Poly-instanton inflation

Abstract

Abstract. We propose a new inflationary scenario in type IIB Calabi-Yau compactifications, where the inflaton is a Kähler modulus parameterising the volume of an internal four-cycle. The inflaton potential is generated via poly-instanton corrections to the superpotential which give rise to a naturally flat direction due to their double exponential suppression. Given that the volume mode is kept stable during inflation, all the inflaton-dependent higher dimensional operators are suppressed. Moreover, string loop effects can be shown to be negligible throughout all the inflationary dynamics for natural values of the underlying parameters. The model is characterised by a reheating temperature of the order T rh ≃ 10 6 GeV which requires N e ≃ 54 e-foldings of inflation. All the inflationary observables are compatible with current observations since the spectral index is n s ≃ 0.96, while the tensor-to-scalar ratio is r ≃ 10 −5 . The volume of the Calabi-Yau is of order 10 3 in string units, corresponding to an inflationary scale around 10 15 GeV.

Inflation and String Theory

“…We give detailed analyses of N-flation [530] and axion monodromy inflation [34]. In §5.5, we describe models in which the inflaton is a Kähler modulus (or the associated axion), including racetrack inflation [618,619] and inflationary scenarios in large volume compactifications [43,620,621]. Finally, in §5.6, we look at dissipative effects as a source of inflation and critically assess the prospects for dissipative inflation in string compactifications [622][623][624][625].…”

“…We will describe three ways in which the inflaton potential is generated: i) via nonperturbative effects [620] ( §5.5.3), ii) via string loops [43] ( §5.5.4), and iii) via poly-instanton effects [621,783] ( §5.5.5).…”

“…[621] (see also [783]) constructed a model in which poly-instanton terms in the superpotential make a critical contribution to the scalar potential. A poly-instanton 81 effect arises when the Euclidean action S a of an instanton a receives corrections from a second instanton b [787] (see also the earlier work [788]), so that 232) where the moduli-dependent prefactors A a and A b are one-loop determinants.…”

“…A poly-instanton 81 effect arises when the Euclidean action S a of an instanton a receives corrections from a second instanton b [787] (see also the earlier work [788]), so that 232) where the moduli-dependent prefactors A a and A b are one-loop determinants. 82 Setup.-The compactification geometry assumed in [621] is the same as in §5.5.4; in particular, the compactification volume is given by (5.225),…”

“…This time, the flat direction is lifted by the poly-instanton contributions in (5.236). As before, one can consistently integrate out V and τ s , as well as the axion partners of all Kähler moduli (see [621] for details). The scalar potential for the distance from the minimum in the τ 1 direction, i.e.τ 1 ≡ τ 1 − τ 1 , is found to be 237) where F poly ≡ O(1)×W 0 and p = O(1).…”