Geometric multipliers and partial teleparallelism in Poincaré gauge theory

Barker, W. E. V.

doi:10.48550/arxiv.2205.13534

Cited by 2 publications

(20 citation statements)

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“…Before proceeding, we introduce the gauge-theoretic formulation of Poincaré gauge theory, as used in [8,13,14,64,[73][74][75]. The gauge picture does not offer any special advantage over the geometric setup in (1), but it is more consistent with previous Hamiltonian analyses in [8,23,45,[60][61][62]76].…”

Section: A Conventionsmentioning

confidence: 99%

“…As with our earlier work [13,14,64], we will neglect the matter Lagrangian M . The field strengths in (6a) and (6b) are independent of the velocities for 0 and 0 , so (11) imply 10 primary constraints of the form…”

Section: A Geometric Setupmentioning

confidence: 99%

“…This is a general rule unless stated otherwise: i.e., tensors whose (Lorentz-invariant) index structure are identical will use the same SO(3) irrep notation, but a different symbol. It is possible, if needed, to recover the explicit 'humanreadable' projection operators used in the above calculations, such as appear in ̂ ́ ≡  ́ ̂ and ̂ ́ ≡  ́ ̂ , where the sectors are represented by and indices according to our conventions in [64]; the ́ accent denotes variable indices, and these projections are defined as obtaining precisely the irreps in Eqs. (16a), (16b), (17b) and (17c).…”

Section: mentioning

confidence: 99%

“…Locality signifies that the underlying functionals contain Dirac distribuions, themselves subject to the total derivatives of the generalised Euler-Lagrange equations. The full ramifications of covariantly removing these Dirac gradients are detailed in [14,64], and some special cases are discussed in electrodynamics on the lightcone [88] and noncritical string theory [89]. Currently, HiGGS is able to accommodate the first order Euler-Lagrange formalism in PoissonBracket[].…”

Section: Module: 'Poissonbracket'mentioning

confidence: 99%

“…In this paper we present a computer algebra implementation of the nonlinear Hamiltonian analysis for a generalisation of the full PGT, in which one may covariantly disable arbitrary irreps of the torsion and curvature by means of Lagrangian multiplier fields. This generalisation was put forward as an antistrong-coupling measure in [14], and its Hamiltonian structure is elucidated in the companion paper [64]. In the conventions of (1), we may write generalised PGT as…”

Section: Introductionmentioning

confidence: 99%

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Supercomputers against strong coupling in gravity with curvature and torsion

Barker¹

2022

Preprint

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Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm for curvature and torsion theories is presented. These non-Riemannian or Poincaré gauge theories suffer notoriously from strong coupling. The implementation forms a package (the 'Hamiltonian Gauge Gravity Surveyor' -HiGGS) for the xAct tensor manipulation suite in Mathematica. Poisson brackets can be evaluated in parallel, meaning that Hamiltonian analysis can be done on silicon, and at scale. Accordingly HiGGS is designed to survey the whole Lagrangian space with high-performance computing resources (clusters and supercomputers). To demonstrate this, the space of 'outlawed' Poincaré gauge theories is surveyed, in which a massive parity-even/odd vector or parity-odd tensor torsion particle accompanies the usual graviton. The survey spans possible configurations of teleparallel-style multiplier fields which might be used to kill-off the strongly coupled modes, with the results to be analysed in subsequent work. All brackets between the known primary and secondary constraints of all theories are made available for future study. Demonstrations are also given for using HiGGS -on a desktop computer -to run the Dirac-Bergmann algorithm on specific theories, such as Einstein-Cartan theory and its minimal extensions.

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Section: A Conventionsmentioning

confidence: 99%

Section: A Geometric Setupmentioning

confidence: 99%

Section: mentioning

confidence: 99%

Section: Module: 'Poissonbracket'mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Supercomputers against strong coupling in gravity with curvature and torsion

Barker¹

2022

Preprint

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The effective inflationary potential of constant-torsion emergent gravity

Rew¹,

Barker²

2023

Preprint

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Constant-torsion emergent gravity (CTEG) has a Lagrangian quadratic in curvature and torsion, but without any Einstein-Hilbert term. CTEG is motivated by a unitary, power-counting renormalisable particle spectrum. The timelike axial torsion adopts a vacuum expectation value, and the Friedmann cosmology emerges dynamically on this torsion condensate. We show that this mechanism -and the whole background cosmology of CTEG -may be understood through the effective potential of a canonical single scalar field model. The effective potential allows for hilltop inflation in the early Universe. In the late Universe, the Hubble friction overdamps the final quadratic approach to the effective minimum at the condensate, where the value of the potential becomes the cosmological constant. We do not consider particle production through spin-torsion coupling, or running of Lagrangian parameters. The model must be completed if reheating and a separation of inflationary and dark energy scales are to be understood. It is suggested that the divergence of the potential at large values of the scalar is inconsistent with the linearised propagator analysis of CTEG around zero-torsion Minkowski spacetime. This background may therefore be a strongly coupled surface in CTEG.

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Geometric multipliers and partial teleparallelism in Poincaré gauge theory

Cited by 2 publications

References 34 publications

Supercomputers against strong coupling in gravity with curvature and torsion

Supercomputers against strong coupling in gravity with curvature and torsion

The effective inflationary potential of constant-torsion emergent gravity

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