Post-COBE predictions for Inflationary Gravity Wave and Density Perturbation spectra

Abstract

We assess the relative contribution to the COBE - measured microwave anisotropy arising both from relic gravity waves as well as primordial density perturbations originating during inflation. We show that the gravity wave contribution to the CMBR anisotropy depends sensitively upon $n$ -- the primordial spectral index ($\dk^2 \propto k^n$), increasing as $n$ deviates from a Harrison - Zeldovich spectrum (n = 1). As a result, for $n < 0.84$ the contribution from gravity waves towards $δT/ T $ is greater than the corresponding contribution from density perturbations, whereas for $n > 0.84$ the reverse is true. ($ n = 0.84$ corresponds to an expansion index $p = 13.5$ in models with power-law inflation $a \propto t^p$. ) Our results show that for a scale-invariant Harrison-Zeldovich spectrum generated by chaotic inflation, gravity waves contribute approximately $24\%$ to the CMBR anisotropy measured by COBE. Applying our results to the cold dark matter scenario for galaxy formation, we find that in general CDM models with tilted power spectra ($n < 1$), require the biasing parameter to be greater than unity, on scales of $16h_{50}^{-1} Mpc$. We also obtain an expression for the COBE - normalised amplitude and spectrum of the stochastic gravity wave background and compare it with the sensitivity of planned laser-interferometer gravity wave detectors.