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Arms, Judith M.; Marsden, Jerrold E.

doi:10.1512/iumj.1979.28.28008

Cited by 28 publications

(14 citation statements)

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“…In the presence of the Killing vectors in the background metric g ab , Fischer, Marsden and Moncrief [9,10], have proved the violation of this condition as the criterion of linearization instability for the vacuum case. Similar results hold for Einstein field equations coupled with matter fields such as scalar fields, electromagnetic fields and Yang-Mills fields [11,38,39].…”

Section: Discussionsupporting

confidence: 58%

Perturbations and Linearization Stability of Closed Friedmann Universes

Noh,

Hwang,

Barrow

2020

Preprint

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We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wavenumbers (L = 0 and 1) are generally known to be fictitious, but here we show that both are physical. The issue is more subtle in Einstein static universes where closed background space has a time-like Killing vector with the consequent occurrence of linearization instability. Solutions of the linearized equation need to satisfy the Taub constraint on a quadratic combination of first-order variables. We evaluate the Taub constraint in the two available fundamental gauge conditions, and show that in both gauges the L ≥ 1 modes should accompany the L = 0 (homogeneous) mode for vanishing sound speed, cs. For c 2 s > 1/5 (a scalar field supported Einstein static model belongs to this case with c 2 s = 1), the L ≥ 2 modes are known to be stable. In order to have a stable Einstein static evolutionary stage in the early universe, before inflation and without singularity, although the Taub constraint does not forbid it, we need to find a mechanism to suppress the unstable L = 0 and L = 1 modes.

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Section: Discussionsupporting

confidence: 58%

Perturbations and Linearization Stability of Closed Friedmann Universes

Noh,

Hwang,

Barrow

2020

Preprint

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“…Now, by the definition (2) of the momentum mapping, any tangent vector to the orbit is annihilated by oc q . As we may decompose any X q εT q Q into the sum of a vector tangential to the orbit and a vector tangential to S q9 (6) follows. The invariance of < /~1(0) under G is obvious by the Ad*-equivariance of / and the statement π( e /~1(0)) -Q is trivial, as O q , mapping any X q eT q Q to zero, is contained in /~ x (0) for any qeQ.…”

Section: The Reduced Phase and Configuration Spacementioning

confidence: 99%

“…Singular points in Q/G are linearization unstable. In [6] it was shown that for these points the linearized constraints have to be supplemented by additional quadratic constraint conditions, which suppress spurious solutions of the linearized constraint equations. The effect of these additional constraints is a suppression of transitions to configurations of lower symmetry.…”

Section: Introductionmentioning

confidence: 99%

Orbifolds as configuration spaces of systems with gauge symmetries

Emmrich

Römer

1990

Commun.Math. Phys.

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In systems like Yang-Mills or gravity theory, which have a symmetry of gauge type, neither phase space nor configuration space is a manifold but rather an orbifold with singular points corresponding to classical states of non-generically higher symmetry. The consequences of these symmetries for quantum theory are investigated. First, a certain orbifold configuration space is identified. Then, the Schrodinger equation on this orbifold is considered. As a typical case, the Schrodinger equation on (double) cones over Riemannian manifolds is discussed in detail as a problem of selfadjoint extensions. A marked tendency towards concentration of the wave function around the singular points in configuration space is observed, which generically even reflects itself in the existence of additional bound states and can be interpreted as a quantum mechanism of symmetry enhancement.

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“…As discussed in ref. [11], Marsden, Fischer, Moncrief, and Arms [12,13,14,15] have proved that compact vacuum solutions of Einstein's equations with Killing symmetries have this subtle property, which is manifested in various other non-linear systems. In fact, in the four-function space of the general cosmological solution, small open neighbourhoods around the homogeneous type IX solution will be dense in spurious linearisations that are not approximations to a true inhomogeneous solution.…”

Section: Introductionmentioning

confidence: 99%

A conjecture about the general cosmological solution of Einstein's equations

Barrow

2020

Preprint

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We introduce consideration of a new factor, synchronisation of spacetime Mixmaster oscillations, that may play a simplifying role in understanding the nature of the general inhomogeneous cosmological solution to Einstein's equations. We conjecture that, on approach to a singularity, the interaction of spacetime Mixmaster oscillations in different regions of an inhomogeneous universe can produce a synchronisation of these oscillations through a coupling to their mean field in the way first demonstrated by the Kuramoto coupled oscillator model.

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Cited by 28 publications

References 0 publications

Perturbations and Linearization Stability of Closed Friedmann Universes

Perturbations and Linearization Stability of Closed Friedmann Universes

Orbifolds as configuration spaces of systems with gauge symmetries

A conjecture about the general cosmological solution of Einstein's equations

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