Translation invariant time-dependent solutions to massive gravity II

Abstract

This paper is a sequel to arXiv:1310.6560 [hep-th] and is also devoted to translation-invariant solutions of ghost-free massive gravity in its moving frame formulation. Here we consider a mass term which is linear in the vielbein (corresponding to a ${\beta }_3$ term in the 4D metric formulation) in addition to the cosmological constant. We determine explicitly the constraints, and from the initial value formulation show that the time-dependent solutions can have singularities at a finite time. Although the constraints give, as in the ${\beta }_1$ case, the correct number of degrees of freedom for a massive spin two field, we show that the lapse function can change sign at a finite time causing a singular time evolution. This is very different to the ${\beta }_1$ case where time evolution is always well defined. We conclude that the ${\beta }_3$ mass term can be pathological and should be treated with care.

19 pages, 1 figure

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Cited by in corpus (4)

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• Covariant constraints for generic massive gravity and analysis of its characteristics
• Massive graviton on arbitrary background: derivation, syzygies, applications
• Translation invariant time-dependent massive gravity: Hamiltonian analysis