Boundary Inflation

TL;DR

This work analyzes inflation in a five-dimensional heterotic M-theory setup with two orbifold boundaries, focusing on inflation driven by boundary potentials. It develops the 5D action and its 4D effective reduction, then explores linear and nonlinear regimes defined by the KK excitation strength $\epsilon_i$, showing that linear boundary inflation maps to conventional 4D supergravity with small KK corrections, while nonlinear dynamics yield a rich set of 5D inflating solutions with horizons or potential instabilities. The study demonstrates how boundary energy sources inherently excite bulk modes and leave imprint on the extra dimension, and it highlights stability and modulus stabilization as crucial for viable nonlinear inflation. It concludes that, in models with more than one large dimension, linear (conventional) inflation is the most robust route, though the nonlinear regime offers intriguing, albeit challenging, alternative scenarios tied to the orbifold modulus stabilization.

Abstract

Inflationary solutions are constructed in a specific five-dimensional model with boundaries motivated by heterotic M-theory. We concentrate on the case where the vacuum energy is provided by potentials on those boundaries. It is pointed out that the presence of such potentials necessarily excites bulk Kaluza-Klein modes. We distinguish a linear and a non-linear regime for those modes. In the linear regime, inflation can be discussed in an effective four-dimensional theory in the conventional way. We lift a four-dimensional inflating solution up to five dimensions where it represents an inflating domain wall pair. This shows explicitly the inhomogeneity in the fifth dimension. We also demonstrate the existence of inflating solutions with unconventional properties in the non-linear regime. Specifically, we find solutions with and without an horizon between the two boundaries. These solutions have certain problems associated with the stability of the additional dimension and the persistence of initial excitations of the Kaluza-Klein modes.

Figures (1)

• Figure 1: Parts of Minkowski space corresponding to the solution in case 1 (left figure) and case 2 (right figure).