Clarifying Inflation Models: Slow-roll as an expansion in 1/N_{efolds}

Abstract

Slow-roll inflation is studied as an effective field theory.We find as consistent form of the inflaton potential V(phi)=N M^4 w(phi/[sqrt{N}M_P]) where phi is the inflaton field, M the inflation energy scale, M_P the Planck mass, and N~50 the number of efolds since the relevant modes exited the horizon till the end of inflation. The dimensionless function w(chi) and field chi are O(1). The WMAP value for the amplitude of scalar adiabatic fluctuations |Δ_{k ad}^(S)| fixes the inflation scale M ~ 0.77 10^16 GeV precisely at the GUT scale. This general form of the potential makes manifest that the slow roll expansion is an expansion in 1/N. Powers of 1/N count the orders in the slow roll expansion.This form of the inflaton potential suggests that the super symmetry breaking scale is at the inflation and GUT scales.A Ginzburg-Landau realization of this inflaton potential reveals that Hubble, inflaton mass and non-linear couplings are of the see-saw form in terms of the small ratio M/M_P. For example, the quartic coupling lambda ~ 1/N (M/M_P)^4.The smallness of the non-linear couplings is not a result of fine tuning but a natural consequence of the validity of the effective field theory. We clarify the Lyth bound which relates the tensor/scalar ratio and the value of phi/M_P.Effective field theory is valid for V(phi)<<M_P^4 allowing inflaton fields phi well beyond M_P.Thus, no bounds based on the value of phi/M_P appear on r.In case one wishes to restrict oneself to chi < 1 in the above potential, values for r larger than the previous bounds are allowed thanks to the new factor sqrt{N}~7.Finally,it is conjectured that inflation is hovering near a trivial gaussian infrared fixed point during slow roll. Slow-roll inflation would then enjoy universality properties as those of critical phenomena.

arXiv comment14 pages, no figures, version to appear in Phys Rev D

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