CAMB - Units for density and quintessence module

Use of Cobaya. camb, CLASS, cosmomc, compilers, etc.
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Paul Anthony Fronteri
Posts: 28
Joined: July 18 2013
Affiliation: University of Oslo

CAMB - Units for density and quintessence module

Post by Paul Anthony Fronteri » March 18 2014

Hey.

I have a question about units.

For the different densities is it written that:
grho is actually 8*pi*G*rho/c^2 at a=1, with units of Mpc**(-2).

It then all the different densities of the different components, baryons, photon, massless and massive neutrinos given in the units of 1/Mpc**2?

Further, there is a quintessence module, Quint. When reading the camb notes it says that:
CMBFAST/CAMB propagate quantities like kappa*a**2*rho, hence it is useful to work with phi = sqrt(kappa)*psi and similarly for V.

From this I understand that the scalar field, quintessence, is actually psi, but because of convience in the code, one uses phi instead? Is this correct? Do one then not need to take this into considuration if one like to change some of the equations?

In the code itself it commented in the potential function: !Returns (8*Pi*G)^(1-deriv/2)*d^{deriv}V(psi)/d^{deriv}psi evaluated at psi times (Mpc/c)^2 to get units in 1/Mpc^2. The input variable phi is sqrt(8*Pi*G)*psi.

However they use a strange way to "normalize" the potential. First they say that they use the dimensionless normalization kappa*V*T_pl^2, where T_pl is the planck time, setting this to: norm= 1d-122
After this they convert this to units of 1/Mpc^2 by taking: norm = norm * (Mpc/c)**2 /Tpl**2.

Later they add even another term m = 100, to the "normalization" of the field.

However does it seem that it need to be of the same units as the density 1/Mpc**2, and of the same order. It this correct?

So does anyone really knows what is going on, and if so, could someone please explain very simple what is going on.

Thanks in advance to anyone that have even a smallest clue, to a confused student.

Paul

Paul Anthony Fronteri
Posts: 28
Joined: July 18 2013
Affiliation: University of Oslo

CAMB - Units for density and quintessence module

Post by Paul Anthony Fronteri » March 26 2014

No one could answer this question? Even for the density in CAMB?

Erick Almaraz
Posts: 29
Joined: June 10 2012
Affiliation: University of Mexico

CAMB - Units for density and quintessence module

Post by Erick Almaraz » October 21 2014

Dear Paul.

As far as I know, all the distances in CAMB are measured in Mpc. In consequence, the units of the grho contribution from the scalar field are 1/Mpc^2 . Now, I don´t know who is the "psi" variable that is mentioned in the code. In my opinion the situation is as follows: in almost all the literature the quintessence field is denoted by phi and is measured in GeV. In CAMB, one makes the definition phi_CAMB= kappa*phi only for the purpose of leaving the field without units. According to this, the potential handled by the code is
V_CAMB= 8*pi*G*V
The factor (Mpc/c)**2/Tpl**2 is for leaving the units in Mpc^-2 . The choice of the normalization factor I think is motivated by the conditions you impose over the universe today, I mean, you want that the equation of the state of the scalar field is close to -1 and that the universe is expanding in our epoch.

I hope this information (it could have errors) might be useful.

Regards

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