Analytic Solution of the Starobinsky Model for Inflation

Understand

We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lema\^{\i}tre-Robertson-Walker constitute an integrable system as the field equations pass the singularity test.

• The analytical solution in terms of a Painlev\'{e} Series for the Starobinsky model is presented for the case of zero and nonzero spatial curvature.
• In both cases the leading-order term describes the radiation era provided by the corresponding higher-order theory.