Hybrid inflation with Planck scale fields

Journal of High Energy Physics, Sep 2015

Abstract Observable B-mode polarization in the CMBR would point to a high scale of inflation and large field excursions during the inflationary era. Non-compact string moduli spaces are a suggestive setting for these phenomena. Although they are unlikely to be described by weak coupling models, effective field theories compatible with known features of cosmology do exist. These models can be viewed as generalizations to a large field regime of hybrid inflation. We note close parallels to small and large field axion models. This paper outlines the requirements for successful modular inflation, and gives examples of effective field theories which satisfy them. The required tunings are readily characterized. These models can also be thought of as models of chaotic inflation, in a way we describe. In the modular framework, one would expect that any would-be Peccei-Quinn symmetry would likely be badly broken during inflation, and the axion would have Hubble scale mass; in this situation, isocurvature fluctuations would be suppressed and the initial misalignment angle would be fixed, rather than being a random variable.

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Hybrid inflation with Planck scale fields

Received: December Hybrid inflation with Planck scale fields Santa Cruz 0 CA 0 U.S.A. 0 Open Access 0 c The Authors. 0 0 Santa Cruz Institute for Particle Physics and Department of Physics Observable B-mode polarization in the CMBR would point to a high scale of inflation and large field excursions during the inflationary era. Non-compact string moduli spaces are a suggestive setting for these phenomena. Although they are unlikely to be described by weak coupling models, effective field theories compatible with known features of cosmology do exist. These models can be viewed as generalizations to a large field regime of hybrid inflation. We note close parallels to small and large field axion models. This paper outlines the requirements for successful modular inflation, and gives examples of effective field theories which satisfy them. The required tunings are readily characterized. These models can also be thought of as models of chaotic inflation, in a way we describe. In the modular framework, one would expect that any would-be Peccei-Quinn symmetry would likely be badly broken during inflation, and the axion would have Hubble scale mass; in this situation, isocurvature fluctuations would be suppressed and the initial misalignment angle would be fixed, rather than being a random variable. Cosmology of Theories beyond the SM; Superstring Vacua - Small vs. large field inflation Hybrid inflation: small field and large field Small field and large field solutions to the strong CP problem A remark on distances in the modulus geometry Non-compact moduli as inflatons Effective theories for modular inflation The effective action on the moduli space Stabilizing moduli in the current universe Stabilizing moduli during inflation Requirements for the transition period 6 Inflationary models: large r Connection to chaotic inflation Moduli inflation: small r Small vs. large field inflation Models of slow roll inflation can be divided into two broad categories: small field and large field, where the small or large is relative to the Planck scale, Mp (there are many good reviews; on this point, see, for example, [1]). These two classes of theories differ dramatically in whether or not they predict observable gravity waves. Each class of models poses in fact, quite clear in what framework (outside of some larger theory of quantum gravity) one might understand such theories. As we will review, small field models also cannot be completely understood without a complete underlying theory of gravity. That said, the problem of inflation in these theories can be described by a small number of parameters. The BICEP2 announcement of the possible observation of gravity waves in the CMB [2] brought the question of large vs small field inflation to the forefront. While there is no longer any claim to an observation [3], there are intense efforts to further constrain (or observe) B mode polarization in the CMBR. The BICEP2 result was suggestive of an energy sale of inflation would be about 2 × 1016 GeV; Planck set limits of order 1/2 of this [4]. A great deal has been written on the subject of large field inflation, trying to accommodate the original BICEP2 claim, and suggesting, in any case, that such radiation should be observable. This work can again be divided into two broad categories (with some overlap): natural inflation [5] and chaotic inflation [6]. Natural inflation involves axion-like fields, with decay constants larger than Mp. Because such decay constants seem hard to realize in string theory [7], much work has focussed on monodromy inflation and its variants (though see [8]), in which axions transit many times their nominal periods [9], or theories with multiple axions (or fields which can wander circuitously through field space) [10]. Chaotic inflation involves fields with monomial potentials with very small coefficients. As implemented in [9], monodromy inflation is actually a realization of chaotic inflation, with a monomial potential for the inflaton. It is argued that the features of the inflaton potential, in this case, can be understood within an ultraviolet complete theory, string theory. Related ideas for achieving inflation have been considered in [11–13]. In this note, we examine a different arena for inflation: non-compact string moduli spaces. Classically, string compactifications with zero cosmological constant (c.c.) typically exhibit moduli of various sorts. Such light fields might exist quantum mechanically. One possible explanation for this is low energy supersymmetry, where the light non-compact moduli would be superpartners of axions. We will take this as our working model throughout this paper.1 By low we mean that during inflation, the soft breaking terms, while possibly quite large compared to the scale at which supersymmetry is ultimately broken, are well below the energy scale of inflation. Supersymmetry breaking during inflation has been discussed in [15], where it is stressed that, (...truncated)


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Michael Dine, Laurel Stephenson-Haskins. Hybrid inflation with Planck scale fields, Journal of High Energy Physics, 2015, pp. 208, Volume 2015, Issue 9, DOI: 10.1007/JHEP09(2015)208