Models with Non-minimal Coupling in Primordial Universe and Cosmological Observations

A non-minimal coupling between gravity and the inflaton field is a generic contribution in inflationary cosmology. In this work, we consider models of inflation with a non-minimal coupling $-\xi\phi^2 R$ and study their observational predictions for the tensor-to-scalar ratio $r$ and the spectral index $n_s$. Unlike the conventional approach of working in the Einstein frame, we perform the analysis in the Jordan frame where the underlying dynamics, particularly the competition between the potential force and the coupling-induced friction, are more transparent. For suitable values of $\xi$, the system exhibits an extended constant-roll regime, in which this friction counteracts the potential force. Focusing on monomial potentials $V(\phi) \propto \phi^n$, we find that negative $\xi$ systematically reduces $r$ in the $(n_s, r)$ plane, while the shift in $n_s$ depends on the power $n$: for $n \geq 4$, the spectral index increases with $|\xi|$, whereas for $n < 4$, it decreases. Notably, the quartic model $V(\phi) = \lambda \phi^4/4$ with $\xi \lesssim -0.1$ shows good agreement with the ACT DR6 data and exhibits a distinct $n_s(\xi)$ dependence compared to other monomial cases. Our results demonstrate that non-minimally coupled models can effectively reconcile Planck and ACT observations, providing a unified framework for interpreting current CMB constraints.