Reconstruction of the Scalar Field Potential in Inflationary Models with   a Gauss-Bonnet term
  We study inflationary models with a Gauss-Bonnet term to reconstruct the scalar field potentials and the Gauss-Bonnet coupling functions from the observable quantities. Using the observationally favored relations for both $n_s$ and $r$, we derive the expressions for both the scalar field potentials and the coupling functions. The implication of the blue-tilted spectrum, $n_t>0$, of the primordial tensor fluctuations is discussed for the reconstructed configurations of the scalar field potential and the Gauss-Bonnet coupling. 
Seoktae Koh, Bum-Hoon Lee and Gansukh Tumurtushaa
gr-qc astro-ph.CO hep-th