3 Inflation in f (R) Theories

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 [564Jump To The Next Citation Point] is related to the conformal anomaly in quantum gravity3. Unlike the models such as “old inflation” [339291524] 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 [565Jump To The Next Citation Point606Jump To The Next Citation Point426Jump To The Next Citation Point]. Moreover it predicts nearly scale-invariant spectra of gravitational waves and temperature anisotropies consistent with CMB observations [563436Jump To The Next Citation Point566Jump To The Next Citation Point355Jump To The Next Citation Point315Jump To The Next Citation Point]. 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: ξ = 0 and m χ = 0
  3.3.2 Case: |ξ| ≳ 1

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