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 $V(\varphi )$ of a non-dynamical auxiliary field $\varphi$ that plays the role of dark energy. Once one fixes a homogeneous and isotropic cosmological background, the form of $V(\varphi )$ is determined and the theory no longer possesses a free parameter or a free function, besides $G_{\mathrm{N}}$. For $V^{\prime }(\varphi )=0$ the theory reduces to general relativity (GR) with $G_N$ being the Newton's constant and $V=const.$ being the cosmological constant. For $V^{\prime }(\varphi )\ne 0$, 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 $V(\varphi )$. Therefore this theory provides the simplest framework of cosmology in which deviations from GR can be tested by observational data.

18 pages

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• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• A Class of Minimally Modified Gravity Theories
• Spatially covariant gravity theories with two tensorial degrees of freedom: the formalism
• New class of generalized coupling theories

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