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(Lovelock)$^2$ inflation: explaining the ACT data and equivalence to Higgs-Gauss-Bonnet inflation

Andrea Addazi, Yermek Aldabergenov, Daulet Berkimbayev, Yifu Cai

TL;DR

The paper addresses a mild tension between Starobinsky inflation and ACT data by proposing a ghost-free quadratic extension of f(L) gravity based on the Lovelock invariant, f(L)=L+L^2/(6M^2). Through a Weyl transformation, the model yields a Horndeski-type scalar–tensor theory with Gauss–Bonnet and derivative couplings, and is shown to be equivalent to Higgs inflation coupled to GB in the Jordan frame. In a slow-roll regime expanded perturbatively in the GB parameter, analytical expressions for the scalar tilt and tensor-to-scalar ratio are derived, indicating that a negative GB coupling can shift $n_s$ upward to better accommodate ACT, while maintaining Starobinsky-like predictions. The framework remains within the Horndeski class, recovers the standard results when the GB coupling vanishes, and implies a Gauss–Bonnet scale around $10^{15}$ GeV, offering a theoretically motivated and testable refinement of early-Universe inflation compatible with current precision data.

Abstract

We revisit the Starobinsky model of inflation in light of recent data from the Atacama Cosmology Telescope (ACT), which indicates a potential preference for a slightly larger scalar spectral index $n_s$ than predicted by the standard $R^2$ scenario. We demonstrate that a natural one-parameter generalization to a quadratic model $\sim L+L^2$ in the Lovelock invariant $L=R+\fracα{4}{\cal G}$ ($\cal G$ is the Gauss--Bonnet term), can effectively resolve this minor tension. Scalar-tensor formulation of this theory yields an Einstein-frame Starobinsky-type scalar potential augmented by Gauss--Bonnet and derivative couplings, which modify the inflationary slow-roll dynamics. We show that a non-zero coupling $α$ for the Gauss-Bonnet term can shift $(n_s, r)$ along a trajectory that brings the predictions into better agreement with the ACT likelihood. We also find that $L+L^2$ gravity, in its scalar-tensor formulation, is equivalent to Higgs inflation coupled to the Gauss--Bonnet term, and belongs to the Horndeski/galileon class of modified gravities. This work establishes the quadratic $f(L)$ gravity as a compelling and physically motivated extension that preserves the successes of Starobinsky inflation while improving its fit to modern precision cosmological data.

(Lovelock)$^2$ inflation: explaining the ACT data and equivalence to Higgs-Gauss-Bonnet inflation

TL;DR

The paper addresses a mild tension between Starobinsky inflation and ACT data by proposing a ghost-free quadratic extension of f(L) gravity based on the Lovelock invariant, f(L)=L+L^2/(6M^2). Through a Weyl transformation, the model yields a Horndeski-type scalar–tensor theory with Gauss–Bonnet and derivative couplings, and is shown to be equivalent to Higgs inflation coupled to GB in the Jordan frame. In a slow-roll regime expanded perturbatively in the GB parameter, analytical expressions for the scalar tilt and tensor-to-scalar ratio are derived, indicating that a negative GB coupling can shift upward to better accommodate ACT, while maintaining Starobinsky-like predictions. The framework remains within the Horndeski class, recovers the standard results when the GB coupling vanishes, and implies a Gauss–Bonnet scale around GeV, offering a theoretically motivated and testable refinement of early-Universe inflation compatible with current precision data.

Abstract

We revisit the Starobinsky model of inflation in light of recent data from the Atacama Cosmology Telescope (ACT), which indicates a potential preference for a slightly larger scalar spectral index than predicted by the standard scenario. We demonstrate that a natural one-parameter generalization to a quadratic model in the Lovelock invariant ( is the Gauss--Bonnet term), can effectively resolve this minor tension. Scalar-tensor formulation of this theory yields an Einstein-frame Starobinsky-type scalar potential augmented by Gauss--Bonnet and derivative couplings, which modify the inflationary slow-roll dynamics. We show that a non-zero coupling for the Gauss-Bonnet term can shift along a trajectory that brings the predictions into better agreement with the ACT likelihood. We also find that gravity, in its scalar-tensor formulation, is equivalent to Higgs inflation coupled to the Gauss--Bonnet term, and belongs to the Horndeski/galileon class of modified gravities. This work establishes the quadratic gravity as a compelling and physically motivated extension that preserves the successes of Starobinsky inflation while improving its fit to modern precision cosmological data.
Paper Structure (6 sections, 27 equations, 1 figure)

This paper contains 6 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The Model
  3. Inflationary solutions
  4. Slow-roll approximation
  5. Estimating $n_s$ and $r$
  6. Conclusions

Figures (1)

  • Figure 1: Predictions of $({\rm Lovelock})^2$ inflation for the spectral index $n_s$, tensor-to-scalar ratio $r$, and the running $dn_s/d\ln k=-dn_s/dN$, compared to the Planck+ACT constraints ACT:2025tim. Solid lines represent the results of numerical integration of the background equations of motion, and the dashed lines (of the same color) represent the corresponding approximations \ref{['n_s_approx']} and \ref{['r_approx']}. The calculations are done for $50\leq N_e\leq 60$ (larger $N_e$ leads to larger $n_s$).