Intrinsic time gravity, heat kernel regularization, and emergence of Einstein’s theory

Ita, Eyo Eyo; Soo, Chopin; Yu, Hoi-Lai

doi:10.1088/1361-6382/abcb0e

Cited by 2 publications

(3 citation statements)

References 21 publications

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“…With suitable regularization, the Hamiltonian can be put [8,23] in the positive-definite self-adjoint form 1…”

Section: Institutional Reviewmentioning

confidence: 99%

Cosmic Time and the Initial State of the Universe

Soo

2023

Universe

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The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein’s theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time Geometrodynamics advocates a paradigm shift from four covariance to just spatial diffeomorphism invariance. Consequently, causal time-ordering and quantum Schrödinger–Heisenberg evolution in cosmic time become meaningful. The natural addition of a Cotton–York term to the physical Hamiltonian changes the initial data problem radically. In the classical context, this is studied with the Lichnerowicz–York equation; quantum mechanically, it lends weight to the origin of the universe as an exact Chern–Simons Hartle–Hawking state, which features Euclidean–Lorentzian instanton tunneling. At the level of expectation values, this quantum state yields a low-entropy hot smooth Robertson–Walker beginning in accord with Penrose’s Weyl Curvature Hypothesis. The Chern–Simons Hartle–Hawking state also manifests transverse traceless quantum metric fluctuations, with, at the lowest approximation, scale-invariant two-point correlations as one of its defining characteristics.

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“…With suitable regularization, the Hamiltonian can be put [8,23] in the positive-definite self-adjoint form 1…”

Section: Institutional Reviewmentioning

confidence: 99%

Cosmic Time and the Initial State of the Universe

Soo

2023

Universe

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“…It is noteworthy that the commutation relations of the momentric variables πi j are in fact the su(3) algebra. The physical Hamiltonian H Phys which generates evolution with respect to intrinsic time T has been elucidated elsewhere [3,8], and it takes the simple form…”

Section: Introductionmentioning

confidence: 99%

“…[3], the Hamiltonian density is the square root of a positive semi-definite, self-adjoint operator that governs the evolution of the theory with respect to intrinsic time T = 2 3 ln(V /V 0 ) wherein V is the spatial volume of the universe. Einstein's Ricci scalar potential and cosmological constant term emerge after regularization of a coincident commutator term [8]. 2 For any ADM decomposition of the metric, N = √ q(∂t ln…”

Section: Introductionmentioning

confidence: 99%

Gravitational waves in intrinsic time geometrodynamics

Ita¹,

Soo²,

Yu³

2018

Eur. Phys. J. C

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Gravitational waves are investigated in Intrinsic Time Geometrodynamics. This theory has a non-vanishing physical Hamiltonian generating intrinsic time development in our expanding universe, and four-covariance is explicitly broken by higher spatial curvature terms. Linearization of Hamilton's equations about the de Sitter solution produces transverse traceless excitations, with the physics of gravitational waves in Einstein's General Relativity recovered in the low curvature low frequency limit. A noteworthy feature of this theory is that gravitational waves always carry positive energy density, even for compact spatial slicings without any energy contribution from boundary Hamiltonian. This study of gravitational waves in compact k = +1 cosmological de Sitter spacetime is in contradistinction to, and complements, previous k = −1 investigations of Hawking, Hertog and Turok and other more familiar k = 0 works. In addition, possible non-four-covariant Horava gravity contributions are considered (hence the use of canonical Hamiltonian, rather than Lagrangian, methods). Recent explicit S 3 transversetraceless mode spectrum of Lindblom, Taylor and Zhang are also employed to complete the discussion.

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Intrinsic time gravity, heat kernel regularization, and emergence of Einstein’s theory

Cited by 2 publications

References 21 publications

Cosmic Time and the Initial State of the Universe

Cosmic Time and the Initial State of the Universe

Gravitational waves in intrinsic time geometrodynamics

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