Complete constraints on a nonminimally coupled chaotic inflationary scenario from the cosmic microwave background

TL;DR

This work constrains the Fakir–Unruh nonminimally coupled chaotic inflation model by computing scalar and tensor CMB perturbations in both the Jordan and Einstein frames, establishing a frame-invariant, complete treatment. The authors show that the model yields a tilted scalar spectrum with $n_s \approx 0.97$ but an extremely small tensor-to-scalar ratio $r \approx 0.002$, due to a flat effective potential when $|\xi|$ is large. They derive a COBE-era quadrupole bound $\frac{\lambda}{\xi^2} < 4 \times 10^{-10}$ and demonstrate that the tensor amplitude remains below detectability for current missions; thus tensor detection would rule out FU, while absence of tensors could favor FU over minimal chaotic inflation. The analysis emphasizes that $n_s$ and $n_t$ are conformally invariant to first order, providing robust, model-specific predictions that can be directly tested with CMB temperature and polarization data.

Abstract

We present complete constraints imposed from observations of the cosmic microwave background radiation (CMBR) on the chaotic inflationary scenario with a nonminimally coupled inflaton field proposed by Fakir and Unruh (FU). Our constraints are complete in the sense that we investigate both the scalar density perturbation and the tensor gravitational wave in the Jordan frame, as well as in the Einstein frame. This makes the constraints extremely strong without any ambiguities due to the choice of frames. We find that the FU scenario generates tiny tensor contributions to the CMBR relative to chaotic models in minimal coupling theory, in spite of its spectral index of scalar perturbation being slightly tilted. This means that the FU scenario will be excluded if any tensor contributions to CMBR are detected by the forthcoming satellite missions. Conversely, if no tensor nature is detected despite the tilted spectrum, a minimal chaotic scenario will be hard to explain and the FU scenario will be supported.