double geff(double Temp, struct relicparam paramrelic)
/* computes geff at the temperature Temp */
{
double heff0=heff(Temp,paramrelic);
return pow(heff0/sgStar(Temp,paramrelic)*(1.+(heff(Temp*1.001,paramrelic)-heff(Temp*0.999,paramrelic))/0.006/heff0),2.);
}
double CosmologyModel::geff(double Temp)
/* computes geff at the temperature Temp */
{
double heff0=heff(Temp);
return pow(heff0/sgStar(Temp)*(1.+(heff(Temp*1.001)-heff(Temp*0.999))/0.006/heff0),2.);
}
double dark_entropy(double T, struct relicparam paramrelic)
/* computes the dark entropy density at temperature T */
{
if((paramrelic.sd0==0.)&&(paramrelic.Sigmad0==0.)) return 0.;
if((paramrelic.Sigmad0==0.)&&(T<paramrelic.Tsend)) return 0.;
if(paramrelic.Sigmad0==0.)
{
double s_rad_1MeV=2.*pi*pi/45.*heff(1.e-3,paramrelic)*1.e-9;
return paramrelic.sd0*s_rad_1MeV*pow(T/1.e-3,paramrelic.nsd);
}
else
{
double lnT,dlnT,Ttmp;
int ie,nmax;
double integ=0.;
nmax=50;
lnT=log(1.e-15);
dlnT=(log(T)-lnT)/nmax;
for(ie=1;ie<nmax;ie++)
{
lnT+=dlnT;
Ttmp=exp(lnT);
integ+=sgStar(Ttmp,paramrelic)*dark_entropy_Sigmad(Ttmp,paramrelic)/sqrt(1.+dark_density(Ttmp,paramrelic)/(pi*pi/30.*geff(Ttmp,paramrelic)*pow(Ttmp,4.)))/pow(heff(Ttmp,paramrelic),2.)/pow(Ttmp,5.);
}
integ+=sgStar(T,paramrelic)*dark_entropy_Sigmad(T,paramrelic)/sqrt(1.+dark_density(T,paramrelic)/(pi*pi/30.*geff(T,paramrelic)*pow(T,4.)))/pow(heff(T,paramrelic),2.)/pow(T,5.)/2.;
integ*=dlnT;
double Mplanck=1.2209e19;
return 3.*Mplanck*sqrt(5./4./pi/pi/pi)*heff(T,paramrelic)*T*T*T*integ;
}
}
double dark_entropy_derivative(double T, struct relicparam paramrelic)
/* computes the dark energy entropy derivative at temperature T */
{
if((paramrelic.sd0==0.)&&(paramrelic.Sigmad0==0.)) return 0.;
if((paramrelic.Sigmad0==0.)&&(T<paramrelic.Tsend)) return 0.;
if(paramrelic.Sigmad0==0.)
{
return (dark_entropy(T*1.001,paramrelic)-dark_entropy(T*0.999,paramrelic))/0.002/T;
}
else
{
double Mplanck=1.2209e19;
return 3.*sgStar(T,paramrelic)/T/heff(T,paramrelic)*(sqrt(geff(T,paramrelic))*dark_entropy(T,paramrelic)-sqrt(5.*Mplanck/4./pi/pi/pi)/T/T*dark_entropy_Sigmad(T,paramrelic)/sqrt(1.+dark_density(T,paramrelic)/(pi*pi/30.*geff(T,paramrelic)*pow(T,4.))));
}
}
double CosmologyModel::dark_entropy_derivative(double T)
/* computes the dark energy entropy derivative at temperature T */
{
if((sd0==0.)&&(Sigmad0==0.)) return 0.;
if((Sigmad0==0.)&&(T<Tsend)) return 0.;
if(Sigmad0==0.)
{
return (dark_entropy(T*1.001)-dark_entropy(T*0.999))/0.002/T;
}
else
{
double Mplanck=1.2209e19;
return 3.*sgStar(T)/T/heff(T)*(sqrt(geff(T))*dark_entropy(T)-sqrt(5.*Mplanck/4./pi/pi/pi)/T/T*dark_entropy_Sigmad(T)/sqrt(1.+dark_density(T)/(pi*pi/30.*geff(T)*pow(T,4.))));
}
}
double dark_entropy_Sigmad(double T, struct relicparam paramrelic)
/* computes the dark entropy production at temperature T */
{
if((paramrelic.sd0==0.)&&(paramrelic.Sigmad0==0.)) return 0.;
if((paramrelic.Sigmad0==0.)&&(T<paramrelic.Tsend)) return 0.;
double Mplanck=1.2209e19;
if(paramrelic.Sigmad0==0.)
{
return 1./Mplanck*(sqrt(24.*pi*(pi*pi/30.*geff(T,paramrelic)*pow(T,4.)+dark_density(T,paramrelic)))*dark_entropy(T,paramrelic)-sqrt(4.*pi*pi*pi/45.)*heff(T,paramrelic)/sgStar(T,paramrelic)*pow(T,3)*sqrt(1.+dark_density(T,paramrelic)/(pi*pi/30.*geff(T,paramrelic)*pow(T,4.)))*dark_entropy_derivative(T,paramrelic));
}
else
{
if(T<paramrelic.TSigmaend) return 0.;
double s_rad_1MeV=2.*pi*pi/45.*heff(1.e-3,paramrelic)*1.e-9;
double Sigma_rad_1MeV= 1./Mplanck*sqrt(4.*pi*pi*pi/5.*geff(1.e-3,paramrelic))*(1.e-6)*s_rad_1MeV;
return paramrelic.Sigmad0*Sigma_rad_1MeV*pow(T/1.e-3,paramrelic.nSigmad);
}
}
double CosmologyModel::dark_entropy_Sigmad(double T)
/* computes the dark entropy production at temperature T */
{
if((sd0==0.)&&(Sigmad0==0.)) return 0.;
if((Sigmad0==0.)&&(T<Tsend)) return 0.;
double Mplanck=1.2209e19;
if(Sigmad0==0.)
{
return 1./Mplanck*(sqrt(24.*pi*(pi*pi/30.*geff(T)*pow(T,4.)+dark_density(T)))*dark_entropy(T)-sqrt(4.*pi*pi*pi/45.)*heff(T)/sgStar(T)*pow(T,3)*sqrt(1.+dark_density(T)/(pi*pi/30.*geff(T)*pow(T,4.)))*dark_entropy_derivative(T));
}
else
{
if(T<TSigmaend) return 0.;
double s_rad_1MeV=2.*pi*pi/45.*heff(1.e-3)*1.e-9;
double Sigma_rad_1MeV= 1./Mplanck*sqrt(4.*pi*pi*pi/5.*geff(1.e-3))*(1.e-6)*s_rad_1MeV;
return Sigmad0*Sigma_rad_1MeV*pow(T/1.e-3,nSigmad);
}
}
