We present a detailed study of inflationary solutions in M theory with higher order quantum corrections. We first exhaust all exact and asymptotic solutions of exponential and power-law expansions in this theory with quartic curvature corrections, and then perform a linear perturbation analysis around fixed points for the exact solutions in order to see which solutions are more generic and give interesting cosmological models. We find an interesting solution in which the external space expands exponentially and the internal space is static both in the original and Einstein frames. Furthermore, we perform a numerical calculation around this solution and find numerical solutions which give enough $e$-foldings. We also briefly summarize similar solutions in type II superstrings.

• Received 24 February 2006

DOI:https://doi.org/10.1103/PhysRevD.73.103506