Unifying Dark Energy & Dark Matter: Investigating the Chaplygin Gas

[kptsilva]

Hello every one!

How many of you have learned about the unification of dark energy and dark matter?
I'm doing my research regarding the Chaplygin gas and I've come across this research paper.
arxiv.org/pdf/grqc/0202064.pdf

At the end, they solve the equation 36 (3/2*ab′′ + (1 − w)ab′ − (1 + w)(1 − 3αw)b = 0
, and only use one boundary which is b′(aeq) = 0. Don't we need another boundary condition since this is a second order DE?


Any knowledge will be much appreciated!

 

[Steely Dan]

The other initial condition must be the value of $b(a_{eq})$. But since what is being plotted is $b / b(a_{eq})$, this is naturally one on the graph.

 

[kptsilva]

thank you for the idea!
I'd like to plot this using mathematica, so first i need solve this for b. So it requires two boundary conditions. I can't use the condition b(aeq)=1 since the plot b/b(aeq) vs. a will not be different from b vs. a, right?