Calculate Comoving distance as a function of parameters

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SUMMARY

This discussion focuses on calculating the comoving distance as a function of parameters derived from the Friedman equation using the Massive Gravity Action H. The integral to evaluate is defined as Integrate[1/Sqrt[a + b (1 + z) + c (1 + z)^2 + d (1 + z)^3 + r (1 + z)^4], {z, 0, Z}]. The user attempted to solve this using Mathematica but encountered difficulties, suggesting the use of Taylor series for simplification. A recommendation was made to utilize NIntegrate as an alternative method for evaluating the integral.

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  • Understanding of the Friedman equation in cosmology
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  • Knowledge of numerical integration techniques, specifically NIntegrate
  • Basic concepts of Taylor series expansion
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Homework Statement


I'm doing research with a Professor and I'm constructing a likelihood function which has parameters the density parameters found in the Friedman equation found using Massive Gravity Action H

Homework Equations


H(z)^2=a + b (1 + z) + c (1 + z)^2 + d (1 + z)^3 + r (1 + z)^4 ignoring units the integral I need to evaluate for the comoving distance is

Integrate[ 1/Sqrt[a + b (1 + z) + c (1 + z)^2 + d (1 + z)^3 + r (1 + z)^4], {z, 0, Z}]

The Attempt at a Solution



I put this into Mathematica and it can't do it. If I expand it out as a Taylor series I can do it. Is there any other way to evaluate this integral as a function of the parameters and Z? [/B]
 
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Why not use NIntegrate?
 

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