Non-linear dynamics of the minimal theory of massive gravity

Hagala, R.; Felice, Antonio De; Mota, David F.; Mukohyama, Shinji

doi:10.1051/0004-6361/202040018

Cited by 12 publications

(8 citation statements)

References 33 publications

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“…The new class of theories, on the one hand, should have the same (two tensorial) degrees of freedom as in GR, but on the other hand, it should be different from GR: namely, it should have a different (and possibly interesting) gravitational phenomenology (see e.g. [12,13,16,17,20]). In particular, for the two theories (VCDM [19] and VCCDM [22]), it was shown recently that in the absence of matter fields, both time-dependent and static spherically symmetric black holes solutions reduce to the standard Schwarzschild de Sitter solutions of GR, provided that physical boundary conditions on the Misner-Sharp mass describing a compact source are imposed [21].…”

Section: Discussionmentioning

confidence: 99%

“…in [6,7,10,11]. Further studies were aimed to find whether these models could accommodate cosmological data [8,[12][13][14][15][16][17][18], or to find other models which could be more suitable for cosmology, especially in the light of the puzzles of today's gravity at large scales. In particular, recently a theory of type-II MMG called VCDM was introduced to implement a dynamical component at the level of the cosmological background without introducing any new degree of freedom [19], which seems to give a promising insight into the H 0 -tension puzzle [20].…”

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confidence: 99%

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Static, spherically symmetric objects in Type-II minimally modified gravity

De Felice,

Mukohyama,

Pookkillath

2021

Preprint

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Static, spherically symmetric solutions representing stars made of barotropic perfect fluid are studied in the context of two theories of type-II minimally modified gravity, VCDM and VCCDM. Both of these theories share the property that no additional degree of freedom is introduced in the gravity sector, and propagate only two gravitational waves besides matter fields, as in General Relativity (GR). We find that, on imposing physical boundary conditions on the Misner-Sharp mass of the system, the solutions in V(C)CDM exactly coincide with the ones in GR, namely they also satisfy the Tolman-Oppenheimer-Volkoff equation. I. INTRODUCTIONWe live in a particular era in cosmology due to the remarkable precision achieved in various cosmological observations. As a matter of fact, since the discovery of gravitational waves [1], General Relativity (GR) has been confirmed by yet another independent experimental data. GR then appears more and more to be the theory of classical gravitational interactions. This picture is quite astonishing for a theory that was introduced more than one hundred years ago.To this beautiful picture and powerful result of theoretical physics, cosmological observations are adding to it several discrepant results. One of the most embarrassing among them is the tension among different measurements of the expansion rate of our universe today, which is called the Hubble parameter H 0 . Although this is one of the oldest and elementary measurements in cosmology, on assuming GR to hold at all times after the big bang, we find that different data sets find different values for this unique observable. The only ways out: experiments are wrong, statistical analysis is not correct, or, surprisingly, the assumed underlining theory does not hold.If GR is not suspicious in the context of cosmology, then either the cosmological data or the statistical analysis in determining H 0 cannot be trusted. Evidently, this statement (if correct) needs then to be completed by finding the reason why the data or/and the analysis are wrong. As long as we do not have a clear explanation for it, the other possibilities need to be explored. One could also conclude that the classical theory of gravity as described by GR is correct; what is missing is a proper description of the matter present in the universe. Then, we need to understand better what kind of matter can be responsible for the different values of H 0 without contradicting with all experiments and observations so far. On top of that, one would like to give possible predictions from the requirement that the extra matter responsible for the tension would be "visible" only in cosmology and have no (or negligible) effects otherwise, e.g. at solar system scales.Recently more cosmological data have been adding to this obscure picture another unsolved puzzle [2][3][4]. In the context of GR, these data sets tend to give a prediction for the growth rate of the structure which is lower than and in tension with the predictions coming from early-times data sets [5]. On top of that...

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Section: Discussionmentioning

confidence: 99%

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confidence: 99%

Static, spherically symmetric objects in Type-II minimally modified gravity

De Felice,

Mukohyama,

Pookkillath

2021

Preprint

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“…However, well before reaching this pole, the phenomenology of the theory was leading to inconsistencies, see e.g. [37,45]. Therefore, just avoiding the poles may not be enough to lead to a viable phenomenology.…”

Section: The Casementioning

confidence: 99%

“…This expression for G eff /G N is well-behaved for negative-squared-mass for the graviton (for which, though, a tachyonic instability, with a time-scale of order H −1 0 , would be affecting modes of order k/(a 0 H 0 ) ≃ 1) [36]. But for a large-enough (but still inside the allowed Ligo bounds) positive-squared-mass graviton, a range of positive µ 2 , for µ ≃ 2H 0 , would lead to strong modifications to G eff /G N , leading in turn to strong constraints from the data even at non-linear scales [37]. In particular, in a recent paper, on studying the effect of Planck data on MTMG, it was discovered that positive µ 2 is actually preferred but because of the above mentioned behavior of G eff /G N , µ 2 is strongly constrained toward values very close to zero [24].…”

Section: Introductionmentioning

confidence: 99%

Extended minimal theories of massive gravity

De Felice,

Mukohyama,

Pookkillath

2022

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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 eff ; 2) the value G eff /GN 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.

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“…Cosmology in MTMG has been studied in Refs. [38][39][40][41], where cosmological solutions in MTMG have been classified into the normal and self-accelerating branches. BH and stellar solutions in MTMG have been investigated in Ref.…”

Section: Introductionmentioning

confidence: 99%

Static and spherically symmetric general relativity solutions in Minimal Theory of Bigravity

Minamitsuji,

De Felice,

Mukohyama

et al. 2022

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We investigate static and spherically symmetric solutions in the Minimal Theory of Bigravity (MTBG). First, we show that a pair of Schwarzschild-de Sitter spacetimes with different cosmological constants and black hole masses written in the spatially-flat Gullstrand-Painlevé (GP) coordinates is a solution in the self-accelerating branch of MTBG, while it cannot be a solution in the normal branch. We then illustrate how Schwarzschild-de Sitter solutions can become compatible with the normal branch when using different coordinates. We also confirm that the self-accelerating branch of MTBG admits static and spherically symmetric general relativity solutions with matter written in the spatially-flat coordinates, including neutron stars with arbitrary matter equations of state. Finally, we show that in the self-accelerating branch nontrivial solutions are given by the Schwarzschild-de Sitter metrics written in nonstandard coordinates.

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Non-linear dynamics of the minimal theory of massive gravity

Cited by 12 publications

References 33 publications

Static, spherically symmetric objects in Type-II minimally modified gravity

Static, spherically symmetric objects in Type-II minimally modified gravity

Extended minimal theories of massive gravity

Static and spherically symmetric general relativity solutions in Minimal Theory of Bigravity

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