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June_cosmo
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Homework Statement
Plot luminosity distance and redshift z
Homework Equations
$$d_L(z)=(1+z)r(z)$$
where [itex]d_L(z)[/itex] 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 [itex]\Omega_K[/itex]is 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 [itex]\Omega_K=0[/itex],and [itex]\Omega_M=1[/itex].
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
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