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Register a new userA self-similar inhomogeneous dust cosmology
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A detailed study of an inhomogeneous dust cosmology contained in a $gamma$-law family of perfect-fluid metrics recently presented by Mars and Senovilla is performed. The metric is shown to be the most general orthogonally transitive, Abelian, $G_2$ on $S_2$ solution admitting an additional homothety such that the self-similar group $H_3$ is of Bianchi type VI and the fluid flow is tangent to its orbits. The analogous cases with Bianchi types I, II, III, V, VIII and IX are shown to be impossible thus making this metric privileged from a mathematical viewpoint. The differential equations determining the metric are partially integrated and the line-element is given up to a first order differential equation of Abel type of first kind and two quadratures. The solutions are qualitatively analyzed by investigating the corresponding autonomous dynamical system. The spacetime is regular everywhere except for the big bang and the metric is complete both into the future and in all spatial directions. The energy-density is positive, bounded from above at any instant of time and with an spatial profile (in the direction of inhomogeneity) which is oscillating with a rapidly decreasing amplitude. The generic asymptotic behaviour at spatial infinity is a homogeneous plane wave. Well-known dynamical system results indicate that this metric is very likely to describe the asymptotic behaviour in time of a much more general class of inhomogeneous $G_2$ dust cosmologies.
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Why is the Universe so homogeneous and isotropic? We summarize a general study of a $gamma$-law perfect fluid alongside an inhomogeneous, massless scalar gauge field (with homogeneous gradient) in anisotropic spaces with General Relativity. The anisotropic matter sector is implemented as a $j$-form (field-strength level), where $j,in,{1,3}$, and the spaces studied are Bianchi space-times of solvable type. Walds no-hair theorem is extended to include the $j$-form case. We highlight three new self-similar space-times: the Edge, the Rope and Wonderland. The latter solution is so far found to exist in the physical state space of types I,II, IV, VI$_0$, VI$_h$, VII$_0$ and VII$_h$, and is a global attractor in I and V. The stability analysis of the other types has not yet been performed. This paper is a summary of ~[1], with some remarks towards new results which will be further laid out in upcoming work.
We investigate a class of cylindrically symmetric inhomogeneous $Lambda$-dust spacetimes which have a regular axis and some zero expansion component. For $Lambda e 0$, we obtain new exact solutions to the Einstein equations and show that they are unique, within that class. For $Lambda=0$, we recover the Senovilla-Vera metric and show that it can be locally matched to an Einstein-Rosen type of exterior. Finally, we explore some consequences of the matching, such as trapped surface formation and gravitational radiation in the exterior.
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 $rho= kp$) 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.
We introduce a generalization of the 4-dimensional averaging window function of Gasperini, Marozzi and Veneziano (2010) that may prove useful for a number of applications. The covariant nature of spatial scalar averaging schemes to address the averaging problem in relativistic cosmology is an important property that is implied by construction, but usually remains implicit. We employ here the approach of Gasperini et al. for two reasons. First, the formalism and its generalization presented here are manifestly covariant. Second, the formalism is convenient for disentangling the dependencies on foliation, volume measure, and boundaries in the averaged expressions entering in scalar averaging schemes. These properties will prove handy for simplifying expressions, but also for investigating extremal foliations and for comparing averaged properties of different foliations directly. The proposed generalization of the window function allows for choosing the most appropriate averaging scheme for the physical problem at hand, and for distinguishing between the role of the foliation itself and the role of the volume measure in averaged dynamic equations. We also show that one particular window function obtained from this generalized class results in an averaging scheme corresponding to that of a recent investigation by Buchert, Mourier and Roy (2018) and, as a byproduct, we explicitly show that the general equations for backreaction derived therein are covariant.
The asymptotic properties of self-similar spherically symmetric perfect fluid solutions with equation of state p=alpha mu (-1<alpha<1) are described. We prove that for large and small values of the similarity variable, z=r/t, all such solutions must have an asymptotic power-law form. Some of them are associated with an exact power-law solution, in which case they are asymptotically Friedmann or asymptotically Kantowski-Sachs for 1>alpha >-1 or asymptotically static for 1>alpha >0. Others are associated with an approximate power-law solution, in which case they are asymptotically quasi-static for 1>alpha >0 or asymptotically Minkowski for 1>alpha >1/5. We also show that there are solutions whose asymptotic behaviour is associated with finite values of z and which depend upon powers of ln z. These correspond either to a second family of asymptotically Minkowski solutions for 1>alpha>1/5 or to solutions that are asymptotically Kasner for 1>alpha>-1/3. There are some other asymptotic power-law solutions associated with negative alpha, but the physical significance of these is unclear. The asymptotic form of the solutions is given in all cases, together with the number of associated parameters.
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