Understanding Matter Density Parameter

[camarman]

Hello, @ja-vazquez and @igomezv

I am a M.Sc. Physics Student at Istanbul Technical University. I am trying to create a new model and in this model I have to define matter density. However, it seems there are two matter density definitions. The first one seems to be Om and the second is Ocb.

In SimpleMC, the only definition I could have find for Om is in simplemc/models/LCDMCosmology.py, and it is written as

# this returns the Wang+Wang variables in a vec
def WangWangVec(self):
    Omh2   = self.Ocb*self.h**2+self.Omnuh2
    ...

Meanwhile, for Ocb there is

self.Ocb = self.Om-self.Omnu-self.Omrad

again at the same file.

But these two definitions are also seems strange and contradictory... Also, In general the RHSquared_a() function defined as

(self.Ocb/a**3+self.Ok/a**2+self.Omrad/a**4+NuContrib+(1.0-self.Om-self.Ok))

So first Ocb is used as a normal matter density, but later while writing the DE energy density, Om is used...which is confusing..

My questions:

1) What are the definitions (mathematically) of Om and Ocb 2) How should I write the matter density, if I want to create a new model ? Should I define a new matter density term by using Ocb and Om ?

Thanks, Arman

[camarman]

Does Ocb represents

$$ \Omega{\rm cb} = \Omega{\rm CDM} + \Omega_{\rm baryon} $$

[igomezv]

Hi Arman,

They are different parameters. $\Omega_{cb}$ represents baryons plus cold dark matter, $\Omega_b$ is only baryonic matter and $\Omega_m$ contains all the matter content (including radiation and neutrinos).

As for your second question, you need to use $\Omega_{cb}$ as matter density for your new model in the Friedmann equation, e. g. E(z) = self.Ocb/a**3+self.Omrad/a**4+NuContrib+(1 -self. Om). And you can use the total matter density $\Omega_m$ for the cosmological constant represented through (1 - self.Om).

I may be neglecting some details, but I hope you find this answer helpful.

Best regards, Isidro.

[igomezv]

Does Ocb represents

Ωcb=ΩCDM+Ωbaryon

That's right.

[camarman]

Thanks for the fast reply @igomezv. I guess what confused me is that writing the H(z) as

(self.Ocb/a**3+self.Omrad/a**4+(1.0-self.Om))

instead of

(self.Ocb/a**3+self.Omrad/a**4+(1.0-self.Ocb-self.Omrad))

But I understand the idea now. Also, self.Omrad is the only the radiation contribution right ?

[igomezv]

But I understand the idea now. Also, self.Omrad is the only the radiation contribution right ? Yes, it is right.

[camarman]

Okay, thanks a lot. I really appreciate it.