematic dipole in the distribution of distant radio sources.

Classical and Quantum Gravity, 2006

We discuss three complementary aspects of scalar curvature singularities: asymptotic causal properties, asymptotic Ricci and Weyl curvature, and asymptotic spatial properties. We divide scalar curvature singularities into two classes: so-called asymptotically silent singularities and singularities that break asymptotic silence. The emphasis in this paper is on the latter class which have not been previously discussed. We illustrate the above aspects and concepts by describing the singularities of a number of representative explicit perfect fluid solutions.

New Journal of Physics, 2006

We elaborate on the proposal that the observed acceleration of the Universe is the result of the backreaction of cosmological perturbations, rather than the effect of a negative-pressure darkenergy fluid or a modification of general relativity. Through the effective Friedmann equations describing an inhomogeneous Universe after smoothing, we demonstrate that acceleration in our local Hubble patch is possible even if fluid elements do not individually undergo accelerated expansion. This invalidates the no-go theorem that there can be no acceleration in our local Hubble patch if the Universe only contains irrotational dust. We then study perturbatively the time behavior of general-relativistic cosmological perturbations, applying, where possible, the renormalization group to regularize the dynamics. We show that an instability occurs in the perturbative expansion involving sub-Hubble modes. Whether this is an indication that acceleration in our Hubble patch originates from the backreaction of cosmological perturbations on observable scales requires a fully non-perturbative approach.

Physical Review D, 2011

At a time when galaxy surveys and other observations are reaching unprecedented sky coverage and precision it seems timely to investigate the effects of general relativistic non-linear dynamics on the growth of structures and on observations. Analytic inhomogeneous cosmological models are an indispensable way of investigating and understanding these effects in a simplified context.

Journal of Cosmology and Astroparticle Physics, 2011

The Szekeres inhomogeneous models can be used to model the true lumpy universe that we observe. This family of exact solutions to Einstein's equations was originally derived with a general metric that has no symmetries. In this work, we develop and use a framework to integrate the angular diameter and luminosity distances in the general Szekeres models. We use the affine null geodesic equations in order to derive a set of first-order ordinary differential equations that can be integrated numerically to calculate the partial derivatives of the null vector components. These equations allow the integration in all generality of the distances in the Szekeres models and some examples are given. The redshift is determined from simultaneous integration of the null geodesic equations. This work does not assume spherical or axial symmetry, and the results will be useful for comparisons of the general Szekeres inhomogeneous models to current and future cosmological data. PACS numbers: 98.80.Es,95.36.+x,98.80.-k * Electronic address: mishak@utdallas.edu

Physical Review D, 2008

We use the Szekeres inhomogeneous relativistic models in order to fit supernova combined data sets. We show that with a choice of the spatial curvature function that is guided by current observations, the models fit the supernova data almost as well as the LCDM model without requiring a dark energy component. The Szekeres models were originally derived as an exact solution to Einstein's equations with a general metric that has no symmetries and are regarded as good candidates to model the true lumpy universe that we observe. The null geodesics in these models are not radial. The best fit model found is also consistent with the requirement of spatial flatness at CMB scales. The first results presented here seem to encourage further investigations of apparent acceleration using various inhomogeneous models and other constraints from CMB and large structure need to be explored next. PACS numbers: 98.80.Es,95.36.+x,

Physical Review D, 2012

This study belongs to a series devoted to using the Szekeres inhomogeneous models in order to develop a theoretical framework where cosmological observations can be investigated with a wider range of possible interpretations. While our previous work addressed the question of cosmological distances versus redshift in these models, the current study is a start at looking into the growth rate of large-scale structure. The Szekeres models are exact solutions to Einstein's equations that were originally derived with no symmetries. We use here a formulation of the Szekeres models that is due to Goode and Wainwright, who considered the models as exact perturbations of a Friedmann-Lemaître-Robertson-Walker (FLRW) background. Using the Raychaudhuri equation we write, for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact non-linear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated cosmic era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres non-linear perturbations. We also find that the Szekeres growth rate with an Einstein-de Sitter background is stronger than that of the well-known non-linear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today. PACS numbers: 98.80.Es,98.80.-k,95.30.Sf * Electronic address: mishak@utdallas.edu

International Journal of Mathematics and Mathematical Sciences, 2009

A new class of cylindrically symmetric inhomogeneous cosmological models for perfect fluid distribution with electromagnetic field is obtained in the context of Lyra's geometry. We have obtained solutions by considering the time dependent displacement field. The source of the magnetic field is due to an electric current produced along the z-axis. Only F 12 is a nonvanishing component of electromagnetic field tensor. To get the deterministic solution, it has been assumed that the expansion θ in the model is proportional to the shear σ. It has been found that the solutions are consistent with the recent observations of type Ia supernovae, and the displacement vector β t affects entropy. Physical and geometric aspects of the models are also discussed in presence and absence of magnetic field.

Physical Review Letters, 1994

The non-linear dynamics of cosmological perturbations of an irrotational collisionless fluid is analyzed within General Relativity. Relativistic and Newtonian solutions are compared, stressing the different role of boundary conditions in the two theories. Cosmological implications of relativistic effects, already present at second order in perturbation theory, are studied and the dynamical role of the magnetic part of the Weyl tensor is elucidated.

International Journal of Modern Physics A, 2007

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to new non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially homogeneous (SH) models of Bianchi type I, at least for the case where the cosmological constant vanish. By exploiting the full set of the constraint equations as expressed in the 1+3 covariant formalism and using elements from the theory of the spacelike congruences, we provide a direct and simple proof of this conjecture for vacuum and dust fluid models, which shows that the Szekeres family of solutions represents the most general class of SIIS models. The suggested procedure also shows that, the uniqueness of the SIIS of the Petrov type D is not, in general, affected by the presence of a non-zero pressure fluid. Therefore, in order to allow a broader class of Petrov type I solutions apart from the SH models of Bianchi type I, one should consider more general "silent" configurations by relaxing the vanishing of the vorticity and the magnetic part of the Weyl tensor but maintaining their "silence" properties i.e. the vanishing of the curls of E ab , H ab and the pressure p.

Physical Review D, 1997

We study the stability of a contracting silent universe, which is a spacetime with irrotational dust and vanishing magnetic part of the Weyl tensor, H ab = 0. Two general relativistic backgrounds are analyzed; one is an attractor of silent universes, i.e., a locally Kasner spacetime, and the other is a particular class of inhomogeneous Szekeres solutions. In both cases their stabilities against perturbations with nonzero magnetic part depend on a contraction configuration; a spindle-like collapse is unstable, while a pancake-like collapse is still stable. We also find that a similar instability exists in spindle collapse for a Newtonian case. We conclude that H ab = 0 is not a generic ansatz even in general relativistic dust collapse.

2008

Based on the distinction between the covariant and contravariant metric tensor components in the framework of the affine geometry approach and the s.c. "gravitational theories with covariant and contravariant connection and metrics", it is shown that a wide variety of third, fourth, fifth, seventh, tenth- degree algebraic equations exists in gravity theory. This is important in view of finding new

Journal of Mathematical Physics, 1983

Journal of Cosmology and Astroparticle Physics

The Universe on scales 10-100 h −1 Mpc is dominated by a cosmic web of voids, filaments, sheets and knots of galaxy clusters. These structures participate differently in the global expansion of the Universe: from non-expanding clusters to the above average expansion rate of voids. In this paper we characterize Hubble expansion anisotropies in the COMPOSITE sample of 4534 galaxies and clusters. We concentrate on the dipole and quadrupole in the rest frame of the Local Group. These both have statistically significant amplitudes. These anisotropies, and their redshift dependence, cannot be explained solely by a boost of the Local Group in the Friedmann-Lemaître-Robertson-Walker (FLRW) model which expands isotropically in the rest frame of the cosmic microwave background (CMB) radiation. We simulate the local expansion of the Universe with inhomogeneous Szekeres solutions, which match the standard FLRW model on > ∼ 100 h −1 Mpc scales but exhibit nonkinematic relativistic differential expansion on small scales. We restrict models to be consistent with observed CMB temperature anisotropies, while simultaneously fitting the redshift variation of the Hubble expansion dipole. We include features to account for both the Local Void and the "Great Attractor". While this naturally accounts for the Hubble expansion and CMB dipoles, the simulated quadrupoles are smaller than observed. Further refinement to incorporate additional structures may improve this. This would enable a test of the hypothesis that some large angle CMB anomalies result from failing to treat the relativistic differential expansion of the background geometry; a natural feature of solutions to Einstein's equations not included in the current standard model of cosmology.

Universe

To get exact solutions to Einstein’s field equations in general relativity, one has to impose some symmetry requirements. Otherwise, the equations are too difficult to solve. However, sometimes, the imposition of too much extra symmetry can cause the problem to become somewhat trivial. As a typical example to illustrate this, the effects of conharmonic flatness are studied and applied to Friedmann–Lemaitre–Robertson–Walker spacetime. Hence, we need to impose some symmetry to make the problem tractable, but not too much so as to make it too simple.

Physical Review D, 2007

The visibility of the shell-focusing singularity in Szekeres space-time-which represents quasispherical dust collapse-has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid. More precisely, we show that the existence of a radial geodesic in Szekeres space-time implies that the space-time is axially symmetric, with the geodesic along the polar direction (i.e. along the axis of symmetry). If there is a second non-parallel radial geodesic, then the space-time is spherically symmetric, and so is a Lemaître-Tolman-Bondi (LTB) space-time. For the case of the polar geodesic in an axially symmetric Szekeres space-time, we give conditions on the free functions (i.e. initial data) of the space-time which lead to visibility of the singularity along this direction. Likewise, we give a sufficient condition for censorship of the singularity. We point out the complications involved in addressing the question of visibility of the singularity both for non-radial null geodesics in the axially symmetric case and in the general (non-axially symmetric) case, and suggest a possible approach.

Journal of Mathematical Physics, 1992

Irrotational dust metrics are considered by requiring the hypersurfaces orthogonal to the matter wordlines to be of constant curvature. The resulting line elements are either contained in the well-known Szekeres dust solutions or they are homogeneous metrics of Bianchi class I or V.

Classical and Quantum Gravity, 2004

We study non-degenerate (Petrov type I) silent universes in the presence of a non-vanishing cosmological constant Λ. In contrast to the Λ = 0 case, for which the orthogonally spatially homogeneous Bianchi type I metrics most likely are the only admissible metrics, solutions are shown to exist when Λ > 0. The general solution is presented for the case where one of the eigenvalues of the expansion tensor is 0.

Classical and Quantum Gravity, 2006

Irrotational dust spacetimes with vanishing magnetic Weyl curvature are called silent universes (Matarrese et al 1994 Phys. Rev. D 72 320). The silent universe conjecture (Sopuerta 1997 Phys. Rev. D 55 5936, van Elst et al 1997 Class. Quantum Grav. 14 1151) states that the only algebraically general silent universes are the orthogonally spatially homogeneous Bianchi I models. In the same paper by Sopuerta, this was confirmed for the subcase where the spacetime also admits a group G3 of isometries. However, the proof contains a conceptual mistake. We recover the result in a different way.

Journal of Physics: Conference Series, 2007

Non-conformally flat, non-vacuum perfect fluid models for which the magnetic, resp. electric, part of the Weyl tensor w.r.t. the fluid congruence vanishes, are called purely electric (PE), resp. purely magnetic (PM), perfect fluids. Their Petrov type is necessarily I or D. They are of particular interest, since the electric part is the relativistic generalization of the tidal tensor in Newtonian theory, whereas the magnetic part has no Newtonian analogue. A survey of recent classification results is presented, with focus on Petrov type D and on the Petrov type I non-accelerating subclass. Important known universe models are naturally embedded in the analysis, while new and physically interesting PE and PM families emerge.

Physical Review D, 2006

Recently the class of purely magnetic non-rotating dust spacetimes has been shown to be empty (Wylleman, Class. Quant. Grav. 23, 2727). It turns out that purely magnetic rotating dust models are subject to severe integrability conditions as well. One of the consequences of the present paper is that also rotating dust cannot be purely magnetic when it is of Petrov type D or when it has a vanishing spatial gradient of the energy density. For purely magnetic and non-rotating perfect fluids on the other hand, which have been fully classified earlier for Petrov type D (Lozanovski, Class. Quant. Grav. 19, 6377), the fluid is shown to be non-accelerating if and only if the spatial density gradient vanishes. Under these conditions, a new and algebraically general solution is found, which is unique up to a constant rescaling, which is spatially homogeneous of Bianchi type V I0, has degenerate shear and is of Petrov type I(M ∞) in the extended Arianrhod-McIntosh classification. The metric and the equation of state are explicitly constructed and properties of the model are briefly discussed. We finally situate it within the class of normal geodesic flows with degenerate shear tensor.

General Relativity and Gravitation

We have solved the Einstein-Maxwell equations for a class of metrics with constant spatial curvature by considering only a primordial magnetic field as source. We assume a slight modification of the Tolman averaging relations so that the energy-momentum tensor of this field possesses an anisotropic pressure component. This inhomogeneous magnetic universe is isotropic and its time evolution is guided by the usual Friedmann equations. In the case of a flat universe, the space-time metric is free of singularities (except the well-known initial singularity at t = 0). It is shown that the anisotropic pressure of our model has a straightforward relation to the Weyl tensor. We then analyze the effect of this new ingredient on the motion of test particles and on the geodesic deviation of the cosmic fluid.

Physical Review D, 2012

We analyze the properties of the tilted Szekeres spacetime, i.e. the version of such spacetime as seen by a congruence of observers with respect to which the fluid is moving. The imperfect fluid and the kinematical variables associated to the four-velocity of the fluid assigned by tilted observers are studied in detail. As it happens for the case of the Lemaitre-Tolman-Bondi spacetime, the fluid evolves nonreversibly (with nonvanishing entropy production) and is nongeodesic. However, unlike the latter case, the tilted observer detects vorticity in the congruence of the fluid world lines. Also, as for the nontilted congruence, the magnetic part of the Weyl tensor vanishes, reinforcing the nonradiative character of this kind of spacetime. Possible physical implications of these results are discussed.

Physical Review D, 2015

We examine the spatial extrema (local maxima, minima and saddle points) of the covariant scalars (density, Hubble expansion, spatial curvature and eigenvalues of the shear and electric Weyl tensors) of the quasi-spherical Szekeres dust models. Sufficient conditions are obtained for the existence of distributions of multiple extrema in spatial comoving locations that can be prescribed through initial conditions. These distributions evolve without shell crossing singularities at least for ever expanding models (with or without cosmological constant) in the full evolution range where the models are valid. By considering the local maxima and minima of the density, our results allow for setting up elaborated networks of "pancake" shaped evolving cold dark matter over-densities and density voids whose spatial distribution and amplitudes can be controlled from initial data compatible with standard early Universe initial conditions. We believe that these results have an enormous range of potential application by providing a fully relativistic non-perturbative coarse grained modelling of cosmic structure at all scales.

Physical Review D

We study the differences and equivalences between the non-perturbative description of the evolution of cosmic structure furnished by the Szekeres dust models (a non-spherical exact solution of Einstein's equations) and the dynamics of Cosmological Perturbation Theory (CPT) for dust sources in a ΛCDM background. We show how the dynamics of Szekeres models can be described by evolution equations given in terms of "exact fluctuations" that identically reduce (at all orders) to evolution equations of CPT in the comoving isochronous gauge. We explicitly show how Szekeres linearised exact fluctuations are specific (deterministic) realisations of standard linear perturbations of CPT given as random fields but, as opposed to the latter perturbations, they can be evolved exactly into the full non-linear regime. We prove two important results: (i) the conservation of the curvature perturbation (at all scales) also holds for the appropriate linear approximation of the exact Szekeres fluctuations in a ΛCDM background, and (ii) the different collapse morphologies of Szekeres models yields, at nonlinear order, different functional forms for the growth factor that follows from the study of redshift space distortions. The metric based potentials used in linear CPT are computed in terms of the parameters of the linearised Szekeres models, thus allowing us to relate our results to linear CPT results in other gauges. We believe that these results provide a solid starting stage to examine the role of non-perturbative General Relativity in current cosmological research.

Physical Review D, 2015

Using a framework based on the 1 þ 3 formalism we carry out a study on axially and reflection symmetric perfect and geodesic fluids, looking for possible models of sources radiating gravitational waves. Therefore, the fluid should be necessarily shearing, for otherwise the magnetic part of the Weyl tensor vanishes, leading to a vanishing of the super-Poynting vector. However, for the family of perfect, geodesic fluids considered here, it appears that all possible cases reduce to conformally flat, shear-free, vorticity-free fluids, i.e., Friedman-Robertson-Walker. The super-Poynting vector vanishes and therefore no gravitational radiation is expected to be produced. The physical meaning of the obtained result is discussed.

Physics Letters A, 1985

We have obtained a new class of inhomogeneous and anisotropic cosmologies on the assumption of a fluid not in the thermal equilibrium state as the source of curvature. These solutions generalize Szekeres' parabolic models. One subclass of our solutions evolve to the FRW models at the limit of a large cosmological time, according to Misner's hypothesis.

Astrophysics and Space Science, 2011

A new class of relativistic perfect fluid cylinders with expansion proportional to shear scalar have been derived by considering the Einstein-Rosen metric. It is shown that the solutions obtained by other workers do not satisfy the isotropy conditions and therefore are erroneous. The solutions derived in this article are analyzed kinematically.

Classical and Quantum Gravity, 2001

Irrotational dust solutions of Einstein's equations are suitable models to describe the general-relativistic aspects of the gravitational instability mechanism for the formation of cosmic structures. In this paper we study their state space by considering the local initial-value problem formulated in the covariant fluid approach. We consider a wide range of models, from homogeneous and isotropic to highly inhomogeneous irrotational dust models, showing how they constitute equilibrium configurations (invariant sets) of the dynamics. Moreover, we give the characterization of such configurations, which provides an initial-data characterization of the models under consideration.

Physical Review D, 1999

In this paper we show a procedure to construct cosmological models which, according to a covariant criterion, can be seen as exact ͑nonlinear͒ perturbations of the standard Friedmann-Lemaître-Robertson-Walker ͑FLRW͒ cosmological models. The special properties of this procedure will allow us to select some of the characteristics of the models and also to study in depth their main geometrical and physical features. In particular, the models are conformally stationary, which means that they are compatible with the existence of isotropic radiation, and the observers that would measure this isotropy are rotating. Moreover, these models have two arbitrary functions ͑one of them is a complex function͒ which control their main properties, and in general they do not have any isometry. We study two examples, focusing on the case when the underlying FLRW models are flat dust models. In these examples we compare our results with those of the linearized theory of perturbations about a FLRW background. ͓S0556-2821͑99͒08320-4͔

New Journal of Physics, 2007

Cosmic acceleration is explained quantitatively, purely in general relativity with matter obeying the strong energy condition, as an apparent effect due to quasilocal gravitational energy differences that arise in the decoupling of bound systems from the global expansion of the universe. "Dark energy" is recognised as a misidentification of those aspects of gravitational energy which by virtue of the equivalence principle cannot be localised. Matter is modelled as an inhomogeneous distribution of clusters of galaxies in bubble walls surrounding voids, as we observe. Gravitational energy differences between observers in bound systems, such as galaxies, and volume-averaged comoving locations in freely expanding space can be so large that the time dilation between the two significantly affects the parameters of any effective homogeneous isotropic model one fits to the universe. A new approach to cosmological averaging is presented, which implicitly solves the Sandage-de Vaucouleurs paradox. Comoving test particles in freely expanding space, which observe an isotropic cosmic microwave background (CMB), possess a quasilocal "rest" energy E = γ(τ, x) mc 2 on the spatial hypersurfaces of homogeneity. Here 1 ≤ γ < 3 2 : the lower bound refers to fiducial reference observers at "finite infinity", which is defined technically in relation to the demarcation scale between bound systems and expanding space. Within voids γ > 1, representing the quasilocal gravitational energy of expansion and spatial curvature variations. Since all our cosmological measurements apart from the CMB involve photons exchanged between objects in bound systems, and since clocks in bound systems are largely unaffected, this is entirely consistent with observation. When combined with a non-linear scheme for cosmological evolution with back-reaction via the Buchert equations, a new observationally viable model of the universe is obtained, without "dark energy". A quantitative scheme is presented for the recalibration of average cosmological parameters. It uses boundary conditions at the time of last scattering consistent with primordial inflation. The expansion age is increased, allowing more time for structure formation. The baryon density fraction obtained from primordial nucleosynthesis bounds can be significantly larger, yet consistent with primordial lithium abundance measurements. The angular scale of the first Doppler peak in the CMB anisotropy spectrum fits the new model despite an average negative spatial curvature at late epochs, resolving the anomaly associated with ellipticity in the CMB anisotropies. Non-baryonic dark matter to baryonic matter ratios of about 3:1 are typically favoured by observational tests. A number of other testable consequences are discussed, with the potential to profoundly change the whole of theoretical and observational cosmology.

Open Astronomy, 2022

This paper discusses the disordering of the principle of cosmology on a small scale, i.e. the possibility of interpreting the observational data of type Ia Supernovae (SNe Ia) through the inhomogeneity and anisotropy of the Universe. The expansion of the Universe may appear to be accelerating due to “dark flows”, changes in the wavelength of light passing through “voids” and clusters, or anisotropy. Different sets of cosmological data are also considered without the need for a dark energy component.

Physical Review D, 2014

It has been argued in the literature that in order to make a matter dominated Friedmann-Lemaitre-Robertson-Walker universe compatible with the generalized second law of thermodynamics, one must invoke dark energy, or modified gravity. In the present article we investigate if in a similar spirit, inhomogeneous cosmological models can be motivated on thermodynamic grounds. We examine a particular minimal void Lemaitre-Tolman-Bondi inhomogeneous model which agrees well with observations. While on the one hand we find that the entropy associated with the apparent horizon is not well-behaved thermodynamically, on the other hand the canonical Weyl curvature entropy shows satisfactory thermodynamic behavior. We suggest that evolution of canonical Weyl curvature entropy might be a useful way to evaluate the thermodynamic viability of inhomogeneous cosmologies.

Synthese, 2020

The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theoryconfirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is not inference to the best explanation, but rather is closer to Peirce's original idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion." Contents 1 Types of Reasoning in Science 2 2 Frameworks 4 3 Abduction 7 4 Framework Confirmation 18 5 This Is True Confirmation 29 6 References 32 † I thank Bill Harper for many enjoyable and edifying discussions about Newton, scientific reasoning, and evidence, and for having written such a wonderful book (Harper 2011). I also thank him for detailed comments on an earlier draft of the paper, including catching an error in §3 in my discussion of Hall, Brown, and the precessions of Mercury and the Moon. I thank Tom Pashby for comments on an earlier draft, including interesting suggestions for elaboration in future work. I thank an anonymous referee for detailed criticisms and questions. I am grateful to Howard Stein as well, as always, for many illuminating and pleasurable conversations on all of these matters.

Physical Review D, 2021

A new formulation for light propagation in geometric optics by means of the Bi-local Geodesic Operators is considered. We develop the BiGONLight Mathematica package, uniquely designed to apply this framework to compute optical observables in Numerical Relativity. Our package can be used for light propagation on a wide range of scales and redshifts and accepts numerical as well as analytical input for the spacetime metric. In this paper we focus on two cosmological observables, the redshift and the angular diameter distance, specializing our analysis to a wall universe modeled within the post-Newtonian approximation. With this choice and the input metric in analytical form, we are able to estimate non-linearities of light propagation by comparing and isolating the contributions coming from Newtonian and post-Newtonian approximations as opposed to linear perturbation theory. We also clarify the role of the dominant post-Newtonian contribution represented by the linear initial seed which, strictly speaking, is absent in the Newtonian treatment. We found that post-Newtonian non-linear corrections are below 1%, in agreement with previous results in the literature.

Journal of Mathematical Physics, 2004

We give a classification of the type D space–times based on the invariant differential properties of the Weyl principal structure. Our classification is established using tensorial invariants of the Weyl tensor and, consequently, besides its intrinsic nature, it is valid for the whole set of the type D metrics and it applies on both, vacuum and nonvacuum solutions. We consider the Cotton-zero type D metrics and we study the classes that are compatible with this condition. The subfamily of space–times with constant argument of the Weyl eigenvalue is analyzed in more detail by offering a canonical expression for the metric tensor and by giving a generalization of some results about the nonexistence of purely magnetic solutions. The usefulness of these results is illustrated in characterizing and classifying a family of Einstein–Maxwell solutions. Our approach permits us to give intrinsic and explicit conditions that label every metric, obtaining in this way an operational algorithm to...

Theoretical and Observational Cosmology, 1999

The aim of this set of lectures is a systematic presentation of a covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic covariant relations for a cosmological fluid, the present lectures cover some of the same ground as a previous set of Cargèse lectures [6], but they then go on to give (ii) the full set of corresponding tetrad equations, (iii) a classification of cosmological models with exact symmetries, (iv) a brief discussion of some of the most useful exact models and their observational properties, and (v) an introduction to the covariant and gauge invariant perturbation theory of almost-Friedmann-Lemaître-Robertson-Walker universes, with fluid descriptions for the matter and a kinetic theory description of the radiation.

Classical and Quantum Gravity, 2020

In a recent paper (Coll et al 2019 Class. Quantum Grav. 36 175004) we have studied a family of Szekeres-Szafron solutions of class II in local thermal equilibrium (singular models). In this paper we deal with a similar study for all other class II Szekeres-Szafron solutions without symmetries. These models in local thermal equilibrium (regular models) are analyzed and their associated thermodynamic schemes are obtained. In particular, we focus on the subfamily of solutions which are compatible with the generic ideal gas equation of state (p =knΘ), and we analyze in depth two notable interpretations that follow on from the choice of two specific thermodynamic schemes: firstly, as a generic ideal gas in local thermal equilibrium and, secondly, as a model having the homogeneous temperature of the FLRW limit. The models above are shown to fulfill the general necessary macroscopic requirements for physical reality (positivity of matter density, internal energy and temperature, energy conditions and compressibility conditions) in wide domains of the spacetime.

Physical Review D, 2015

We analyze the spectrum of cosmic microwave background (CMB) anisotropies in the timescape cosmology: a potentially viable alternative to homogeneous isotropic cosmologies without dark energy. We exploit the fact that the timescape cosmology is extremely close to the standard cosmology at early epochs to adapt existing numerical codes to produce CMB anisotropy spectra, and to match these as closely as possible to the timescape expansion history. A variety of matching methods are studied and compared. We perform Markov chain Monte Carlo analyses on the parameter space, and fit CMB multipoles 50 ≤ ℓ ≤ 2500 to the Planck satellite data. Parameter fits include a dressed Hubble constant, H 0 = 61.0 km sec −1 Mpc −1 (±1.3% stat) (±8% sys), and a present void volume fraction fv0 = 0.627 (±2.3% stat) (±13% sys). We find best fit likelihoods which are comparable to that of the best fit ΛCDM cosmology in the same multipole range. In contrast to earlier results, the parameter constraints afforded by this analysis no longer admit the possibility of a solution to the primordial lithium abundance anomaly. This issue is related to a strong constraint between the ratio of baryonic to nonbaryonic dark matter and the ratio of heights of the second and third acoustic peaks, which cannot be changed as long as the standard cosmology is assumed up to the surface of last scattering. These conclusions may change if backreaction terms are also included in the radiation-dominated primordial plasma.

Journal of Cosmology and Astroparticle Physics

Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) “at rest”, while “space” is expanding. But this is merely a specific coordinate choice; and it is important to realise that for certain purposes other, (sometimes radically, different) coordinate choices might also prove useful and informative, but without changing the underlying physics. Specifically, herein we shall consider the k= 0 spatially flat FLRW cosmology but in Painlevé-Gullstrand coordinates — these coordinates are very explicitly not co-moving: “space” is now no longer expanding, although the distance between galaxies is still certainly increasing. Working in these Painlevé-Gullstrand coordinates provides an alternate viewpoint on standard cosmology, and the symmetries thereof, and also makes it somewhat easier to handle cosmological horizons. With a longer view, we hope that investigating these Painlevé-Gullstrand...

General Relativity and Gravitation, 2012

Keyword Relativistic cosmology • Line element • Robertson-Walker metric • Stationary and non-stationary universes • Golden Oldie 1 The context H. P. Robertson's paper "Relativistic Cosmology" [48] was the first review paper on the subject of relativistic cosmological models: "This report deals with the attempts which have been made during the past decade and a half to solve the general problem of the structure of the universe as a whole." Such models had been initiated by Einstein's 1917 paper [12] on the Einstein static solution, 1 and then developed by a small group of pioneers: Einstein, de Sitter, Friedmann, Lanczos, Weyl, Lemaître, Robertson, Tolman, and Eddington. A second wave of pioneers-von Laue, Heckmann, McCrea, McVittie, Whittaker, Ward, Milne, and Walker 2 -joined in after the idea of an expanding universe became accepted in 1931, providing a sound theoretical basis for Hubble's observations of the magnitude-redshift relation for galaxies. Robertson's article was written 16 years after the first General Relativistic cosmological model and 11 years after the first expanding universe models

Physical Review D, 1999

Using the renormalization group method, we improved the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of Lie group, we can regularize the secular divergence caused by the spatial gradient terms and absorb it to the background seed metric. The solution of the renormalization group equation shows that the renormalized metric describes the behavior of gravitational collapse in the expanding universe qualitatively well.