Inflation from (R+γRn-2 Λ) gravity in higher dimensions

We propose a derivation of the inflaton scalar potential from the higher (D) dimensional (R+γRn-2Λ) gravity, with the new coupling constant γ and the cosmological constant Λ. We assume that a compactification of extra dimensions happened before inflation, so that the inflaton scalar potential in four spacetime dimensions appears to be dependent upon the parameters (γ,Λ,D,n). We find that phenomenology and consistency require n=D/2, while the dimension D has to be a multiple of four. We calculate the potential for any D, and determine the values of γ and Λ from observations. The cases of D=8 and D=12 are considered in more detail. Our approach results in the viable models of chaotic large-field inflation, and leads to the sharp predictions of an observable value of the tensor-to-scalar ratio r of the cosmic microwave background radiation.