Quintessence in CAMB - Units of the potential?

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Paulo Santos
Posts: 2
Joined: December 17 2013
Affiliation: Institute of Theoretical Astrophysics, University of Oslo

Quintessence in CAMB - Units of the potential?

Post by Paulo Santos » December 17 2013

Hi all

I have been using the Quintessence equations for CAMB and have been having some doubts on the way the potential is defined.

From what I can see in the code, the potential should be given in units of 1/Mpc^2 as it is multiplied by 8*Pi*G.

Those units are considered in the norm parameter, but looking carefully at it, I don't understand how it changes from a dimensionless quantity to a quantity with 1/Mpc^2 by multiplying it with a factor (Mpc/c)^2/Tpl^2.

Shouldn't it remain dimensionless?


Thanks in advance,
Best

Paulo

Paulo Santos
Posts: 2
Joined: December 17 2013
Affiliation: Institute of Theoretical Astrophysics, University of Oslo

Quintessence in CAMB - Units of the potential?

Post by Paulo Santos » February 21 2014

Hi

Could anyone provide some insight on this subject?

I still couldn't figure out exactly how to make the code work for an m^2\phi^2/2 potential as I need to.
I guess that the problems likely lie in the normalisations considered in the potential.


I was also checking that in the code and there is one more thing that confuses me a bit.

Why does the normalisation factor presented features a power of the Planck Time?
Since the potential depends usually on a mass, wouldn’t it make more sense to input the Planck Mass in the normalisation?


Thanks in advance,
All the best,

Paulo

Chudaikin Anton
Posts: 6
Joined: April 26 2013
Affiliation: inr

Quintessence in CAMB - Units of the potential?

Post by Chudaikin Anton » February 25 2014

I suppose the potential is given in units of (1/Mpc)^2 really because there isn't kappa=8*pi*G (ussually [V]=(1/Mpc)^4). I made this decision as in the code I saw

grhoex_t=phidot**2/2 + a2*Vofphi(phi,0)
grho=grho+grhoex_t

But we know that

grho = a^2 kappa rho

therefore Vofphi(phi,0) is in fact kappa*V.

Hitherto I don't understand the sence of constant "norm" which equals 1d-122 (it's very strange value). In my mind there is to be no "norm" constant.

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

Quintessence in CAMB - Units of the potential?

Post by Erick Almaraz » October 21 2014

Dear all. I think that the motivation of the definition
phi_code= kappa*phi
is for leaving the phi_code variable with no units.

So, if anyone wants to work with a potential of the form
m*phi**2
and if phi is originally measured in GeV, one has to change to the variable phi_code described above. The value of the normalisation factor is determined by the conditions of the equation of state today (close to -1) and by the current acceleration of the expansion, but otherwise I think there are no more restriction for the choice of a particular value.

Regards

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