Simple exercises to flatten your potential

Abstract

We show how backreaction of the inflaton potential energy on heavy scalar fields can flatten the inflationary potential, as the heavy fields adjust to their most energetically favorable configuration. This mechanism operates in previous UV-complete examples of axion monodromy inflation - flattening a would-be quadratic potential to one linear in the inflaton field - but occurs more generally, and we illustrate the effect with several examples. Special choices of compactification minimizing backreaction may realize chaotic inflation with a quadratic potential, but we argue that a flatter potential such as power-law inflation $V(\phi) \propto \phi^p$ with $p<2$ is a more generic option at sufficiently large values of $\phi$.Comment: 20 pages, 2 figures. v2: new references adde

Inflation in string theory confronts data

“…The direction it goes fits very well with basic expectations from the point of view of UV completing gravity [12]: adjustments of heavy fields involved in the UV completion tend to flatten the potential since that is energetically favorable. It is worth emphasizing that this might be expected in any UV completion of gravity, since new degrees of freedom would be expected to take over at or below the Planck scale where the gravitational coupling becomes strong.…”

“…One basic question is whether it has simply been a coincidence that the predictions originally landed within the viable region of r and n s and remain so at the present writing. Starting from the quadratic model, we had explained this improvement of fit in a simple way above via the energetically favorable flattening effect [12]. But as described in [20] and [19], there exist couplings in the theory which admit a starting (un-backreacted) power V ∝ φ n with higher n. In fact, n is in principle unbounded, taking into account that perturbative string theory can be formulated in any total dimensionality D, as long as one properly accounts for the tree level potential energy ∝ (D−10)g 2 ef f , with g ef f the four-dimensional effective string coupling.…”

“…This mechanism descends in a robust way from higher dimensional gauge potentials and their couplings to magnetic fluxes, as well as various analogues related by string duality symmetries. Examples of this mechanism predict potentials flattened [12][20] [19] compared to fiducial monomial forms φ n (and with small oscillatory features derived from the underlying periodicity of the theory in axionic directions). For n = 2, the adjustments of heavy fields typically produce a potential of the form φ p<2 (for the single field version of the mechanism).…”

Inflation and String Theory

“…In particular, given sufficiently high barriers around a local minimum of the moduli potential, a time-dependent inflationary energy can induce evolution of the moduli within the basin of attraction of the minimum. Incorporating the motion of the moduli can then change the form of the inflaton potential, as in the rather general flattening mechanism of [532]. 16 Thus, although shifts of the moduli do not necessarily end inflation, their effects must be taken into account.…”

“…A general mechanism known as flattening [532] can affect the asymptotic form of the scalar potential for a light field φ in the presence of additional heavy fields Ψ. Given appropriate couplings of φ to Ψ, integrating out Ψ flattens V (φ) at large φ, in the sense of reducing the exponent p. It was argued in [532] that the linear potential of (5.161) is an example of flattening: the type IIB action includes terms proportional to 163) which naively give rise to an energy that is quadratic in φ ∝ C 2 , but the actual potential (5.161) is linear. The claim of [532] is that backreaction of localized D3-brane charge, which shifts the moduli vevs, is responsible for the flattening from p = 2 to p = 1.…”