A Horizon Ratio Bound for Inflationary Fluctuations

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Abstract
Inflation predicts a spectrum of scalar and tensor perturbations that can be tested by present cosmological observations. The precise nature of this spectrum depends on, among other things, the amount of expansion between the time the scales of interest leave the horizon and the end of inflation. The scale factor grows by e^N between these two times. Here we point out that N is bounded from above by considering the ratio of the horizon at the end of inflation to the present horizon. Adding this bound to the constraints on the amplitude of the primordial gravity wave spectrum leads to the model-independent bound: N < 60, for the scale k = 0.002/Mpc, with a logarithmic correction for other scales. This bound should be incorporated when confronting inflationary models with observations. Its implications on the observable quantities are model dependent -- we describe them for small field, large field and hybrid models. As an example, we show that chaotic inflation with a \phi^4 potential is indeed ruled out by recent observations of anisotropies in the cosmic microwave background and large scale structure.

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