Abstract
We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling ξg(ϕ)R and a specific scalar potential. The defining property of these models is that the scalar field takes a vev in the vacuum and thus induces an effective Planck mass. We study this model as a function of the coupling parameter ξ. At large ξ, the predictions of the theory are known to have an attractor behavior, converging to a universal result independent on the choice of the function g(ϕ). We find that at small ξ, the theory approaches a second attractor. The inflationary predictions of this class of theories continuously interpolate between those of the Starobinsky model and the predictions of the simplest chaotic inflation with a quadratic potential.
Highlights
JHEP09(2014)062 in the leading approximation in 1/N, where N is the number of e-folding of inflation
We describe an induced inflation, which refers to a class of inflationary models with a generalized non-minimal coupling ξg(φ)R and a specific scalar potential
Several different classes of models with a similar attractor behavior have been found and their supergravity generalizations have been constructed. They include, in particular, a broad class of models of conformal inflation [9, 10], α-attractors [11], and the models with generalized non-minimal coupling [12]; see [13] for a recent review. It was shown in [12] that this attractor behavior is valid for a broad class of functions Ω(φ) = 1 + ξf (φ) and Jordan frame potentials VJ = λf 2(φ)
Summary
We will first review the universal attractor that arises for a sufficiently strong non-minimal coupling ξ → ∞ of a particular form, following [12, 14, 15]. If f (φ) is an odd function of φ, the Einstein frame inflaton potential in the large ξ limit coincides with the potential in the Starobinsky model (1.2). For even f (φ), it coincides with the large ξ limit of the Higgs inflation potential (1.1) [12]. Note that these potentials differ for negative φ, but they have an identical inflationary plateau for positive φ. There the difference between these two potentials disappears for all values of the Higgs field This set of models allow various generalizations described in [12, 14, 15]. We will discuss one of them, called induced inflation [14, 15]
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