Inflation from superstring and M-theory compactification with higher order corrections

We study time-dependent solutions in M and superstring theories with higher-order corrections. We first present general field equations for theories of Lovelock type with stringy corrections in arbitrary dimensions. We then exhaust all exact and asymptotic solutions of exponential and power-law expansions in the theory with Gauss-Bonnet terms relevant to heterotic strings and in the theories with quartic corrections corresponding to the M theory and type II superstrings. We discuss interesting inflationary solutions that can generate enough e foldings in the early universe.