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 [564] is related to the conformal anomaly in quantum
gravity^{3}.
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.

3.1 Inflationary dynamics

3.2 Dynamics in the Einstein frame

3.3 Reheating after inflation

3.3.1 Case: and

3.3.2 Case:

3.2 Dynamics in the Einstein frame

3.3 Reheating after inflation

3.3.1 Case: and

3.3.2 Case:

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