Clarifying inflation models: The precise inflationary potential from effective field theory and the WMAP data
Abstract
We clarify inflaton models by considering them as effective field theories in the GinzburgLandau spirit. In this new approach, the precise form of the inflationary potential is constructed from the present WMAP data, and a useful scheme is prepared to confront with the forthcoming data. In this approach, the WMAP statement excluding the pure ϕ^{4} potential implies the presence of an inflaton mass term at the scale m∼10^{13} GeV. Chaotic, new and hybrid inflation models are studied in an unified way. In all cases the inflaton potential takes the form V(ϕ)=m^{2}M^{2}_{Pl}v(ϕ/M_{Pl}), where all coefficients in the polynomial v(φ) are of order one. If such potential corresponds to supersymmetry breaking, the corresponding susy breaking scale is √(mM_{Pl})∼10^{16} GeV which turns to coincide with the grand unification (GUT) scale. The inflaton mass is therefore given by a seesaw formula m∼M^{2}_{GUT}/M_{Pl}. The observables turn to be twovalued functions: one branch corresponds to new inflation and the other to chaotic inflation, the branch point being the pure quadratic potential. For red tilted spectrum, the potential which fits the best the present data (1n_{s}≲0.1,r≲0.1) and which best prepares the way for the forthcoming data is a trinomial polynomial with negative quadratic term (new inflation). For blue tilted spectrum, hybrid inflation turns to be the best choice. In both cases we find an analytic formula relating the inflaton mass with the ratio r of tensor to scalar perturbations and the spectral index n_{s} of scalar perturbations: 10^{6}(m/M_{Pl})=127√(r1n_{s}) where the numerical coefficient is fixed by the WMAP amplitude of adiabatic perturbations. Implications for string theory are discussed.
 Publication:

Physical Review D
 Pub Date:
 May 2005
 DOI:
 10.1103/PhysRevD.71.103518
 arXiv:
 arXiv:astroph/0412634
 Bibcode:
 2005PhRvD..71j3518C
 Keywords:

 98.80.Cq;
 11.10.z;
 98.70.Vc;
 Particletheory and fieldtheory models of the early Universe;
 Field theory;
 Background radiations;
 Astrophysics;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology;
 High Energy Physics  Theory
 EPrint:
 LaTeX, 33 pages, 24 .ps figures. Improved version published in Phys Rev D