2025/06/11 by Eugenio Bianchi, Bianchi, Eugenio, Mauricio Gamonal +1 · 1 voice · 3 citations
Physics and Astronomy · #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.2506.10081
arxiv published 2025/06/11 · arxiv updated 2025/12/02
Starobinsky's R+αR2 inflation provides a compelling one-parameter inflationary model that is supported by current cosmological observations. However, at the same order in spacetime derivatives as the R2 term, an effective theory of spacetime geometry must also include the Weyl-squared curvature invariant W2. In this paper, we study the inflationary predictions of the gravitational theory with action of the form R+αR2 - βW2, where the coupling constant α sets the scale of inflation, and corrections due to the W2 term are treated self-consistently via reduction of order in an expansion in the coupling constant β, at the linear order in β/α. Cosmological perturbations are found to be described by an effective action with a nontrivial speed of sound c_\textrms for scalar and c_\textrmt for tensor modes, satisfying the relation c_\textrmt/c_\textrms ≃ 1+ \fracβ6 α during the inflationary phase. Within this self-consistent framework, we compute several primordial observables up to the next-to-next-to-next-to leading order (N3LO). We find the tensor-to-scalar ratio r ≃ 3(1-\fracβ6α)(n_\textrms-1)2, the tensor tilt n_\textrmt≃-(r)/(8) and the running of the scalar tilt \mathfraka_\textrms≃-(1)/(2) (n_\textrms - 1)2, all expressed in terms of the observed scalar tilt n_\textrms. We also provide the corresponding corrections up to N3LO, O((n_\textrms - 1)3).