The Starobinsky model of inflation, consistent with Planck 2015, has a peculiar form of the action, which contains the leading Einstein term R, the R^2 term with a huge coefficient, and negligible higher order terms. We propose an explanation of this form based on compactification of extra dimensions. Once tuning of order 10^(-4) is accepted to suppress the linear term R, we no more have to suppress higher order terms, which give nontrivial corrections to the Starobinsky model. We show our predictions of the spectral index, its running, and the tensor-to-scalar ratio. Finally, we discuss quantum gravity may appear at the scale greater than O(10^16) GeV.
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