Can one tell Einstein's unimodular theory from Einstein's general relativity?

Álvarez, Enrique

doi:10.1088/1126-6708/2005/03/002

Cited by 125 publications

(125 citation statements)

References 19 publications

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“…It is thus of interest to investigate a quantum theory of unimodular gravity. Unimodular gravity in both its quantum and classical form has sparked considerable interest since it was originally proposed [3][4][5][6][7][8][9][10][11][12][13][14][15][16].…”

Section: Jhep04(2015)096mentioning

confidence: 99%

The Renormalization Group flow of unimodular f(R) gravity

Eichhorn

2015

J. High Energ. Phys.

129

101

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Unimodular gravity is classically equivalent to General Relativity. This equivalence extends to actions which are functions of the curvature scalar. At the quantum level, the dynamics could differ. Most importantly, the cosmological constant is not a coupling in the unimodular action, providing a new vantage point from which to address the cosmological constant fine-tuning problem. Here, a quantum theory based on the asymptotic safety scenario is studied, and evidence for an interacting fixed point in unimodular f (R) gravity is found. We study the fixed point and its properties, and also discuss the compatibility of unimodular asymptotic safety with dynamical matter, finding evidence for its compatibility with the matter degrees of freedom of the Standard Model.

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Section: Jhep04(2015)096mentioning

confidence: 99%

The Renormalization Group flow of unimodular f(R) gravity

Eichhorn

2015

J. High Energ. Phys.

129

101

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“…Therefore, the only "observable" differences between both theories may be in the quantum theory [2,3,11,12,13,14]). …”

Section: Nonlinear Theorymentioning

confidence: 99%

“…The best known example is Einstein' s 1919 theory (cf. [2] for a recent reference), which corresponds to the traceless part of the usual Einstein's equations.…”

mentioning

confidence: 99%

“…If the mass is large enough, this leads us back to the situation where the extra scalar does not propagate at low energies, which is effectively equivalent to the scenario described by Eq. (2) mass terms necessarily break all invariance under diffeomorphisms. For massive particles, the little group is that of ordinary spatial rotations O(3), which leads to finite dimensional unitary representations without the need of invoking any gauge symmetry.…”

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confidence: 99%

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Transverse Fierz–Pauli symmetry

et al. 2006

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We consider some flat space theories for spin 2 gravitons, with less invariance than full diffeomorphisms. For the massless case, classical stability and absence of ghosts require invariance under transverse diffeomorphisms (TDiff), h µν → h µν + 2∂ (ν ξ µ) , with ∂ µ ξ µ = 0. Generic TDiff invariant theories contain a propagating scalar, which disappears if the symmetry is enhanced in one of two ways. One possibility is to consider full diffeomorphisms (Diff). The other (which we denote WTDiff) adds a Weyl symmetry, by which the Lagrangian becomes independent of the trace. The first possibility corresponds to General Relativity, whereas the second corresponds to "unimodular" gravity (in a certain gauge). Phenomenologically, both options are equally acceptable. For massive gravitons, the situation is more restrictive. Up to field redefinitions, classical stability and absence of ghosts lead directly to the standard Fierz-Pauli Lagrangian. In this sense, the WTDiff theory is more rigid against deformations than linearized GR, since a mass term cannot be added without provoking the appearance of ghosts.

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“…These particular transformations have been called unimodular transformations, and in a preceding paper the name transverse diffeomorphisms (TDiffs) spanning a subgroup TDiff(M) has been used. Please refer to [1] where other relevant references can also be found. To be specific, transverse diffeomorphisms (TDiffs) in a spacetime manifold whose points are described in a particular coordinate chart by x µ (P ), µ = 0, 1, .…”

Section: Introductionmentioning

confidence: 99%