Physical Foundations of Cosmology

68 Propagation of light and horizons

In a flat universe, where
0 =1 and (^) = 1 − (^) m, the redshift drift,v≡
z/(1+z),is equal to
v
z ̇t
1 +z
=−H 0 t

{

[ (^) m(1+z)+( 1 − (^) m)(1+z)−^2 ]^1 /^2 − 1

}

. (2.88)

The drift is negative for a matter-dominated universe( (^) m→ 1 )and positive
if the cosmological constant dominates( (^) m→ 0 ).For (^) m=1 and (^) = 0 ,its
magnitude is
v≈−2(

√

1 +z−1) cm s−^1

for observations made a periodt=1 year apart. Although the velocity shift is
tiny and beyond current detection capabilities, redshift is one of the most precisely
measured physical observables. Current technology would enable measurements
of shifts of perhaps 10 m s−^1 per year. The required improvement by a few or-
ders of magnitude in the next few decades is conceivable. Such a measurement
would represent a direct detection of acceleration which would complement the
luminosity–redshift tests.