Calculating the redshift drift

Question

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 $$H_0 = frac{dot{a}(t_0)}{a(t_0)}$$
$$H = frac{dot{a}(t_e)}{a(t_e)}$$

Buzz · Answer

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.

Calculating the redshift drift

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