Abstract
In the gravitational effective theories including higher curvature terms, cosmological solutions can have nontrivial de Sitter fixed points. We study phenomenological implications of such points, focusing on a theory in which a massive scalar field is nonminimally coupled to the Euler density. We first analyze the phase portrait of the dynamical system and show that the fixed point can be a sink or a saddle, depending on the strength of the coupling. Then, we compute the perturbation spectra generated in the vicinity of the fixed point in order to investigate whether the fixed point may be considered as cosmic inflation. We find parameter regions that are consistent with the cosmological data, given that the anisotropies in the cosmic microwave background are seeded by the fluctuations generated near the fixed point. Future observation may be used to further constrain the coupling function of this model. We also comment briefly on the swampland conjecture.
Highlights
Realizing a de Sitter-like solution in a consistent theory of high energy physics is known to be difficult
Slow-roll inflation is not possible in supergravity with a canonical Kähler potential, a generic superpotential, and F-term supersymmetry breaking. This is known as the supergravity η problem [1,2,3,4]
Broadly in quantum gravity, there have been a lot of activities under the name of the swampland program [10,11]
Summary
Realizing a de Sitter-like solution in a consistent theory of high energy physics is known to be difficult. In order to avoid difficulties such as the Ostrogradski instability and to make our discussions simple, we focus on a well-behaved gravity theory in which a scalar field φ is coupled to the four-dimensional Euler density ( called the Gauss-Bonnet term in the literature) R2GB ≡ R2 − 4RμνRμν þ RμνρσRμνρσ This type of correction to the Einstein gravity is expected for example in inflationary effective field theory [13]. Based on the action (1), various cosmological models have been studied by many authors, with different assumptions on the potential VðφÞ and the coupling function ξðφÞ. [23] analyzes inflation with the quadratic V ∝ φ2 and the quartic V ∝ φ4 scalar potential These models are strongly disfavored by the recent observational data, but they can be made compatible if a Gauss-Bonnet term with the exponential coupling is included.
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