An exponential correction to Starobinsky's inflationary model
  We analyse $f(R)$ theories of gravity from a dynamical system perspective, showing how the $R^2$ correction in Starobinsky's model plays a crucial role from the viewpoint of the inflationary paradigm. Then, we propose a modification of Starobinsky's model by adding an exponential term in the $f(R)$ Lagrangian. We show how this modification could allow to test the robustness of the model by means of the predictions on the scalar spectral index $n_s$. 
J\'ulio C. Fabris, Tays Miranda, Oliver F. Piattella
gr-qc astro-ph.CO hep-th