Hybrid inflation with Planck scale fields
Received: December
Hybrid inflation with Planck scale fields
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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
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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)