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In this paper, we discuss a general method to obtain exact cosmologicalsolutions in modified gravity, to demonstrate the method it is employed toobtain exact cosmological solutions in $f(R,\phi)$ gravity. Here, we show that,given a particular evolution of the Universe, we could obtain different modelsof gravity that give that evolution, using the same construction. Further, weobtain an exact inflationary solution for Starobinsky action with a negligiblecosmological constant. This analysis helps us to have a better understanding ofStarobinsky inflation. With our analysis we could refine the parameter valuesand predictions of Starobinsky inflation. Also, we make an observation thatthere exist a no-go theorem for a bounce from Starobinsky action in the absenceof scalar fields or a cosmological constant.

Starobinsky inflation and its spin-offs in the light of exact solutions