Perturbations and linearization stability of closed Friedmann universes
Abstract
We consider perturbations of closed Friedmann universes. Perturbation modes of two lowest wave numbers (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 timelike Killing vector with the consequent occurrence of linearization instability. Proper 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 cs2>1 /5 (a scalar field supported Einstein static model belongs to this case with cs2=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.
- Publication:
-
Physical Review D
- Pub Date:
- June 2020
- DOI:
- 10.1103/PhysRevD.101.123527
- arXiv:
- arXiv:2003.14108
- Bibcode:
- 2020PhRvD.101l3527N
- Keywords:
-
- General Relativity and Quantum Cosmology;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- 19 pages, no figure, published in Phys. Rev. D