Graviton Production in Elliptical and Hyperbolic Universes

Details Graviton Production in Elliptical and Hyperbolic Universes Graviton Production in Elliptical and Hyperbolic Universes

1996-06-14

arxiv.org/abs/gr-qc/9606032v1

Phys.Rev. D54 (1996) 6111-6121

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, uses REVTEX

Scientific paper

10.1103/PhysRevD.54.6111

The problem of cosmological graviton creation for homogeneous and isotropic universes with elliptical ($\vae =+1$) and hyperbolical ($\vae =-1$) geometries is addressed. The gravitational wave equation is established for a self-gravitating fluid satisfying the barotropic equation of state $p=(\gamma -1)\rho$, which is the source of the Einstein's equations plus a cosmological $\Lambda$-term. The time dependent part of this equation is exactly solved in terms of hypergeometric functions for any value of $\gamma$ and spatial curvature $\vae$. An expression representing an adiabatic vacuum state is then obtained in terms of associated Legendre functions whenever $\gamma\neq \frac{2}{3}\; \frac{(2n+1)}{(2n-1)}$, where n is an integer. This includes most cases of physical interest such as $\gamma =0,\;4/3\;,1$. The mechanism of graviton creation is reviewed and the Bogoliubov coefficients related to transitions between arbitrary cosmic eras are also explicitly evaluated.

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