Scale Dependent Spectral Index in Slow Roll Inflation

Abstract

Recent observations suggest that the spectral index of the primordial perturbations is very close to unity, as expected in models of slow roll inflation. It is still possible for such models to produce spectra which are scale dependent. We present a formula for the spectrum produced by an arbitrary inflaton potential (within the context of slow roll models); this formula explicitly illustrates and accounts for the possiblity of scale dependence. A class of examples are studied and comparisons made with the standard slow roll formula.

Figures (1)

• Figure 1: Power spectrum of the gravitational potential in two inflationary models corresponding to potentials of the form in Eq. (\ref{['pot']}). $k_*$ is a fiducial wavenumber depending on the dynamics of the inflaton. The Harrison-Zel'dovich spectrum is flat. The thick solid line is the result of Eq. (\ref{['final']}); the thin line is the standard slow roll approximation in which $Q\rightarrow 1$; and the dashed line is the assumption of no running. The top panel has parameters $\lambda=0.03,\nu=1/\lambda$ while the bottom has $\nu = 7,\lambda=0.3$. In both cases, $A=\lambda^3/\nu$.