Naturally inflating on steep potentials through electromagnetic dissipation

Abstract

In models of natural inflation, the inflaton is an axion-like particle. Unfortunately, axion potentials in UV-complete theories appear to be too steep to drive inflation. We show that, even for a steep potential, natural inflation can occur if the coupling between axion and gauge fields is taken into account. Due to this coupling, quanta of the gauge field are produced by the rolling of the axion. If the coupling is large enough, such a dissipative effect slows down the axion, leading to inflation even for a steep potential. The spectrum of perturbations is quasi-scale invariant, but in the simplest construction its amplitude is larger than 10 −5 . We discuss a possible way out of this problem.PACS numbers: 98.80.CqAxion-like particles are the simplest spin-zero degrees of freedom with a nontrivial radiatively stable potential. Moreover, they are abundant in string theory. As a consequence, axions provide excellent inflaton candidates in a UV complete theory that includes gravity. Inflation driven by axions was proposed as early as in 1990 as natural inflation [1]. The axion potential is radiatively stable thanks to a (broken) shift symmetry, and has the form V (Φ) = Λ 4 [cos(Φ/f ) + 1], where f is the axion constant. Neglecting all interactions of Φ apart from those in V (Φ) and those with gravity, the condition for inflation is that V (Φ) is flat in units of the Planck scale (i.e.,for a sufficiently wide range of Φ. In the case of the axion, these conditions are equivalent to f ≫ M P . Unfortunately, string theory appears not to allow such large values of f [2]. Moreover, f < ∼ M P appears also as a consequence of the "gravity as the weakest force" conjecture of [3].In this paper, we show that natural inflation can be realized also for a steep potential. Our mechanism relies on the coupling of the inflaton to gauge fields through the operator Φ F µνF µν . As Φ rolls down its potential, it provides a time-dependent background for the gauge field whose vacuum fluctuations are thus amplified into physical excitations. This production of quanta of gauge field occurs at the expenses of the kinetic energy of the inflaton, slowing it down. If the coupling between Φ and F µν is strong enough, such a dissipation effect can allow to obtain a sufficiently long period of inflation even if f ≪ M P . This way, the question of finding natural inflation in string theory is formulated in a new way: is there, among the many axions of string theory [4], one whose coupling to the gauge fields is large enough? We will argue in Appendix B that the answer to this question might be positive.

Inflation and String Theory

“…65 We will assume α ≤ 1. The case α 1 is discussed in [767], while estimates for α in type IIB string theory appear in [759]. Both bottom-up and top-down naturalness of the regime α 1 remain to be established.…”

“…Most of the power in the produced gauge field is in modes with (8ξ) −1 < k/(aH) < 2ξ. In this regime, the solution can be written as [767] A…”

“…It is natural to ask whether dissipation through production of gauge fields can slow φ sufficiently to give inflation. In [767], it was shown a successful inflationary period with phenomenologically viable perturbations requires large couplings, α i ∼ O(100), to a large number of gauge fields, N ∼ 10 5 . The top-down naturalness of this mechanism remains to be established, and in particular no complete string theory realization has been constructed.…”

“…Suppose first [767] that the inflaton is an axion φ that couples to N U (1) gauge fields A i via the standard axionic coupling…”

“…85 An effective field theory of dissipative inflation was constructed in [793]. Related work on warm inflation [794] is reviewed in [795] (see also [767,796]). …”