New family of inhomogeneous $γ$-law cosmologies: example of gravitational waves in a homogeneous $p=\varrho/3$ background

Details New family of inhomogeneous $γ$-law cosmologies: example of gravitational waves in a homogeneous $p=\varrho/3$ background New family of inhomogeneous $γ$-law cosmologies: example of gravitational waves in a homogeneous $p=\varrho/3$ background

2000-10-19

arxiv.org/abs/gr-qc/0010071v2

Phys.Rev. D63 (2001) 084008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

LaTeX, 25 pages, 3 figures. Uses epsfig package. One reference added; minor changes. To appear in Phys.Rev.D

Scientific paper

10.1103/PhysRevD.63.084008

We present an explicit three-parameter class of $p=\gamma \varrho$, ($-1/3\leq\gamma<1$), 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 non-tilted 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 $p=\varrho /3$ constitutes a new two-parameter inhomogeneous subfamily which can be viewed as a Bianchi V background with a gravitational wave travelling orthogonally to the surfaces of transitivity of the $G_{2}$ group. This wave generates the {\it inhomogeneity} of the spacetime and is related to the sound waves {\it tilting} the perfect fluid. It seems to be the first explicit exact example of a gravitational wave travelling along a homogeneous background that has a realistic equation of state $p=\varrho /3$.

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