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

We study time-dependent solutions in Mand 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.