Reconstructing G-inflation: From the attractors $n_S(N)$ and $r(N)$

TL;DR

This paper reconstructs G-inflation models by deriving the effective potential and coupling function from specified spectral index and tensor-to-scalar ratio attractors, providing new insights into inflationary dynamics.

Contribution

It introduces a method to reconstruct G-inflation models using attractors for $n_S(N)$ and $r(N)$, deriving explicit forms of potential and coupling functions.

Findings

Reconstructed $V(\,phi)$ and $g(\,phi)$ for different attractor examples.

Provided explicit relations between cosmological parameters and model functions.

Demonstrated the impact of different attractor choices on inflationary potentials.

Abstract

The reconstruction of an inflationary universe in the context of the Galileon model or G-model, considering as attractors the scalar spectral index $n_S(N)$ and the tensor to scalar ratio $r(N)$ as a function of the number of e-folding $N$ is studied. By assuming a coupling of the form $G(\phi,X)=g(\phi)\,X$, we obtain the effective potential $V$ and the coupling parameter $g$ in terms of the cosmological parameters $n_S$ and $r$ under the slow roll approximation. From some examples for $n_S(N)$ and $r(N)$, different results for the effective potential $V(\phi)$ and the coupling parameter $g(\phi)$ are found.