Problem of inflation in nonlinear multidimensional cosmological models

Change of title : On the problem of inflation in nonlinear multidimensional cosmological models. We consider a multidimensional cosmological model with nonlinear quadratic R2 and quartic R4 actions. As a matter source, we include a monopole form field, a D-dimensional bare cosmological constant and the tensions of branes located at fixed points. In the spirit of the universal extra dimension model, the standard model fields are not localized on branes, but rather they can move in the bulk. We define conditions that ensure stable compactification of the internal space in zero minima of the effective potentials. Such effective potentials may have a rather complicated form with a number of local minima, maxima, and saddle points. We investigate inflation in such models. It is shown that the R2- and R4 models can produce up to 10 and 22 e-foldings, respectively. These values are not sufficient to solve the homogeneity and isotropy problem, but they are large enough to explain recent cosmic microwave background data. Additionally, the R4 model can provide conditions for eternal topological inflation. The main drawback of the obtained inflationary models consists in a spectral index ns that is less than the presently observed ns˜1. For the R4 model we find, e.g., ns˜0.61.