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.

arXiv comment5 pages, references added, to appear in EPJC

References in corpus (38)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• f(R) theories
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Curvature Quintessence
• Cosmological Tests of Modified Gravity
• Are f(R) dark energy models cosmologically viable ?
• Inflationary cosmology in modified gravity theories
• The Power of General Relativity
• On the Starobinsky Model of Inflation from Supergravity
• Cosmological Solutions of $f(T)$ Gravity
• Equivalence of the Einstein and Jordan frames
• Cosmological Constraints on f(R) Acceleration Models
• A polynomial f(R) inflation model
• Dark energy from modified gravity with Lagrange multipliers
• On the evolution of universes in quadratic theories of gravity
• Further Exact Cosmological Solutions to Higher-Order Gravity Theories
• Noether symmetry approach in phantom quintessence cosmology
• Noether symmetry in $f(R)$ cosmology
• Constraints and analytical solutions of $f(R)$ theories of gravity using Noether symmetries
• Latest supernovae constraints on f(R) cosmologies
• A question mark on the equivalence of Einstein and Jordan frames
• $f(R)$-gravity from Killing Tensors
• Noether Symmetry Approach in multiple scalar fields Scenario
• Cosmological Constraints from Hubble Parameter on f(R) Cosmologies
• Kantowski-Sachs Einstein-æther perfect fluid models
• Stable Isotropic Cosmological Singularities in Quadratic Gravity
• Analytical solutions in $R+q{R}^n$ cosmology from singularity analysis
• No scale SUGRA SO(10) derived Starobinsky Model of Inflation
• Symmetries and Singularities of the Szekeres System
• Power law Starobinsky model of inflation from no-scale SUGRA
• Topological inflation from the Starobinsky model in supergravity
• Dark Matter and Inflation in $R+\zeta R^2$ Supergravity
• The initial state of generalized radiation universes
• Asymptotic vacua with higher derivatives
• FLRW cosmology in Weyl-Integrable Space-Time
• Chaos Removal in the $R+q{R}^2$ gravity: the Mixmaster model

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• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector
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