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 \geq 1 modes should accompany the L = 0 ( homogeneous ) mode for vanishing sound speed , c _ { s } .
For c _ { s } ^ { 2 } > 1 / 5 ( a scalar field supported Einstein static model belongs to this case with c _ { s } ^ { 2 } = 1 ) , the L \geq 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 .