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Link redshift with luminosity distance?

  1. Oct 25, 2015 #1
    1. The problem statement, all variables and given/known data
    Plot luminosity distance and redshift z

    2. Relevant 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].
    3. 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
     
    Last edited: Oct 25, 2015
  2. jcsd
  3. Oct 26, 2015 #2

    andrewkirk

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    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.
     
  4. Oct 26, 2015 #3
    Oh so you mean just work out
    $$\int_0^6\frac{dz'}{\sqrt{(1+z')^3}}$$
    which is approximate 1.24, then just plot
    $$H_0d_L(z)=1.24(1+z)?$$
     
  5. Oct 26, 2015 #4

    andrewkirk

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    Yes, that's it.
     
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