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

Understand

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.