Cosmological solutions with Calabi-Yau compactification

Assuming a Calabi-Yau compactification, cosmological solutions are presented in ten-dimensional, N=1 Yang-Mills supergravity theory with the curvature squared term (R²_μνϱσ −4R_μν² + R²). In a vacuum state, Kasner-type soluti ons exist as well as (four-dimensional Minkoswki space-time)×(a Calabi-Yau space). In the later stage of the universe the (four-dimensional Friedmann universe)×(a constant Calabi-Yau space) is realized asymptotically like an attractor. This solution is asymptotically stable against small perturbations.