Tilted two-fluid Bianchi type I models

In this paper we investigate expanding Bianchi type I models with two tilted fluids with the same linear equation of state, characterized by the equation of state parameter w. Individually the fluids have non-zero energy fluxes w.r.t. the symmetry surfaces, but these cancel each other because of the Codazzi constraint. We prove that when w=0 the model isotropizes to the future. Using numerical simulations and a linear analysis we also find the asymptotic states of models with w>0. We find that future isotropization occurs if and only if $w \leq 1/3$. The results are compared to similar models investigated previously where the two fluids have different equation of state parameters.Comment: 14 pages, 3 figure

Late-time behaviour of the tilted Bianchi type VI−1/9_{-1/9} models

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VI$_{-1/9}$ using dynamical systems methods and numerical simulations. We study models with and without vorticity, with an emphasis on their future asymptotic evolution. We show that for models with vorticity there exists, in a small region of parameter space, a closed curve acting as the attractor.Comment: 13 pages, 1 figure, v2: typos fixed, minor changes, matches published versio

All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property

We prove a generalisation of the $\epsilon$-property, namely that for any dimension and signature, a metric which is not characterised by its polynomial scalar curvature invariants, there is a frame such that the components of the curvature tensors can be arbitrary close to a certain "background". This "background" is defined by its curvature tensors: it is characterised by its curvature tensors and has the same polynomial curvature invariants as the original metric.Comment: 6 page

Universality and constant scalar curvature invariants

A classical solution is called universal if the quantum correction is a multiple of the metric. Universal solutions consequently play an important role in the quantum theory. We show that in a spacetime which is universal all of the scalar curvature invariants are constant (i.e., the spacetime is CSI)

Gravitational Entropy and Quantum Cosmology

We investigate the evolution of different measures of ``Gravitational Entropy'' in Bianchi type I and Lema\^itre-Tolman universe models. A new quantity behaving in accordance with the second law of thermodynamics is introduced. We then go on and investigate whether a quantum calculation of initial conditions for the universe based upon the Wheeler-DeWitt equation supports Penrose's Weyl Curvature Conjecture, according to which the Ricci part of the curvature dominates over the Weyl part at the initial singularity of the universe. The theory is applied to the Bianchi type I universe models with dust and a cosmological constant and to the Lema\^itre-Tolman universe models. We investigate two different versions of the conjecture. First we investigate a local version which fails to support the conjecture. Thereafter we construct a non-local entity which shows more promising behaviour concerning the conjecture.Comment: 20 pages, 7 ps figure

Supergravity solutions with constant scalar invariants

We study a class of constant scalar invariant (CSI) spacetimes, which belong to the higher-dimensional Kundt class, that are solutions of supergravity. We review the known CSI supergravity solutions in this class and we explicitly present a number of new exact CSI supergravity solutions, some of which are Einstein.Comment: 12 pages; to appear in IJMP

Fluid observers and tilting cosmology

We study perfect fluid cosmological models with a constant equation of state parameter $\gamma$ in which there are two naturally defined time-like congruences, a geometrically defined geodesic congruence and a non-geodesic fluid congruence. We establish an appropriate set of boost formulae relating the physical variables, and consequently the observed quantities, in the two frames. We study expanding spatially homogeneous tilted perfect fluid models, with an emphasis on future evolution with extreme tilt. We show that for ultra-radiative equations of state (i.e., $\gamma>4/3$), generically the tilt becomes extreme at late times and the fluid observers will reach infinite expansion within a finite proper time and experience a singularity similar to that of the big rip. In addition, we show that for sub-radiative equations of state (i.e., $\gamma < 4/3$), the tilt can become extreme at late times and give rise to an effective quintessential equation of state. To establish the connection with phantom cosmology and quintessence, we calculate the effective equation of state in the models under consideration and we determine the future asymptotic behaviour of the tilting models in the fluid frame variables using the boost formulae. We also discuss spatially inhomogeneous models and tilting spatially homogeneous models with a cosmological constant

Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

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 \emph{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 $p$.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an appendix are added; (v3) minor changes to match published versio

Tilt and phantom cosmology

We show that in tilting perfect fluid cosmological models with an ultra-radiative equation of state, generically the tilt becomes extreme at late times and, as the tilt instability sets in, observers moving with the tilting fluid will experience singular behaviour in which infinite expansion is reached within a finite proper time, similar to that of phantom cosmology (but without the need for exotic forms of matter).Comment: 9 pages, v2: more discussion, added reference