Graviton Production in Elliptical and Hyperbolic Universes

Abstract

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 $\gamma \ne \frac{2}{3}\frac{(2n+1)}{(2n-1)}$, 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.

25 pages, uses REVTEX

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Cited by in corpus (8)

• Primordial backgrounds of relic gravitons
• Quantized fields and gravitational particle creation in f(R) expanding universes
• Primordial Gravitational Waves From Open Inflation
• MAX 4 and MAX 5 CMB anisotropy measurement constraints on open and flat-Lambda CDM cosmogonies
• Primordial Gravitational Waves in Running Vacuum Cosmologies
• Electromagnetic potentials in curved spacetimes
• Production of primordial gravitational waves in a simple class of running vacuum cosmologies
• Cosmological gravitons and the expansion dynamics during the matter age