  We consider an action for gravity that, in addition to the Einstein-Hilbert
term, contains a function of the Ricci scalar and the Gauss-Bonnet invariant.
The specific form of the function considered is motivated by holographic
cosmology. At background level the field equations imply modified Friedmann
equations of the same form as those in the holographic cosmology. We calculate
the cosmological perturbations and derive the corresponding power spectra
assuming a general $k$-inflation. We find that the resulting power spectra
differ substantially from those obtained in both holographic and standard
cosmology. The estimated spectral index and tensor-to-scalar ratio are
confronted with the Planck results.
