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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 :(

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# A Different equations for the growth factor

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