Hamiltonian analysis of unimodular gravity and its quantization in the connection representation

We give a detailed account of the Hamiltonian GNH analysis of the parametrized unimodular extension of the Holst action. The purpose of the paper is to derive, through the clear geometric picture furnished by the GNH method, a simple Hamiltonian formulation for this model and explain why it is difficult to arrive at it in other approaches. We will also show how to take advantage of the field equations to anticipate the simple form of the constraints that we find in the paper.

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“…• Some incomplete analyses of the Hamiltonian formulation for unimodular gravity in terms of tetrads can be found in [11,32].…”

Section: Some Reflections On the Existing Literaturementioning

confidence: 99%

“…Its Hamiltonian analysis in metric variables is well known [10]. However, and despite some claims to the effect [11], a similar analysis in terms of tetrads starting from the Holst action has not been performed yet. The Holst action has several features that make the study of its parametrized unimodular version quite attractive.…”

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confidence: 99%

Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

2021

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“…In recent years, there appeared in the literature conflicting statements about the equivalence, or lack thereof, between GR and UG at the quantum level, see, e.g., [17,18,[21][22][23][24][25][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. We believe that some of these contradictions may be just due to different quantization procedures.…”

Section: Jhep12(2021)090mentioning

confidence: 99%

Can quantum fluctuations differentiate between standard and unimodular gravity?

Brito

Melichev

Percacci

et al. 2021

J. High Energ. Phys.

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We formally prove the existence of a quantization procedure that makes the path integral of a general diffeomorphism-invariant theory of gravity, with fixed total spacetime volume, equivalent to that of its unimodular version. This is achieved by means of a partial gauge fixing of diffeomorphisms together with a careful definition of the unimodular measure. The statement holds also in the presence of matter. As an explicit example, we consider scalar-tensor theories and compute the corresponding logarithmic divergences in both settings. In spite of significant differences in the coupling of the scalar field to gravity, the results are equivalent for all couplings, including non-minimal ones.

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“…As a consequence, nowadays, Unimodular Gravity could be effectively seen as an alternative to the cosmological constant problem [44,45] and even to the problem of quantization of gravity [46,47]. Further applications of Unimodular gravity can be seen in cosmology [48,49] and stellar astrophysics [50].…”

Section: Introductionmentioning

confidence: 99%

Unimodular Gravity Traversable Wormholes

Moraes¹,

Agrawal²,

Mishra³

2022

Preprint

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Wormholes are outstanding solutions of Einstein's General Relativity. They were worked out in the late 1980's by Morris and Thorne, who have figured out a recipe that wormholes must obey in order to be traversable, that is, safely crossed by travelers. A remarkable feature is that General Relativity Theory wormholes must be filled by exotic matter, which Morris and Thorne define as matter satisfying −p r > ρ, in which p r is the radial pressure and ρ is the energy density of the wormhole. In the present letter, we introduce, for the first time in the literature, traversable wormhole solutions of Einstein's Unimodular Gravity Theory. Unimodular Gravity was proposed by Einstein himself as the theory for which the field equations are the traceless portion of General Relativity field equations. Later, Weinberg has shown that this approach elegantly yields the solution of the infamous cosmological constant problem. The wormhole solutions here presented satisfy the metric conditions of "traversability" and remarkably evade the exotic matter condition, so we can affirm that Unimodular Gravity wormholes can be filled by ordinary matter.

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Hamiltonian analysis of unimodular gravity and its quantization in the connection representation

Cited by 13 publications

References 22 publications

Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

Hamiltonian Gotay-Nester-Hinds analysis of the parametrized unimodular extension of the Holst action

Can quantum fluctuations differentiate between standard and unimodular gravity?

Unimodular Gravity Traversable Wormholes

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