Eur. Phys. J. C (2017) 77: 438
https://doi.org/10.1140/epjc/s10052-017-5009-0

Regular Article - Theoretical Physics

Analytic solution of the Starobinsky model for inflation

¹ Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
² Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban, 4000, Republic of South Africa

^* e-mail: anpaliat@phys.uoa.gr

Received: 21 April 2017
Accepted: 20 June 2017
Published online: 1 July 2017

Abstract

We prove that the field equations of the Starobinsky model for inflation in a Friedmann–Lemaître–Robertson–Walker metric constitute an integrable system. 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.