Inflation as an attractor in scalar cosmology

Abstract

We study an inflation mechanism based on attractor properties in cosmological evolutions of a spatially flat Friedmann-Robertson-Walker spacetime based on the Einstein-scalar field theory. We find a new way to get the Hamilton-Jacobi equation solving the field equations. The equation relates a solution `generating function' with the scalar potential. We analyze its stability and find a later time attractor which describes a Universe approaching to an eternal-de Sitter inflation driven by the potential energy, $V_0>0$. The attractor exists when the potential is regular and does not have a linear and quadratic terms of the field. When the potential has a mass term, the attractor exists if the scalar field is in a symmetric phase and is weakly coupled, $\lambda <9V_0/16$. We also find that the attractor property is intact under small modifications of the potential. If the scalar field has a positive mass-squared or is strongly coupled, there exists a quasi-attractor. However, the quasi-attractor property disappears if the potential is modified. On the whole, the appearance of the eternal inflation is not rare in scalar cosmology in the presence of an attractor.

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References in corpus (6)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• The Standard Model Higgs boson as the inflaton
• Reconstructing the universe history, from inflation to acceleration, with phantom and canonical scalar fields
• Can Standard Model Higgs Seed the Formation of Structures in Our Universe?
• A Phase Transition between Small and Large Field Models of Inflation
• On exact solutions to the scalar field equations in standard cosmology

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