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arXiv · 1308.4498

Time-reparametrization invariance and Hamilton-Jacobi approach to the cosmological sigma-model

Jan-Willem van Holten·Richard Kerner
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Abstract

The construction of physical models with local time-reparametrization invariance is reviewed. Negative-energy contributions to the hamiltonian are shown to be crucial for the realization of this reparametrization symmetry. The covariant formulation of the dynamics is used to develop a time and gauge invariant Hamilton-Jacobi theory. This formalism is applied to solve for the cosmology of a homogeneous universe of the Friedmann-Lemaitre-Robertson-Walker type. After a discussion of empty universes, the FLRW theory is extended with homogeneous scalar fields generically described by a $\sg$-model on some scalar manifold. An explicit gauge-invariant solution is constructed for the non-linear O(N)-models.

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Jan-Willem van Holten, Richard Kerner. 2013-08-21. Time-reparametrization invariance and Hamilton-Jacobi approach to the cosmological sigma-model. https://doi.org/10.1002/prop.201400008

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