A non linear multidimensional gravitational model R+R^(-1) with form fields and stabilized extra dimensions

We studied multidimensional gravitational models with scalar curvature nonlinearity of the type R -1 and with form fields (fluxes) as a matter source. It is assumed that the higher-dimensional space–time undergoes Freund–Rubin-like spontaneous compactification to a warped product manifold. It is shown that for certain parameter regions the model allows for freezing stabilization of the internal space near the positive minimum of the effective potential, which plays the role of the positive effective cosmological constant. However, the parameters of model should be fine tuned to obtain the observable dark energy.