(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 $L=R+\fracα{4}{\cal G}$ ($\cal G$ 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.