Positive running of the spectral index is achievable in Einstein-Gauss-Bonnet gravity with viable inflation, unlike standard scalar field and F(R) models which face challenges.
Cosmological inflation in $F(R,\mathcal{G})$ gravity
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abstract
Cosmological inflation is discussed in the framework of $F(R,{\cal G})$ gravity where $F$ is a generic function of the curvature scalar $R$ and the Gauss-Bonnet topological invariant $\cal G$. The main feature that emerges in this analysis is the fact that this kind of theory can exhaust all the curvature budget related to curvature invariants without considering derivatives of $R,$ $R_{\mu\nu}$, $R^{\lambda}_{\sigma\mu\nu}$ etc. in the action. Cosmological dynamics results driven by two effective masses (lenghts) related to the $R$ scalaron and the $\cal G$ scalaron working respectively at early and very early epochs of cosmic evolution. In this sense, a double inflationary scenario naturally emerges.
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Three standard inflationary potentials remain compatible with Planck, BICEP/Keck, DESI DR2, and ACT DR6 data when placed in minimally coupled f(R,T)=R+16πGλT gravity for suitable ranges of the model parameters and coupling λ.
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Positive Running of the Spectral Index for Scalar Theory and Modified Gravity
Positive running of the spectral index is achievable in Einstein-Gauss-Bonnet gravity with viable inflation, unlike standard scalar field and F(R) models which face challenges.
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Inflationary models in a minimally coupled $f(R,T)$ gravity: Constraints from $Planck$, BICEP/$Keck$, and ACT
Three standard inflationary potentials remain compatible with Planck, BICEP/Keck, DESI DR2, and ACT DR6 data when placed in minimally coupled f(R,T)=R+16πGλT gravity for suitable ranges of the model parameters and coupling λ.