A theory of type-II minimally modified gravity

Abstract

We propose a modified gravity theory that propagates only two local gravitational degrees of freedom and that does not have an Einstein frame. According to the classification in JCAP 01 (2019) 017 [arXiv:1810.01047 [gr-qc]], this is a type-II minimally modified gravity theory. The theory is characterized by the gravitational constant $G_{\mathrm{N}}$ and a function $V(\ddot{I}•)$ of a non-dynamical auxiliary field $\ddot{I}•$ that plays the role of dark energy. Once one fixes a homogeneous and isotropic cosmological background, the form of $V(\ddot{I}•)$ is determined and the theory no longer possesses a free parameter or a free function, besides $G_{\mathrm{N}}$. For $V^{\prime }(\ddot{I}•)=0$ the theory reduces to general relativity (GR) with $G_N$ being the Newton's constant and $V=const.$ being the cosmological constant. For $V^{\prime }(\ddot{I}•)\ne 0$, it is shown that gravity behaves differently from GR but that GR with $G_{\mathrm{N}}$ being the Newton's constant is recovered for weak gravity at distance and time scales sufficiently shorter than the scale associated with $V(\ddot{I}•)$. Therefore this theory provides the simplest framework of cosmology in which deviations from GR can be tested by observational data.

18 pages