We review a possible origin of cosmological inflation from higher ( D ) spacetime dimensions in the context of modified gravity theory. It is demonstrated that it requires a spontaneous warped compactification of higher ( D ) spacetime dimensions together with the stabilization of extra ( D − 4 ) dimensions by Freund–Rubin mechanism. The relevant tools include an extra gauge ( D / 2 − 1 ) -form field with a non-vanishing flux in compact dimensions and a positive cosmological constant in D

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... ions. Those features are illustrated on the specific example in eight spacetime dimensions compactified on a four-sphere with a warped factor and a flux, which leads to a viable Starobinsky-like inflationary model in four (non-compact) spacetime dimensions.