Perturbations of Single-field Inflation in Modified Gravity Theory

Abstract

In this paper, we study the case of single field inflation within the framework of modified gravity theory where the gravity part has an arbitrary form $f(R)$. Via a conformal transformation, this case can be transformed into its Einstein frame where it looks like a two-field inflation model. However, due to the existence of the isocurvature modes in such a multi-degree-of-freedom (m.d.o.f.) system, the (curvature) perturbations are not equivalent in two frames, so in despite of its convenience, it is illegal to treat the perturbations in its Einstein frame as the "real" ones as we always do for pure $f(R)$ theory or single field with nonminimal coupling. Here by pulling the results of curvature perturbations back into its original Jordan frame, we show explicitly the power spectrum and spectral index of the perturbations in the Jordan frame, as well as how it differs from the Einstein frame. We also fit our results with the newest Planck data. Since there are large parameter space in these models, we show that it is easy to fit the data very well.

arXiv comment9 pages, 1 figure, substantially improved, matching with the published version

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Cited by in corpus (12)

• Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves
• Frame-dependence of higher-order inflationary observables in scalar-tensor theories
• Inflation and reheating in theories with spontaneous scale invariance symmetry breaking
• A simple $F(\mathcal{R},\varphi )$ deformation of Starobinsky inflationary model
• Higgs Inflation with a Gauss-Bonnet term in the Jordan Frame
• On the Trans-Planckian Censorship Conjecture and the Generalized Non-Minimal Coupling
• Integrable modified gravity cosmological models with an additional scalar field
• Gravitational constant in multiple field gravity
• Decay of $f(R)$ quintessence into dark matter: mitigating the Hubble tension?
• Non-minimally assisted chaotic inflation
• Super-horizon effects on the gauge invariant effective energy density in f(R) gravity
• Conformal invariant cosmological perturbations via the covariant approach: multicomponent universe