Four-year COBE normalization of inflationary cosmologies

Abstract

We supply fitting formulae enabling the normalization of slow-roll inflation models to the four-year COBE data. We fully include the effect of the gravitational wave modes, including the predicted relation of the amplitude of these modes to that of the density perturbations. We provide the normalization of the matter power spectrum, which can be directly used for large-scale structure studies. The normalization for tilted spectra is a special case. We also provide fitting functions for the inflationary energy scale of COBE-normalized models and discuss the validity of approximating the spectra by power-laws. In an Appendix, we extend our analysis to include models with a cosmological constant, both with and without gravitational waves.