M-Theory Inflation from Multi M5-Brane Dynamics

TL;DR

This work derives inflation from heterotic M-theory by leveraging assisted inflation from N M5-branes whose inter-brane open-membrane instanton interactions yield exponential potentials that are collectively flat enough. After equidistant-nearest-neighbor domination, the M5-brane distance modes map to a single canonical field with a power-law inflationary expansion a(t) ∝ t^{p(N)} where $p(N) = 4N(N^2-1)/(3Qt)$ and $n = 1 - 2/p$. Observables are compatible with data for moderate N, e.g., with $N \approx 89$ giving $p \approx 100$, $n \approx 0.98$, and $N_e \approx 345$. Inflation ends when brane separations grow and branes dissolve via small-instanton transitions, with gaugino condensation stabilizing the orbifold modulus T and reheating the visible sector. This provides a concrete M-theory inflation scenario linking brane dynamics to observable inflationary predictions and end-states.

Abstract

We derive inflation from M-theory on S^1/Z_2 via the non-perturbative dynamics of N M5-branes. The open membrane instanton interactions between the M5-branes give rise to exponential potentials which are too steep for inflation individually but lead to inflation when combined together. The resulting type of inflation, known as assisted inflation, facilitates considerably the requirement of having all moduli, except the inflaton, stabilized at the beginning of inflation. During inflation the distances between the M5-branes, which correspond to the inflatons, grow until they reach the size of the S^1/Z_2 orbifold. At this stage the M5-branes will reheat the universe by dissolving into the boundaries through small instanton transitions. Further flux and non-perturbative contributions become important at this late stage, bringing inflation to an end and stabilizing the moduli. We find that with moderate values for N, one obtains both a sufficient amount of e-foldings and the right size for the spectral index.

Figures (3)

• Figure 1: The realization of new inflation (left figure) requires an extremely flat potential in the direction of the modulus ${\cal{M}}$ playing the role of the inflaton. This ensures that the ${\cal{M}}$ kinetic term is small and leads approximately to an exponential expansion $a(\mathsf{t})\sim e^{H\mathsf{t}}$ where $H\simeq \sqrt{U/3M_{Pl}^2}$. Necessarily the potential in all other moduli directions ${\cal{M}} _a$ has to be strongly curved upwards. In contrast, for the realization of assisted inflation (right figure) we use identical steeply decreasing exponential potentials for many moduli $Y_{ji}$ which serve as inflatons. The outcome is a power-law inflation $a(\mathsf{t})\sim \mathsf{t}^{p(N)}$. Since the potential in the $Y_{ji}$ directions are the steepest directions available during inflation, the universe will follow their path even if the potential has a mild runaway in some of the remaining moduli directions ${\cal{M}} _b$.
• Figure 2: At the beginning of the inflationary epoch, we assume all $N$ M5-branes to be grouped around some common location on the ${\mathbf{S}^1/\mathbf{Z}_2}$ interval such that the open membrane instanton interactions between the M5-branes dominate the potential.
• Figure 3: Inflation comes to an end when the distance between adjacent M5-branes has grown to a size comparable to the orbifold size itself. At this stage most of the M5-branes have coalesced with the boundaries through small instanton transitions. This reheats partly the visible boundary and therefore our universe.