Slow-roll inflation in $f(R,T)$ gravity with a $RT$ mixing term

Abstract

We consider slow-roll inflationary models in a class of modified theories of gravity which contains non-minimal curvature-inflaton couplings, i.e., the $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the inflaton energy-momentum tensor. On top of the minimally coupled $T$ that has been widely investigated in the literature, we further include a $RT$ mixing term in the theory. This mixing term introduces non-minimal derivative couplings and plays an important role in inflationary dynamics. Taking chaotic and natural inflation as examples, we find that the predictions for spectral tilt and the tensor-to-scalar ratio are sensitive to the existence of the $RT$ mixing term. In particular, by turning on this mixing term, it is possible to bring chaotic and natural inflation into better agreement with observational data.

17 pages, 4 figures, updated to match the published version

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• The first variation of the matter energy-momentum tensor with respect to the metric, and its implications on modified gravity theories
• Dynamical reconstruction of the $\Lambda$CDM model in scalar-tensor $f(R,T)$ gravity
• Moment of inertia and compactness of quark stars within the context of $f(R,T,L_m)$ gravity
• Testing scale-invariant inflation against cosmological data
• Warm Inflation in $f(R,T)$ gravity
• Are $f(R,\mathrm{Matter})$ theories really relevant to cosmology?
• Tsallis holographic inflation in $f(R,T)$ gravity: CMB constraints, reheating, and swampland implications
• Holographic inflation and holographic dark energy from entropy of the anti-de Sitter black hole
• Evolution of the early universe in Einstein-Cartan theory
• Inflationary models in a minimally coupled $f(R,T)$ gravity: Constraints from $Planck$, BICEP/$Keck$, and ACT
• Energy conditions in consistent perfect fluid cosmology