Extended minimal theories of massive gravity

Abstract

In this work, we introduce a class of extended Minimal Theories of Massive Gravity (eMTMG), without requiring a priori that the theory should admit the same homogeneous and isotropic cosmological solutions as the de Rham-Gabadadze-Tolley massive gravity. The theory is constructed as to have only two degrees of freedom in the gravity sector. In order to perform this step we first introduce a precursor theory endowed with a general graviton mass term, to which, at the level of the Hamiltonian, we add two extra constraints as to remove the unwanted degrees of freedom, which otherwise would typically lead to ghosts and/or instabilities. On analyzing the number of independent constraints and the properties of tensor mode perturbations, we see that the gravitational waves are the only propagating gravitational degrees of freedom which do acquire a non-trivial mass, as expected. In order to understand how the effective gravitational force works for this theory we then investigate cosmological scalar perturbations in the presence of a pressureless fluid. We then restrict the whole class of models by imposing the following conditions at all times: 1) it is possible to define an effective gravitational constant, $G_{\mathrm{eff}}$; 2) the value $G_{\text{eff}}/G_N$ is always finite but not always equal to unity (as to allow some non-trivial modifications of gravity, besides the massive tensorial modes); and 3) the square of mass of the graviton is always positive. These constraints automatically make also the ISW-effect contributions finite at all times. Finally we focus on a simple subclass of such theories, and show they already can give a rich and interesting phenomenology.

arXiv comment20 pages+appendices, 1 figure

References in corpus (41)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Modified Gravity and Cosmology
• The Confrontation between General Relativity and Experiment
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• A Comprehensive Measurement of the Local Value of the Hubble Constant with 1 km/s/Mpc Uncertainty from the Hubble Space Telescope and the SH0ES Team
• In the Realm of the Hubble tension $-$ a Review of Solutions
• Resummation of Massive Gravity
• Beyond the Cosmological Standard Model
• Massive Gravity
• Primordial Black Holes as Dark Matter
• The trouble with $H_0$
• Cosmological Tests of Modified Gravity
• Action functionals for relativistic perfect fluids
• Cosmology Intertwined III: $f{\sigma }_8$ and $S_8$
• Dark Energy Survey Year 3 Results: Cosmology from Cosmic Shear and Robustness to Data Calibration
• The Atacama Cosmology Telescope: A Measurement of the Cosmic Microwave Background Power Spectra at 98 and 150 GHz
• Massive gravity: nonlinear instability of the homogeneous and isotropic universe
• Open FRW universes and self-acceleration from nonlinear massive gravity
• Nonlinear stability of cosmological solutions in massive gravity
• Lorentz Breaking Massive Gravity in Curved Space
• Minimal theory of massive gravity
• Addressing $H_0$ tension by means of VCDM
• Phenomenology in minimal theory of massive gravity
• Minimally Modified Gravity: a Hamiltonian Construction
• Scaling solutions and weak gravity in dark energy with energy and momentum couplings
• Reducing the $H_0$ tension with generalized Proca theory
• Minimally Modified Gravity fitting Planck data better than $\Lambda$CDM
• Graviton mass might reduce tension between early and late time cosmological data
• Minimal theory of massive gravity in the light of CMB data and the $S_8$ tension
• Weakening gravity for dark matter in a type-II minimally modified gravity
• Minimal theory of massive gravity and constraints on the graviton mass
• Suppressed cosmic growth in coupled vector-tensor theories
• Minimal Theory of Bigravity: construction and cosmology
• Integrated Sachs-Wolfe-galaxy cross-correlation bounds on the two branches of the minimal theory of massive gravity
• Distinguishing modified gravity models
• Minimal theory of quasidilaton massive gravity
• Nonderivative Modified Gravity: a Classification
• Baryon Physics and Tight Coupling Approximation in Boltzmann Codes
• Horndeski extension of the minimal theory of quasidilaton massive gravity
• Non-linear dynamics of the minimal theory of massive gravity
• Phenomenology of minimal theory of quasidilaton massive gravity

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