Clarifying inflation models: Slow roll as an expansion in 1/N{sub efolds}

Journal Article · Sun Jan 15 04:00:00 EST 2006 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.73.0· OSTI ID:20795691

Boyanovsky, D ^[1]; Vega, H J. de ^[2]; Sanchez, N G ^[3]

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1. Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)
2. LPTHE, Laboratoire Associe au CNRS UMR 7589, Universite Pierre et Marie Curie (Paris VI) et Denis Diderot (Paris VII), Tour 24, 5 eme. etage, 4, Place Jussieu, 75252 Paris, Cedex 05 (France)
3. Observatoire de Paris, LERMA, Laboratoire Associe au CNRS UMR 8112, 61, Avenue de l'Observatoire, 75014 Paris (France)

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({phi})=NM{sup 4}w(({phi}/{radical}(N)M{sub Pl})), where {phi} is the inflaton field, M is the inflation energy scale, and N{approx}50 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 {phi}={radical}(N)M{sub Pl}{chi}. The dimensionless function w({chi}) and field {chi} are generically O(1). The WMAP value for the amplitude of scalar adiabatic fluctuations {delta}{sub kad}{sup (S)2} fixes the inflation scale M{approx}0.77x10{sup 16}. 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/M{sub Pl}. For example, the quartic coupling {lambda}{approx}(1/N)((M/M{sub Pl})){sup 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 {phi}/M{sub Pl}. The effective field theory is valid for V({phi})<<M{sub Pl}{sup 4} for general inflaton potentials allowing amplitudes of the inflaton field {phi} well beyond M{sub Pl}. Hence bounds on r based on the value of {phi}/M{sub Pl} 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.

• OSTI ID: 20795691
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 73; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
AMPLITUDES
ANISOTROPY
APPROXIMATIONS
COSMIC RADIATION
COSMOLOGY
COUPLING
FLUCTUATIONS
GINZBURG-LANDAU THEORY
INFLATIONARY UNIVERSE
NONLINEAR PROBLEMS
POTENTIALS
PROBES
QUANTUM FIELD THEORY
RELICT RADIATION
SCALARS
TENSORS