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Register a new userA theory of type-II minimally modified gravity
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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.
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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 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.
Gravitational theories differing from General Relativity may explain the accelerated expansion of the Universe without a cosmological constant. However, to pass local gravitational tests, a screening mechanism is needed to suppress, on small scales, the fifth force driving the cosmological acceleration. We consider the simplest of these theories, i.e. a scalar-tensor theory with first-order derivative self-interactions, and study isolated (static and spherically symmetric) non-relativistic and relativistic stars. We produce screened solutions and use them as initial data for non-linear numerical evolutions in spherical symmetry. We find that these solutions are stable under large initial perturbations, as long as they do not cause gravitational collapse. When gravitational collapse is triggered, the characteristic speeds of the scalar evolution equation diverge, even before apparent black-hole or sound horizons form. This casts doubts on whether the dynamical evolution of screened stars may be predicted in these effective field theories.
Working directly with a general Hamiltonian for the spacetime metric with the $3+1$ decomposition and keeping only the spatial covariance, we investigate the possibility of reducing the number of degrees of freedom by introducing an auxiliary constraint. The auxiliary constraint is considered as part of the definition of the theory. Through a general Hamiltonian analysis, we find the conditions for the Hamiltonian as well as for the auxiliary constraint, under which the theory propagates two tensorial degrees of freedom only. The class of theories satisfying these conditions can be viewed as a new construction for the type-II minimally modified gravity theories, which propagate the same degrees of freedom of but are not equivalent to general relativity in the vacuum. We also illustrate our formalism by a concrete example, and derive the dispersion relation for the gravitational waves, which can be constrained by observations.
We study new FRW type cosmological models of modified gravity treated on the background of Palatini approach. These models are generalization of Einstein gravity by the presence of a scalar field non-minimally coupled to the curvature. The models employ Starobinskys term in the Lagrangian and dust matter. Therefore, as a by-product, an exhausted cosmological analysis of general relativity amended by quadratic term is presented. We investigate dynamics of our models, confront them with the currently available astrophysical data as well as against LCDM model. We have used the dynamical system methods in order to investigate dynamics of the models. It reveals the presence of a final sudden singularity. Fitting free parameters we have demonstrated by statistical analysis that this class of models is in a very good agreement with the data (including CMB measurements) as well as with the standard LCDM model predictions. One has to use statefinder diagnostic in order to discriminate among them. Therefore Bayesian methods of model selection have been employed in order to indicate preferred model. Only in the light of CMB data the concordance model remains invincible.
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