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Higher Curvature Inflation and the Species Scale

Joaquin Masias

TL;DR

This work investigates how infinite higher-curvature corrections in $f(R)$ gravity generate scalar potentials and how a dynamical, circle-compactification–driven species scale can dynamically flatten these potentials into plateaus suitable for inflation. The key mechanism is a matched exponential decay between the curvature-induced potential and the field-dependent cutoff, which arises from the radion in circle compactification, allowing a plateau that reproduces Starobinsky-like predictions while remaining consistent with Swampland constraints. The authors derive explicit forms for plateau potentials from various curvature series, identify the parameter regimes (notably coefficient spectra $c_n\propto n^\alpha$) that yield viable inflation, and discuss implications for M-theory and string theory, including limits on curvature series coefficients and potential moduli issues. Overall, the paper provides a concrete route to embed Starobinsky-type inflation into higher-curvature gravity with a UV-sensitive cutoff, linking EFT control, Swampland constraints, and higher-dimensional origins.

Abstract

We study the scalar potentials that arise from higher curvature corrections in general $f(R)$ theories of gravity and their connection to a dynamical species scale. Starting from general considerations in arbitrary dimensions, we show that at large field values, the scalar potential generated by an infinite series of curvature terms and the field dependent species scale arising from circle compactification both decay exponentially, in complementary ways. We identify conditions under which these two effects precisely balance out, giving rise to exponentially flat, plateau-like potentials. We additionally find a precise embedding of Starobinsky inflation consistent with the Swampland program, and we discuss possible implications the mechanism proposed could have for M and string theory.

Higher Curvature Inflation and the Species Scale

TL;DR

This work investigates how infinite higher-curvature corrections in gravity generate scalar potentials and how a dynamical, circle-compactification–driven species scale can dynamically flatten these potentials into plateaus suitable for inflation. The key mechanism is a matched exponential decay between the curvature-induced potential and the field-dependent cutoff, which arises from the radion in circle compactification, allowing a plateau that reproduces Starobinsky-like predictions while remaining consistent with Swampland constraints. The authors derive explicit forms for plateau potentials from various curvature series, identify the parameter regimes (notably coefficient spectra ) that yield viable inflation, and discuss implications for M-theory and string theory, including limits on curvature series coefficients and potential moduli issues. Overall, the paper provides a concrete route to embed Starobinsky-type inflation into higher-curvature gravity with a UV-sensitive cutoff, linking EFT control, Swampland constraints, and higher-dimensional origins.

Abstract

We study the scalar potentials that arise from higher curvature corrections in general theories of gravity and their connection to a dynamical species scale. Starting from general considerations in arbitrary dimensions, we show that at large field values, the scalar potential generated by an infinite series of curvature terms and the field dependent species scale arising from circle compactification both decay exponentially, in complementary ways. We identify conditions under which these two effects precisely balance out, giving rise to exponentially flat, plateau-like potentials. We additionally find a precise embedding of Starobinsky inflation consistent with the Swampland program, and we discuss possible implications the mechanism proposed could have for M and string theory.

Paper Structure

This paper contains 14 sections, 100 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Scalar Potentials from f(R) Gravity
  3. Asymptotically Flat Potentials from f(R) Gravity
  4. Exponential Potentials from f(R) Gravity
  5. f(R) gravity on a circle
  6. Einstein-frame Action
  7. f(R) = R + Rⁿ
  8. $f(R)=R+M^2\sum_{n} n^\alpha \dfrac{R^n}{M^{2n}}$
  9. Phenomenology
  10. Inflation with exponentially decaying potentials
  11. Curvature corrections in M-theory and $f(R)$
  12. Conclusion
  13. Higher curvature Terms in Quasi–de Sitter
  14. Asymptotic Behavior of Infinite Series

Figures (1)

  • Figure 1: Potentials obtained from series of higher (scalar) curvature corrections to EH gravity after modifying the mass scale as $M(\phi)=e^{\frac{\phi}{\sqrt{(d-2)(d-1)}}}$, for series with decreasing polynomial coefficients $c_n=n^\alpha$. Blue: $\alpha=-1$. Orange: $\alpha=-2$, computed numerically. Black: Starobinsky model presented for comparison.