Matter Loops Corrected Modified Gravity in Palatini Formulation

Recently,corrections to the standard Einstein Hilbert action were proposed to explain the current cosmicacceleration in stead of introducing dark energy.In the Palatini formulation of those modified gravity models,thereis an important observation due to Arkani Hamed:matter loops will give rise to a correction to the modified gravityaction proportional to the Ricci scalar of the metric.In the presence of such a term,we show that the current formsof modified gravity models in Palatini formulation,specifically,the 1/R gravity and in R gravity,will have phantoms.Then we study the possible instabilities due to the presence of phantom fields.We show that the strong instability inthe metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales forthe phantom fields may be long enough for the theories to make sense as effective field theory.On the other hand,if wechange the sign of the modification terms to eliminate the phantoms,some other inconsistencies will arise for the variousversions of the modified gravity models.Finally,we comment on the universal property of the Palatini formulation ofthe matter loops corrected modified gravity models and its implications.