New family of inhomogeneous γ-law cosmologies: Example of gravitational waves in a homogeneousp=ϱ/3background

Abstract

We present an explicit three-parameter class of $p=\ensuremath{\gamma}\ensuremath{\varrho}(\ensuremath{-}\frac{1}{3}<~\ensuremath{\gamma}<1)$ cosmological models admitting a two-dimensional group ${G}_{2}$ of isometries acting on spacelike surfaces. The family is self-similar in the sense that it has a further homothetic vector field and it contains subfamilies of both (previously unknown) tilted and nontilted Bianchi models with that equation of state. This is the first algebraically general class of solutions of this kind including dust inhomogeneous solutions. The whole class presents a universal spacelike big-bang singularity in the finite past. More interestingly, the case $p=\ensuremath{\varrho}/3$ constitutes a new two-parameter inhomogeneous subfamily which can be viewed as a Bianchi type V background with a gravitational wave traveling orthogonally to the surfaces of transitivity of the ${G}_{2}$ group. This wave generates the inhomogeneity of the spacetime and is related to the sound waves tilting the perfect fluid. It seems to be the first explicit exact example of a gravitational wave traveling along a homogeneous background that has a realistic equation of state $p=\ensuremath{\varrho}/3.$