Most models of inflation in the early universe are based on scalar fields appearing in superstring and supergravity theories. Meanwhile, the first inflation model proposed by Starobinsky  is related to the conformal anomaly in quantum gravity3. Unlike the models such as “old inflation” [339, 291, 524] this scenario is not plagued by the graceful exit problem – the period of cosmic acceleration is followed by the radiation-dominated epoch with a transient matter-dominated phase [565, 606, 426]. Moreover it predicts nearly scale-invariant spectra of gravitational waves and temperature anisotropies consistent with CMB observations [563, 436, 566, 355, 315]. In this section we review the dynamics of inflation and reheating. In Section 7 we will discuss the power spectra of scalar and tensor perturbations generated in f (R) inflation models.
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