Ghost Constraints on Modified Gravity

TL;DR

This paper demonstrates that most infrared modifications of gravity involving curvature invariants introduce ghosts or light scalars, and only higher-dimensional theories avoid these issues, challenging the viability of such modifications.

Contribution

It shows that generic infrared modifications of gravity with curvature invariants are not viable due to ghost or scalar instabilities, except in higher-dimensional scenarios.

Findings

Infrared curvature modifications contain ghosts or scalars.

Fine-tuning cannot fully eliminate ghosts without changing gravity's nature.

Higher-dimensional theories evade ghost problems by introducing infinite degrees of freedom.

Abstract

We show that general infrared modifications of the Einstein-Hilbert action obtained by addition of curvature invariants are not viable. These modifications contain either ghosts or light gravity scalars. A very specific fine-tuning might solve the problem of ghosts, but the resulting theory is still equivalent to a scalar-tensor gravity and thus gives a corrupted picture of gravity at the solar system scale. The only known loophole is that the theory becomes higher dimensional at large distances. The infinite number of degrees of freedom introduced in this way is not reducible to the addition of an arbitrary function of curvature invariants.