Reconstructing G inflation: From the attractors nS (N) and r (N)

The reconstruction of an inflationary universe in the context of the Galileon model or G-model, considering as attractors the scalar spectral index nS(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(φ,X)=g(φ)X, we obtain the effective potential V and the coupling parameter g in terms of the cosmological parameters nS and r under the slow roll approximation. From some examples for nS(N) and r(N), different results for the effective potential V(φ) and the coupling parameter g(φ) are found.