Higher-dimensional cosmology with Gauss-Bonnet terms and the cosmological-constant problem

Cosmological solutions of field equations derived from a ten-dimensional (10D) action containing higher-derivative terms in the Gauss-Bonnet combination have been studied. An attempt has been made to construct a scenario which includes a spontaneous compactification and an inflationary epoch followed by a four-dimensional radiation-dominated stage. It is noted that one can have a realistic scenario, provided there is an inflationary stage of the early 10D universe. A mechanism is suggested which makes the 4D cosmological constant small. The action considered is different from the superstring-corrected action. The study reveals a rich structure of the theory due to the presence of Gauss-Bonnet terms, although one gets back the usual Einstein equation in 4D at a large time.