Calculate Comoving distance as a function of parameters

In summary, the conversation discusses constructing a likelihood function with density parameters found in the Friedman equation using Massive Gravity Action H. The integral needed to evaluate for the comoving distance is given, and while it cannot be solved using Mathematica, it can be solved by expanding it as a Taylor series. An alternative method, NIntegrate, is suggested.
  • #1
QFT25
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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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  • #2
Why not use NIntegrate?
 

1. What is comoving distance and why is it important in scientific research?

Comoving distance is a measure of the physical separation between two objects in the universe, taking into account the expansion of the universe. It is important in scientific research because it allows us to accurately calculate the distance between objects, which is crucial in understanding the structure and evolution of the universe.

2. What are the parameters that affect the calculation of comoving distance?

The parameters that affect the calculation of comoving distance include the redshift of the objects, the cosmological model being used, and the Hubble constant. The redshift is a measure of how much the light from an object has been stretched due to the expansion of the universe. The cosmological model describes the overall geometry and composition of the universe. The Hubble constant is a measure of the rate of expansion of the universe.

3. How is comoving distance different from other measures of distance in the universe?

Comoving distance differs from other measures of distance in the universe, such as proper distance and luminosity distance, because it takes into account the expansion of the universe. Proper distance is the physical distance between two objects at a specific point in time, while luminosity distance is based on the amount of light received from an object. Comoving distance, on the other hand, is a measure of the distance between objects at the present time, factoring in the expansion of the universe.

4. Can comoving distance be calculated for objects outside of our observable universe?

No, comoving distance can only be calculated for objects within our observable universe. This is because the observable universe is limited by the speed of light, and objects beyond this limit are moving away from us faster than the speed of light. Therefore, their comoving distance cannot be accurately calculated.

5. How is comoving distance used in cosmological studies and research?

Comoving distance is used in various cosmological studies and research, such as measuring the expansion of the universe, understanding the large-scale structure of the universe, and studying the evolution of galaxies. It is also an important factor in the calculation of cosmological distances, such as the age of the universe and the Hubble parameter, which are crucial in determining the fundamental properties of the universe.

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