Modified gravity without new degrees of freedom
  We show that the new type of "non-metric" gravity theories introduced independently by Bengtsson and Krasnov can in fact be reexpressed explicitely as a metrical theory coupled to an auxiliary field. We unravel why such theories possess only one propagating graviton by looking at the quadratic perturbation around a fixed solution. And we give a general construction principle with a new class of example of such modified gravity theories still possessing only two propagating degrees of freedom. 
Laurent Freidel