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

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 $L=R+\frac{\alpha }{4}\mathcal{G}$ ($\mathcal{G}$ 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 $\alpha$ 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.

v1: 8 pages, 1 figure. v2: 10 pages, 1 figure, accepted to PLB

References in corpus (13)

• Extended Theories of Gravity and their Cosmological and Astrophysical Applications
• Higgs inflation: consistency and generalisations
• Horndeski theory and beyond: a review
• Power-counting and the Validity of the Classical Approximation During Inflation
• On Inflation with Non-minimal Coupling
• Higgs inflation still alive
• Higgs inflation from Standard Model criticality
• Inevitable ghost and the degrees of freedom in f(R,G) gravity
• Curvature corrections to Starobinsky inflation can explain the ACT results
• Kinetically Modified Palatini Inflation Meets ACT Data
• Tree-level unitarity in Higgs inflation in the metric and the Palatini formulation
• Ultraviolet behaviour of Higgs inflation models
• Gravitational reheating in Starobinsky inflation