Weakening gravity for dark matter in a type-II minimally modified gravity

TL;DR

This paper introduces a novel cosmological framework where dark matter experiences a weaker gravitational force than standard matter, achieved through a minimally modified gravity approach that addresses key cosmological tensions without adding extra gravitational degrees of freedom.

Contribution

The authors develop a new framework coupling dark matter and a cosmological constant via a canonical transformation, enabling control over the gravitational strength on dark matter without extra degrees of freedom.

Findings

Framework can modify dark matter gravity strength over time.

Potential to address H0 and S8 cosmological tensions.

Introduces the VCCDM model with variable effective gravitational constant.

Abstract

We propose a new cosmological framework in which the strength of the gravitational force acted on dark matter at late time can be weaker than that on the standard matter fields without introducing extra gravitational degrees of freedom. The framework integrates dark matter into a type-II minimally modified gravity that was recently proposed as a dark energy mimicker. The idea that makes such a framework possible consists of coupling a dark matter Lagrangian and a cosmological constant to the metric in a canonically transformed frame of general relativity (GR). On imposing a gauge fixing constraint, which explicitly breaks the temporal diffeomorphism invariance, we keep the number of gravitational degrees of freedom to be two, as in GR. We then make the inverse canonical transformation to bring the theory back to the original frame, where one can add the standard matter fields. This framework contains two free functions of time which specify the generating functional of the above mentioned canonical transformation and which are then used in order to realize desired time evolutions of both the Hubble expansion rate $H(z)$ and the effective gravitational constant for dark matter $G_{\rm eff}(z)$. The aim of this paper is therefore to provide a new framework to address the two puzzles present in today's cosmology, i.e. the $H_0$ tension and the $S_8$ tension, simultaneously. When the dark matter is cold in this framework, we dub the corresponding cosmological model the V Canonical Cold Dark Matter (VCCDM), as the cosmological constant $\Lambda$ in the standard $\Lambda$CDM is replaced by a function $V(\phi)$ of an auxiliary field $\phi$ and the CDM is minimally coupled to the metric in a canonically transformed frame.