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We explore the mechanics of inflation in simplified extra-dimensional modelsinvolving an inflaton interacting with the Einstein-Maxwell system in two extradimensions. The models are Goldilocks-like in that they are just complicatedenough to include a mechanism to stabilize the extra-dimensional size, yetsimple enough to solve the full 6D field equations using basic tools. Thesolutions are not limited to the effective 4D regime with H << m_KK (the latterreferring to the mass splitting of the Kaluza-Klein excitations) because thefull 6D Einstein equations are solved. This allows an exploration ofinflationary physics in a controlled regime away from the usual 4D lamp-post.The inclusion of modulus stabilization is important as experience with stringmodels teaches that this is usually what makes models fail: stabilizationenergies dominate the shallow potentials required by slow roll and open updirections to evolve that are steeper than those of the putative inflationarydirection. We explore three representative inflationary scenarios within thissimple setup. In one the radion is trapped in an inflaton-dependent localminimum whose non-zero energy drives inflation. Inflation ends as this energyrelaxes to zero when the inflaton finds its minimum. The others involvepower-law solutions during inflation. One is an attractor whose features arerelatively insensitive to initial conditions but whose slow-roll parameterscannot be arbitrarily small; the other is not an attractor but can roll muchmore slowly, until eventually decaying to the attractor. These solutions cansatisfy H > m_KK, but when they do standard 4D fluctuation calculations neednot apply. When in a 4D regime the solutions predict eta ~ 0 hence r ~ 0.11when n_s ~ 0.96 and so are ruled out if tensor modes remain unseen. Analysis ofgeneral parameters is difficult without a full 6D fluctuation calculation.

Goldilocks Models of Higher-Dimensional Inflation (including modulus stabilization)