de Rham-Gabadadze-Tolley massive gravity with degenerate reference metrics

Recently, a practical approach to holographic renormalization has been developed based on the Hamilton-Jacobi formulation. Using a simple Einstein-scalar theory, we clarify that this approach does not conflict with the Hamiltonian constraint as it seems. Then we apply it to the holographic renormalization of massive gravity. We assume that the shift vector is falling off fast enough asymptotically. We derive the counterterms up to the boundary dimension d=4. Interestingly, we find that the conformal anomaly can even occur in odd dimensions, which is different from the Einstein gravity. We check that the counterterms cancel the divergent part of the on-shell action at the background level. At the perturbation level, they are also applicable in several time-dependent cases.

show abstract

“…(C.1)-(C.4) have originally been listed in [23] and eq. (C.6) was proved in [49]. The rest part of this appendix is our demonstration for eqs.…”

Section: Some Basic Formulasmentioning

confidence: 87%

Hamilton-Jacobi approach to holographic renormalization of massive gravity

Chen

Peng

2019

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…And then, we shall demonstrate how the growth behavior of holographic complexity of a quantum field in the FLRW universe link the conserved charge and some geometric quantities on boundary cosmology by holographic dual, and what role the graviton mass term can play on this growth rate. First, let us write down the neutral massive Einstein action consisting of the Ricci scalar, cosmological constant term, graviton mass terms [57][58][59][60][61], which can be expressed as…”

Section: The Case For the Neutral Massive Black Holementioning

confidence: 99%

Holographic complexity growth in an FLRW universe

Cai

et al. 2020

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

In this paper, taking the large R limit and using the complexity-volume duality, we investigate the holographic complexity growth rate of a field state defined on the universe located at an asymptotical AdS boundary in Gauss-Bonnet gravity and massive gravity, respectively. For the Gauss-Bonnet gravity case, its growth behavior of the state mainly presents three kinds of contributions: one, as a finite term viewed as an interaction term, comes from a conserved charge, the second one is from the spatial volume of the universe and the third one relates the curvature of the horizon in the AdS Gauss-Bonnet black hole, where the Gauss-Bonnet effect plays a vital role on such growth rate. For massive gravity case, except the first divergent term still obeying the growth rate of the spatial volume of the Universe, its results reveal the more interesting novel phenomenons: beside the conserved charge E, the graviton mass term also provides its effect to the finite term ; and the third divergent term is determined by the spatial curvature of its horizon k and graviton mass effect; furthermore, the graviton mass effect can be completely responsible for the second divergent term as a new additional term saturating an area law. * Electronic address: wjpan˙zhgkxy@163.com

show abstract

“…This is one of the key point in our study, and deserves to be demonstrated in a little more detailed way. First of all, the ghost problem of the general theory of dRGT with singular reference metrics has been thoroughly discussed in [12,13]. In these previous works, the dRGT massive gravity with singular reference metrics is demonstrated to be ghost-free.…”

Section: Difficulty and Way Out Of Drgt Massive Cosmologymentioning

confidence: 99%

Towards a sound massive cosmology

Zhang

2019

Physics of the Dark Universe

View full text Add to dashboard Cite

It is known that de Rham-Gabadadze-Tolley (dRGT) massive gravity does not permit a homogeneous and isotropic universe with flat or spherical spatial metrics. We demonstrate that a singular reference metric solves this problem in an economic and straightforward way.In the dRGT massive gravity with a singular reference metric, there are sound homogeneous and isotropic cosmological solutions. We investigate cosmologies with the static and dynamical singular reference metrics, respectively. The term like dark energy appears naturally and the universe accelerates itself in some late time evolution. The term simulating dark matter also naturally emerges. We make a preliminary constraint on the parameters in the dRGT massive gravity in frame of the present cosmological model by using the data of supernovae, cosmic microwave back ground radiations, and baryonic acoustic oscillations.

show abstract

de Rham-Gabadadze-Tolley massive gravity with degenerate reference metrics

Cited by 18 publications

References 48 publications

Hamilton-Jacobi approach to holographic renormalization of massive gravity

Hamilton-Jacobi approach to holographic renormalization of massive gravity

Holographic complexity growth in an FLRW universe

Towards a sound massive cosmology

Contact Info

Product

Resources

About