Different equations for the growth factor

[shadishacker]

Hi everyone,

I am looking for the correct form of the growth factor in large scale structure.
I have found two different equations which I think are not consistent! Can anyone please tell me why it is like this?

The first one if from the book "formation of the structure in the universe" Edited by Avishai Dekel. In equation (2.9) it is said:

\begin{equation}
D(z) = H \int{\dot{a}^{-2} dt}
\end{equation}

in which D(z) is the growth function, a is the scale factor, H is the Hubble parameter and t is the time.The second one if from the book "principles of physical cosmology" Edited by Peebles. In equation (13.78) it is said:

\begin{equation}
D(z) = E \frac{5}{2} \Omega \int{\frac{1+z}{E^3}dz}
\end{equation}

in which D(z) is the growth function, z is the redshift, H is the Hubble parameter, E = H/H0 and Omega is the matter density parameter.

Can anyone tell me why are these two different?!
They for sure give different results for the mass function :(

 

[AndyW]

Hello,

Thank you for your question and for bringing this discrepancy to our attention. it is important to carefully evaluate and compare different equations and theories to ensure accuracy in our understanding of the natural world.

After reviewing the two equations you have provided, I can see that the first equation is using the scale factor (a) and the second equation is using the redshift (z). These are two different variables that are related but not equivalent. The scale factor is a measure of the expansion of the universe, while the redshift is a measure of the shift in the spectrum of light from distant objects due to the expansion of the universe.

Additionally, the two equations are using different parameters such as the Hubble parameter (H) and the matter density parameter (Omega), which can also lead to different results. It is important to note that there are many different models and theories in cosmology, and they may use different equations and parameters to describe the same phenomena. It is up to us as scientists to carefully evaluate and choose the most accurate and consistent equations for our research.

In this case, it is possible that one of the equations may be outdated or based on different assumptions. I suggest doing further research and consulting with experts in the field to determine which equation is more appropriate for your specific research and to understand the underlying reasons for the differences.

I hope this helps to clarify the discrepancy between the two equations and I wish you the best in your research endeavors.