Analytic Solution of the Starobinsky Model for Inflation

Abstract

We prove that the field equations of the Starobinsky model for inflation in a Friedmann-Lema\^ıtre-Robertson-Walker constitute an integrable system as the field equations pass the singularity test. The analytical solution in terms of a Painlevé 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.

5 pages, references added, to appear in EPJC

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Cited by in corpus (8)

• Traversable Wormholes in $R+\alpha R^n$ Gravity
• Two-fluid solutions of particle-creation cosmologies
• New integrable models and analytical solutions in $f(R)$~cosmology with an ideal gas
• (Compactified) black branes in four dimensional f(R)-gravity
• Similarity solutions for the Wheeler-DeWitt equation in $f\left(R\right)$-cosmology
• Investigating the physical and geometrical parameters of the cosmological models with anisotropic background
• Semiclassical analysis of the Starobinsky inflationary model
• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector