Reconstruction of a Nonminimal Coupling Theory with Scale-invariant Power Spectrum

TL;DR

This paper explores how nonminimal coupling scalar field theories with scale-invariant power spectra can be reconstructed from minimal coupling models using frame transformations, potentially solving early universe puzzles.

Contribution

It demonstrates a method to reconstruct nonminimal coupling theories with desired spectra from minimal models via frame transformation, addressing key cosmological issues.

Findings

Reconstruction of nonminimal theories from minimal models.

Relaxation of the universe's equation of state constraints.

Potential solutions to horizon, flatness, and anisotropy problems.

Abstract

A nonminimal coupling single scalar field theory, when transformed from Jordan frame to Einstein frame, can act like a minimal coupling one. Making use of this property, we investigate how a nonminimal coupling theory with scale-invariant power spectrum could be reconstructed from its minimal coupling counterpart, which can be applied in the early universe. Thanks to the coupling to gravity, the equation of state of our universe for a scale-invariant power spectrum can be relaxed, and the relation between the parameters in the action can be obtained. This approach also provides a means to address the Big-Bang puzzles and anisotropy problem in the nonminimal coupling model within Jordan frame. Due to the equivalence between the two frames, one may be able to find models that are free of the horizon, flatness, singularity as well as anisotropy problems.