Matter loops corrected modified gravity in Palatini formulation

TL;DR

This paper investigates how matter loop corrections affect modified gravity models in the Palatini formulation, revealing the emergence of phantom fields and analyzing their stability and implications for cosmic acceleration explanations.

Contribution

It demonstrates that matter loop corrections induce phantom fields in Palatini modified gravity models and analyzes their stability, providing insights into their viability as effective theories.

Findings

Matter loops generate Ricci scalar corrections leading to phantom fields.

Strong instabilities in metric formulation are absent in Palatini formulation.

Long decay timescales suggest theories may be viable as effective field theories.

Abstract

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