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Clarifying inflation models: The precise inflationary potential from effective field theory and the WMAP data

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Cirigliano, D., de Vega, H. J., Sanchez, N. G.·2005·Physical Review D
DOI 10.1103/physrevd.71.103518
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Abstract

We clarify inflaton models by considering them as effective field theories in the Ginzburg-Landau 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 ${\ensuremath{\phi}}^{4}$ potential implies the presence of an inflaton mass term at the scale $m\ensuremath{\sim}{10}^{13}\text{ }\text{ }\mathrm{GeV}$. Chaotic, new and hybrid inflation models are studied in an unified way. In all cases the inflaton potential takes the form $V(\ensuremath{\phi})={m}^{2}{M}_{\mathrm{Pl}}^{2}v(\ensuremath{\phi}/{M}_{\mathrm{Pl}})$, where all coefficients in the polynomial $v(\ensuremath{\varphi})$ are of order one. If such potential corresponds to supersymmetry breaking, the corresponding susy breaking scale is $\sqrt{m{M}_{\mathrm{Pl}}}\ensuremath{\sim}{10}^{16}\text{ }\text{ }\mathrm{GeV}$ which turns to coincide with the grand unification (GUT) scale. The inflaton mass is therefore given by a seesaw formula $m\ensuremath{\sim}{M}_{\mathrm{GUT}}^{2}/{M}_{\mathrm{Pl}}$. The observables turn to be two-valued 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 ($|1\ensuremath{-}{n}_{s}|\ensuremath{\lesssim}0.1,r\ensuremath{\lesssim}0.1$) 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: ${10}^{6}(m/{M}_{\mathrm{Pl}})=127\sqrt{r|1\ensuremath{-}{n}_{s}|}$ where the numerical coefficient is fixed by the WMAP amplitude of adiabatic perturbations. Implications for string theory are discussed.

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  • The standard model of particle physics has the main ingredients for baryogenesis.

    “Notably, the standard model of particle physics has the main ingredients for baryogenesis[45, 48]:”

    From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [48]

  • An alternative scenario for baryogenesis proposes that a primordial asymmetry between leptons and antileptons, or leptogenesis, is responsible for generating the baryon asymmetry.

    “An alternative scenario for baryogenesis proposes that a primordial asymmetry between leptons and antileptons or leptogenesis is responsible for generating the baryon asymmetry[48, 59].”

    From Phase Transitions in the Early and Present Universe (2006) · cites this paper as [48]

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Authors
Cirigliano, D., de Vega, H. J., & Sanchez, N. G.
Affiliations
Centre National de la Recherche Scientifique (FR)
ORCID
Sanchez, N. G.
Venue
Physical Review D
Publisher
American Physical Society (APS)
Published
2005-05-23
Volume
71
Issue
10
Pages
103518
ISSN
  • 0556-2821 (ISSN-L)
  • 1550-7998
  • 1550-2368
DOI
10.1103/physrevd.71.103518
OpenAlex
W4301936057
Cited by
24
References
47
Citations by year
2026: 1 · 2024: 2 · 2023: 1 · 2021: 1 · 2019: 1
FWCI
2.91
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields (publishedVersion)
  • HAL (submittedVersion, other-oa)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Particle physics theoretical and experimental studies
Keywords
cosmic inflation, inflaton potential, effective field theory, Ginzburg-Landau theory, WMAP data, chaotic inflation, new inflation, hybrid inflation, inflaton mass, supersymmetry breaking scale, unification scale, seesaw mechanism, spectral index, tensor-to-scalar ratio, adiabatic perturbations, string theory

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