Fibre inflation: observable gravity waves from IIB string compactifications

Abstract

We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential V = V 0 3 − 4e −φ/ √ 3 . Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient V 0 , and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of e -foldings, N e , and so are not independent: ε ≃ 3 2 η 2 . This implies similar relations among observables like the primordial scalar-to-tensor amplitude, r, and the scalar spectral tilt, n s : r ≃ 6(n s − 1) 2 . N e is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of T rh ≃ 10 9 GeV gives N e ≃ 58, corresponding to n s ≃ 0.970 and r ≃ 0.005, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kähler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kähler potential. The inflaton field is a combination of Kähler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class -'high-fibre models' -in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.

Poly-instanton inflation

“…However, as noticed in [15], the model of [14] is plagued by the η-problem since loop corrections dominate over the non-perturbative potential and spoil inflation.…”

“…In section 3 we first show how the poly-instanton corrections to the superpotential can generate a potential for the fibre modulus, and then we study its inflationary applications both analytically and numerically. In the same section we also present a detailed discussion of the η-problem stressing the similarities and the differences of our model with the previous ones developed in [14] and [15], where the inflaton was still a Kähler modulus. We finally conclude in section 4.…”

“…Notice that these g s corrections would spoil inflation in the region rather close to the minimum where the non-perturbative potential would give rise to slow-roll. On the other hand, in regions further away from the minimum, due to the 'extended no-scale structure', these perturbative loop corrections would actually drive inflation in a way very similar to [15].…”

Inflation and String Theory

“…30 See [368] for a study of the incidence of the form (3.123) in a class of Calabi-Yau manifolds. 31 As we will explain in §5.5.2, it has been suggested [43,367] that the leading g s correction to K, with form conjectured in [324] following computations in [322,323], can stabilize the N b − 1 flat directions. However, a more detailed demonstration of stability would be valuable.…”

“…The geometric perspective afforded by compactifications, and by D-branes moving inside them, complements the more algebraic tools used to construct effective theories in particle physics. The effective theories in D-brane inflation [41,42], DBI inflation [38], fibre inflation [43], and axion monodromy inflation [34], for example, all exist in their own right as low-energy theories, but would likely have gone undiscovered without the approach provided by string theory. Generating effective theories from the top down in string theory also leads to modified notions of what constitutes a natural inflationary model, or a minimal one.…”