Link redshift with luminosity distance?

[June_cosmo]

Homework Statement

Plot luminosity distance and redshift z

Homework Equations

$$d_L(z)=(1+z)r(z)$$
where d_L(z) is luminosity distance and r(z) is the comoving distance.
and we have
$$r(z)= \frac{H_0^{-1}}{\sqrt\Omega_K}*sinn[\sqrt{\Omega_K}\int_0^z\frac{dz'}{\sqrt{\Omega_M(1+z')^3}}]$$
where \Omega_Kis a measure of openness or closedness of the universe, sinn(x)=x in flat universe.
Suppose we consider a universe that is both flat and matter dominant, where \Omega_K=0,and \Omega_M=1.

The Attempt at a Solution

From the information given we know that
$$H_0d_L(z)=(1+z)\int_0^6\frac{dz'}{\sqrt{(1+z')^3}}$$
but I don't know how do I deal with z' when I plot it in, for example python? Since I don't know what z' equals to

 

[andrewkirk]

$$H_0d_L(z)=(1+z)\int_0^6\frac{dz'}{\sqrt{(1+z')^3}}$$
but I don't know how do I deal with z' when I plot it in, for example python? Since I don't know what z' equals to

z' is not equal to anything. It's what's called a dummy variable, like a looping variable in Python.
Nor do you need to program the integral calculation. Just work out the definite integral and you'll get a number that does not change with z. Work out the number once, then hard-code it into your program as a constant.

 

[June_cosmo]

z' is not equal to anything. It's what's called a dummy variable, like a looping variable in Python.
Nor do you need to program the integral calculation. Just work out the definite integral and you'll get a number that does not change with z. Work out the number once, then hard-code it into your program as a constant.

Oh so you mean just work out
$$\int_0^6\frac{dz'}{\sqrt{(1+z')^3}}$$
which is approximate 1.24, then just plot
$$H_0d_L(z)=1.24(1+z)?$$

 

[andrewkirk]

Yes, that's it.