I am trying to calculate the redshift drift where its written as

$$\frac{dz}{dt} = (1+z)H_0 - H \tag{1}$$

We also know that $$1+z = a(t_o) / a(t_e) \tag{2}$$

and $$H_0 = \frac{\dot{a}(t_0)}{a(t_0)}$$

$$H = \frac{\dot{a}(t_e)}{a(t_e)}$$

  • $\begingroup$ Related question: physics.stackexchange.com/q/400386 $\endgroup$
    – D. Halsey
    Sep 30, 2020 at 12:45
  • $\begingroup$ Layla, can you specify your problem? If you know the scale factors then the redshift is given by your equation (2). $\endgroup$
    – psm
    Sep 30, 2020 at 15:13
  • $\begingroup$ @psm What information do you need ? $\endgroup$
    – seVenVo1d
    Oct 3, 2020 at 18:29

1 Answer 1


You have an inaccuracy in the first equation regarding "H". Normally in the context of differentiating with respect to t, functions are assumed to be having a function of t as an argument, and if none is given, then it is normally assumed that H=H(t). In the case of your equation, H=H(z)=H(z(t)). See

What is the cosmological redshift drift effect? .

I suggest the other equations should also be in terms of z rather than t. You should also note that z(t0)=0, and z(t)=(1/a(t))-1.

I hope this helps.


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