Inflationary dynamics in modified gravity models

Higher-order theories of gravity are a branch of modified gravity wherein the geometrodynamics of the four-dimensional Riemannian manifold is determined by field equations involving derivatives of the metric tensor of order higher than two. This paper considers a general action built with the Einstein-Hilbert term plus additional curvature-based invariants, viz. the Starobinsky R²-type term, a term scaling with R³, and a correction of the type R R. The focus is on the background inflationary regime accommodated by these three models. For that, the higher-order field equations are built and specified for the FLRW line element. The dynanical analysis in the phase space is carried in each case. This analysis shows that the Starobinsky-plus-R³ model keeps the good features exhibited by the pure Starobinsky inflationary model, although the set of initial conditions for the inflaton field χ leading to a graceful exit scenario is more contrived; the coupling constant α₀ of the R³ invariant is also constrained by the dynamical analysis. The Starobinsky-plus-R R model turns out being a double-field inflation model; it consistently enables an almost-exponential primordial acceleration followed by a radiation dominated universe if its coupling β₀ takes values in the interval 0≤β₀≤3/4. The models introducing higher-order correction to Starobinsky inflation are interesting due to the possibility of a running spectral index nₛ, something that is allowed by current CMB observations.