For the specified flat matter-vacuum model,
Its small-redshift behaviour is , since . At high redshift, matter dominates and , so the initially positive redshift drift must turn negative. To locate the crossing, square ; both sides are positive, so squaring introduces no positive- spurious root. Factorization gives
Besides , the physical nonzero redshift-drift root in flat matter-Lambda cosmology is
The redshift drift is positive for and negative for . Its maximum satisfies and lies near , where . This zero is distinct from the acceleration transition at : redshift drift compares expansion at two epochs, while acceleration is local to one epoch.
Figure 1.
Redshift drift in three flat cosmologies, with the positive-to-negative crossing of the matter-vacuum model
. Details.