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Register a new userWeakening gravity for dark matter in a type-II minimally modified gravity
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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 todays 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.
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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 $G_{rm N}$ and a function $V(phi)$ of a non-dynamical auxiliary field $phi$ that plays the role of dark energy. Once one fixes a homogeneous and isotropic cosmological background, the form of $V(phi)$ is determined and the theory no longer possesses a free parameter or a free function, besides $G_{rm N}$. For $V(phi) = 0$ the theory reduces to general relativity (GR) with $G_N$ being the Newtons constant and $V=const.$ being the cosmological constant. For $V(phi) e 0$, it is shown that gravity behaves differently from GR but that GR with $G_{rm N}$ being the Newtons constant is recovered for weak gravity at distance and time scales sufficiently shorter than the scale associated with $V(phi)$. Therefore this theory provides the simplest framework of cosmology in which deviations from GR can be tested by observational data.
We consider a model where a light scalar field (with mass $lesssim 30, {rm eV}$), conjectured to be dark matter, has a non-minimal coupling to gravity. In the non-relativistic limit, this new coupling introduces a self-interaction term in the scalar-field equation of motion, and modifies the source term for the gravitational field. Moreover, in the small-coupling limit justified by the observed dark-matter density, the system further reduces to the Gross-Pitaevskii-Poisson equations, which remarkably also arise from a self-gravitating and self-interacting Bose-Einstein condensate system. We derive predictions of our model on linear and non-linear structure formation by exploiting this unexpected connection.
We study the phenomenology of a class of minimally modified gravity theories called $f(mathcal{H})$ theories, in which the usual general relativistic Hamiltonian constraint is replaced by a free function of it. After reviewing the construction of the theory and a consistent matter coupling, we analyze the dynamics of cosmology at the levels of both background and perturbations, and present a concrete example of the theory with a $3$-parameter family of the function $f$. Finally, we compare this example model to Planck data as well as some later-time probes, showing that such a realization of $f(mathcal{H})$ theories fits the data significantly better than the standard $Lambda$CDM model, in particular by modifying gravity at intermediate redshifts, $zsimeq743$.
In the context of the recently proposed type-II minimally modified gravity theory, i.e. a metric theory of gravity with two local physical degrees of freedom that does not possess an Einstein frame, we study spherically symmetric vacuum solutions to explore the strong gravity regime. Despite the absence of extra degrees of freedom in the gravity sector, the vacuum solutions are locally different from the Schwarzschild or Schwarzschild-(A)dS metric in general and thus the Birkhoff theorem does not hold. The general solutions are parameterized by several free functions of time and admit regular trapping and event horizons. Depending on the choice of the free functions of time, the null convergence condition may be violated in vacuum. Even in the static limit, while the solutions in this limit reduce to the Schwarzschild or Schwarzschild-(A)dS solutions, the effective cosmological constant deduced from the solutions is in general different from the cosmological value that is determined by the action. Nonetheless, once a set of suitable asymptotic conditions is imposed so that the solutions represent compact objects in the corresponding cosmological setup, the standard Schwarzschild or Schwarzschild-(A)dS metric is recovered and the effective cosmological constant agrees with the value inferred from the action.
We study perturbation theory for large-scale structure in the most general scalar-tensor theories propagating a single scalar degree of freedom, which include Horndeski theories and beyond. We model the parameter space using the effective field theory of dark energy. For Horndeski theories, the gravitational field and fluid equations are invariant under a combination of time-dependent transformations of the coordinates and fields. This symmetry allows one to construct a physical adiabatic mode which fixes the perturbation-theory kernels in the squeezed limit and ensures that the well-known consistency relations for large-scale structure, originally derived in general relativity, hold in modified gravity as well. For theories beyond Horndeski, instead, one generally cannot construct such an adiabatic mode. Because of this, the perturbation-theory kernels are modified in the squeezed limit and the consistency relations for large-scale structure do not hold. We show, however, that the modification of the squeezed limit depends only on the linear theory. We investigate the observational consequences of this violation by computing the matter bispectrum. In the squeezed limit, the largest effect is expected when considering the cross-correlation between different tracers. Moreover, the individual contributions to the 1-loop matter power spectrum do not cancel in the infrared limit of the momentum integral, modifying the power spectrum on non-linear scales.
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