New family of inhomogeneous gamma-law cosmologies: Example of gravitational waves in a homogeneous p = rho/3 background - art. no. 084008

We present an explicit three-parameter class of p = gamma rho (-1/3 less th an or equal to gamma <1) cosmological models admitting a two-dimensional gr oup G(2) of isometries acting on spacelike surfaces. The family is self-sim ilar in the sense that it has a further homothetic vector held and it conta ins subfamilies of both (previously unknown) tilted and nontilted Bianchi m odels 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 fin ite past. More interestingly, the case p = <rho>/3 constitutes a new two-pa rameter inhomogeneous subfamily which can be viewed as a Bianchi type V bac kground with a gravitational wave traveling orthogonally to the surfaces of transitivity of the G(2) group. This wave generates the inhomogeneity of t he spacetime and is related to the sound waves tilting the perfect fluid. I t seems to be the first explicit exact trample of a gravitational wave trav eling along a homogeneous background that has a realistic equation of state p = rho /3.