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Slow-roll inflation with a Gauss-Bonnet correction

Zong-Kuan Guo, Dominik J. Schwarz

TL;DR

This work extends single-field slow-roll inflation by incorporating a Gauss-Bonnet (GB) coupling, introducing a combined hierarchy of Hubble and GB flow parameters to characterize slow-roll. The authors derive the scalar and tensor perturbation spectra, showing that the GB coupling modifies the scalar spectral index while leaving the tensor index at leading order, and breaks the standard tensor-to-scalar consistency relation. They apply the formalism to a monomial potential with an inverse monomial GB coupling, obtaining analytic expressions for the scalar tilt and tensor-to-scalar ratio: $n_{\mathcal{R}}-1 = -\frac{2(n+2)}{4N+n}$ and $r = \frac{16 n (1-\alpha)}{4N+n}$, where $\alpha = \tfrac{4V_0\xi_0}{3}$, showing that a positive GB coupling can reduce $r$ and improve compatibility with data. The results provide a generic framework for GB-inflation and yield observationally testable predictions that differ from standard slow-roll models, with implications for the viability of large-field potentials.

Abstract

We consider slow-roll inflation for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. By introducing a combined hierarchy of Hubble and Gauss-Bonnet flow functions, we analytically derive the power spectra of scalar and tensor perturbations. The standard consistency relation between the tensor-to-scalar ratio and the spectral index of tensor perturbations is broken. We apply this formalism to a specific model with a monomial potential and an inverse monomial Gauss-Bonnet coupling and constrain it by the 7-year Wilkinson Microwave Anisotropy Probe data. The Gauss-Bonnet term with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio and hence may revive the quartic potential ruled out by recent cosmological data.

Slow-roll inflation with a Gauss-Bonnet correction

TL;DR

This work extends single-field slow-roll inflation by incorporating a Gauss-Bonnet (GB) coupling, introducing a combined hierarchy of Hubble and GB flow parameters to characterize slow-roll. The authors derive the scalar and tensor perturbation spectra, showing that the GB coupling modifies the scalar spectral index while leaving the tensor index at leading order, and breaks the standard tensor-to-scalar consistency relation. They apply the formalism to a monomial potential with an inverse monomial GB coupling, obtaining analytic expressions for the scalar tilt and tensor-to-scalar ratio: and , where , showing that a positive GB coupling can reduce and improve compatibility with data. The results provide a generic framework for GB-inflation and yield observationally testable predictions that differ from standard slow-roll models, with implications for the viability of large-field potentials.

Abstract

We consider slow-roll inflation for a single scalar field with an arbitrary potential and an arbitrary nonminimal coupling to the Gauss-Bonnet term. By introducing a combined hierarchy of Hubble and Gauss-Bonnet flow functions, we analytically derive the power spectra of scalar and tensor perturbations. The standard consistency relation between the tensor-to-scalar ratio and the spectral index of tensor perturbations is broken. We apply this formalism to a specific model with a monomial potential and an inverse monomial Gauss-Bonnet coupling and constrain it by the 7-year Wilkinson Microwave Anisotropy Probe data. The Gauss-Bonnet term with a positive (or negative) coupling may lead to a reduction (or enhancement) of the tensor-to-scalar ratio and hence may revive the quartic potential ruled out by recent cosmological data.

Paper Structure

This paper contains 5 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Slow-roll inflation with the GB correction
  3. Power spectra
  4. An example model
  5. Conclusions and discussions

Figures (2)

  • Figure 1: Two-dimensional joint marginalized constraint (68% and 95% confidence level) on the scalar spectral index $n_{\cal{R}}$ and the tensor-to-scalar ratio $r$ derived from the data combination of WMAP7+BAO+$H_0$ by imposing the standard consistency relation. The symbols show the predictions from the $\phi^4$-potential (solid line) and $\phi^2$-potential (dashed line) models with the number of e-folds equal to 50 (small) and 60 (large).
  • Figure 2: Tensor-to-scalar ratio $r$ versus the spectral index $n_{\cal{R}}$ for the inflation model (\ref{['poco']}) with $n=2$ (top panel) and $n=4$ (bottom panel). The contours show the 68% and 95% confidence level derived from WMAP7+BAO+$H_0$ without the consistency relation.