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Journal Articles Physical Review D Year : 2006

Clarifying inflation models: Slow roll as an expansion in 1/Nefolds

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Slow-roll inflation is studied as an effective field theory. We find that the form of the inflaton potential consistent with Wilkinson Microwave Anisotropy Probe (WMAP) data and slow roll is V(varphi)=NM4w((varphi)/(NMPl)), where varphi is the inflaton field, M is the inflation energy scale, and Ñ50 is the number of e-folds since the cosmologically relevant modes crossed the Hubble radius until the end of inflation. The inflaton field scales as varphi=NMPlchi. The dimensionless function w(chi) and field chi are generically O(1). The WMAP value for the amplitude of scalar adiabatic fluctuations |Deltakad(S)|2 fixes the inflation scale M˜0.77×1016. This form of the potential makes manifest that the slow-roll expansion is an expansion in 1/N. A Ginzburg-Landau realization of the slow-roll inflaton potential reveals that the Hubble parameter, inflaton mass and nonlinear couplings are of the seesaw form in terms of the small ratio M/MPl. For example, the quartic coupling lambda˜(1)/(N)((M)/(MPl))4. The smallness of the nonlinear couplings is not a result of fine-tuning but a natural consequence of the validity of the effective field theory and slow-roll approximation. We clarify Lyth's bound relating the tensor/scalar ratio and the value of varphi/MPl. The effective field theory is valid for V(varphi)≪MPl4 for general inflaton potentials allowing amplitudes of the inflaton field varphi well beyond MPl. Hence bounds on r based on the value of varphi/MPl are overly restrictive. Our observations lead us to suggest that slow-roll, single field inflation may well be described by an almost critical theory, near an infrared stable Gaussian fixed point.
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hal-03724153 , version 1 (10-09-2022)



Daniel Boyanovsky, Hector J. de Vega, Norma G. Sánchez. Clarifying inflation models: Slow roll as an expansion in 1/Nefolds. Physical Review D, 2006, 73, pp.23008. ⟨10.1103/PhysRevD.73.023008⟩. ⟨hal-03724153⟩
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