## Equations in Quint module in quintessence equations file for CAMB

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Joseph P Johnson
Posts: 2
Joined: January 30 2020
Affiliation: IIT Bombay

### Equations in Quint module in quintessence equations file for CAMB

Hi all,

I am trying to modify the equation file for quintessence for CAMB provided at https://camb.info/equations_quint.f90.
In subroutine EvolveBackground, the energy density of the scalar field is defined as

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tmp=a2*(0.5d0*phidot**2 + a2*Vofphi(phi,0))
which is consistent with the standard definition (eq. 6.5 in Theory of cosmological perturbations ) upto a overall factor of where prime denotes the derivative with respect to the conformal time.
But later in the file in function Quint_GetOmegaFromInitial, it is given that

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Quint_GetOmegaFromInitial=(0.5d0*y(2)**2 + Vofphi(y(1),0))/(3*adot**2)
which is supposed to produce the value of , which should be multiplied by an overall factor.
But considering the definition

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y(2)=phidot*astart**2
this doesn't seem to be consistent with the definition

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tmp=a2*(0.5d0*phidot**2 + a2*Vofphi(phi,0))
since

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(0.5d0*y(2)**2 + Vofphi(y(1),0))
is equivalent to which cannot be same as the definition of $\rho_{\phi}$ or $\Omega_{\phi}$ irrespective of any overall factor.

I am not sure if it is an error in the code, or if I am missing something.

Best
Joseph

Antony Lewis
Posts: 1609
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: Equations in Quint module in quintessence equations file for CAMB

Omega is only calculated at a=1?

Joseph P Johnson
Posts: 2
Joined: January 30 2020
Affiliation: IIT Bombay

### Re: Equations in Quint module in quintessence equations file for CAMB

Thanks for the reply. I had not noticed that Omega was calculated at a=1.