double dark_density(double T, struct relicparam paramrelic)
/* computes the dark energy density at temperature T */
{
if((paramrelic.dd0==0.)||(T<paramrelic.Tdend)) return 0.;
double rho_rad_1MeV=pi*pi/30.*geff(1.e-3,paramrelic)*1.e-12;
return paramrelic.dd0*rho_rad_1MeV*pow(T/1.e-3,paramrelic.ndd);
}
double CosmologyModel::dark_density(double T)
/* computes the dark energy density at temperature T */
{
if((dd0==0.)||(T<Tdend)) return 0.;
double rho_rad_1MeV=pi*pi/30.*geff(1.e-3)*1.e-12;
return dd0*rho_rad_1MeV*pow(T/1.e-3,ndd);
}
static double weight_integrand(double v)
{ double x,gf;
double sqrt_gStar;
if(v==0.) return 0;
x=xf_-3*log(v)/(y_pass-2);
gf=geff(x);
termod(M/x,&sqrt_gStar,NULL);
return K1pol(1/(x*y_pass))*3*v*v*sqrt_gStar/(sqrt(x)*gf*gf*(y_pass-2));
}
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);
}
}
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 CosmologyModel::dark_entropy(double T)
/* computes the dark entropy density at temperature T */
{
if((sd0==0.)&&(Sigmad0==0.)) return 0.;
if((Sigmad0==0.)&&(T<Tsend)) return 0.;
if(Sigmad0==0.)
{
double s_rad_1MeV=2.*pi*pi/45.*heff(1.e-3)*1.e-9;
return sd0*s_rad_1MeV*pow(T/1.e-3,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)*dark_entropy_Sigmad(Ttmp)/sqrt(1.+dark_density(Ttmp)/(pi*pi/30.*geff(Ttmp)*pow(Ttmp,4.)))/pow(heff(Ttmp),2.)/pow(Ttmp,5.);
}
integ+=sgStar(T)*dark_entropy_Sigmad(T)/sqrt(1.+dark_density(T)/(pi*pi/30.*geff(T)*pow(T,4.)))/pow(heff(T),2.)/pow(T,5.)/2.;
integ*=dlnT;
double Mplanck=1.2209e19;
return 3.*Mplanck*sqrt(5./4./pi/pi/pi)*heff(T)*T*T*T*integ;
}
}
static double Yeq(double X)
{ double heff;
termod(M/X,NULL,&heff);
return (45/(4*M_PI*M_PI*M_PI*M_PI))*X*X*
geff(X)*sqrt(M_PI/(2*X))*exp(-X)/heff;
}
static double aRate(double X, int everage,int Fast, float ** wPrc)
{
double Sum=0.;
int i,l1,l2;
int nPrc=0;
char* pname[5];
gridStr grid,grid1;
double MassCutOut=MassCut+M*log(100.)/X;
double Msmall,Mlarge;
int nPrcTot=0;
if(MassCutOut<M*(2+10/X)) MassCutOut=M*(2+10/X);
xf_=X;
exi=everage;
if(wPrc) *wPrc=NULL;
for(l1=0;l1<NC;l1++)
{ int k1=sort[l1]; if(M+inMass[k1]>MassCut) break;
for(l2=0;l2<NC;l2++)
{
double Sumkk=0.;
double x[2],f[2];
double factor;
int k2=sort[l2];
CalcHEP_interface * CI;
if(inMass[k1]+inMass[k2] > MassCut) break;
if(inC[k1*NC+k2]<=0) continue;
if(code22[k1*NC+k2]==NULL) new_code(k1,k2);
if(inC[k1*NC+k2]<=0) continue;
if(!code22[k1*NC+k2]->init)
{ numout * cd=code22[k1*NC+k2];
CalcHEP_interface *cdi=cd->interface;
for(i=1;i<=cdi->nvar;i++) if(cd->link[i]) cdi->va[i]=*(cd->link[i]);
if( cdi->calcFunc()>0 ) {FError=1; return -1;}
cd->init=1;
}
if(wPrc)
{ nPrcTot+=code22[k1*NC+k2]->interface->nprc;
*wPrc=(float*)realloc(*wPrc,sizeof(float)*(nPrcTot));
}
sqme=code22[k1*NC+k2]->interface->sqme;
DeltaXf=(inDelta[k1]+inDelta[k2])*X;
inBuff=0;
M1=inMass[k1];
M2=inMass[k2];
Msmall=M1>M2? M1-M*(1-sWidth): M2-M*(1-sWidth);
Mlarge=M1>M2? M2+M*(1-sWidth): M1+M*(1-sWidth);
u_max=m2u(MassCutOut);
if(Fast)
{
if(Fast==1)
{ double c[4];
for(Npow=0;Npow<4;Npow++) c[Npow]=simpson(s_pow_integrand, 0. ,1. ,1.E-4);
gaussC2(c,x,f);
for(i=0;i<2;i++){ x[i]=sqrt(x[i]); f[i]*=2*x[i]/M;}
}else
{
double c[2];
for(Npow=0;Npow<2;Npow++) c[Npow]=simpson(s_pow_integrand, 0. ,1. ,1.E-4);
x[0]= sqrt(c[1]/c[0]);
f[0]= c[0]*2*x[0]/M;
}
}
factor=inC[k1*NC+k2]*inG[k1]*inG[k2]*exp(-DeltaXf);
CI=code22[k1*NC+k2]->interface;
for(nsub=1; nsub<= CI->nprc;nsub++,nPrc++)
{ double u_min=0.;
double a=0;
if(wPrc) (*wPrc)[nPrc]=0;
for(i=0;i<4;i++) pname[i]=CI->pinf(nsub,i+1,pmass+i,NULL);
if(pmass[2]+pmass[3]>MassCutOut) continue;
if( (pmass[2]>Mlarge && pmass[3]<Msmall)
||(pmass[3]>Mlarge && pmass[2]<Msmall))
{ *(CI->twidth)=1; *(CI->gtwidth)=1;}
else { *(CI->twidth)=0; *(CI->gtwidth)=0;}
*(CI->gswidth)=0;
if(pmass[2]+pmass[3] > pmass[0]+pmass[1])
{ double smin=pmass[2]+pmass[3];
if((pmass[0]!=M1 || pmass[1]!=M2)&&(pmass[0]!=M2 || pmass[1]!=M1))
{ double ms=pmass[0]+pmass[1];
double md=pmass[0]-pmass[1];
double Pcm=sqrt((smin-ms)*(smin+ms)*(smin-md)*(smin+md))/(2*smin);
smin=sqrt(M1*M1+Pcm*Pcm)+sqrt(M2*M2+Pcm*Pcm);
}
u_min=m2u(smin);
}else u_min=0;
repeat:
neg_cs_flag=0;
if(!Fast) a=simpson(s_integrand,u_min,1.,eps);
else if(Fast!=1) a=f[0]*sigma(x[0]); else
{
int isPole=0;
char * s;
int m,w,n;
double mass,width;
for(n=1;(s=code22[k1*NC+k2]->interface->den_info(nsub,n,&m,&w));n++)
if(m && w && strcmp(s,"\1\2")==0 )
{ mass=code22[k1*NC+k2]->interface->va[m];
width=code22[k1*NC+k2]->interface->va[w];
if(mass<MassCutOut && mass+8*width > pmass[0]+pmass[1]
&& mass+8*width > pmass[2]+pmass[3])
{ if((pmass[0]!=M1 || pmass[1]!=M2)&&(pmass[0]!=M2 || pmass[1]!=M1))
{ double ms=pmass[0]+pmass[1];
double md=pmass[0]-pmass[1];
double Pcm=sqrt((mass-ms)*(mass+ms)*(mass-md)*(mass+md))/(2*mass);
mass=sqrt(M1*M1+Pcm*Pcm)+sqrt(M2*M2+Pcm*Pcm);
}
grid1=makeGrid(mass,width);
if(isPole) grid=crossGrids(&grid,&grid1); else grid=grid1;
isPole++;
}
}
if(isPole==0)
{ grid.n=1;
grid.ul[0]=u_min;
grid.ur[0]=u_max;
grid.pow[0]=3;
}
if(grid.n==1 && pmass[0]+pmass[1]> 1.1*(pmass[2]+pmass[3]))
a=f[0]*sigma(x[0])+f[1]*sigma(x[1]);
else for(i=0;i<grid.n;i++)if(u_min<=grid.ur[i])
{
double ul= u_min<grid.ul[i]? grid.ul[i]:u_min;
double da=gauss(s_integrand,ul,grid.ur[i],grid.pow[i]);
a+=da;
}
}
if(neg_cs_flag && *(CI->gswidth)==0)
{ *(CI->gswidth)=1;
goto repeat;
}
/*
printf("X=%.2E (%d) %.3E %s %s %s %s\n",X,everage, a, pname[0],pname[1],pname[2],pname[3]);
*/
Sumkk+=a;
if(wPrc) (*wPrc)[nPrc] = a*factor;
}
Sum+=factor*Sumkk;
/*
printf("Sum=%E\n",Sum);
*/
}
}
if(wPrc) for(i=0; i<nPrc;i++) (*wPrc)[i]/=Sum;
if(!everage) { double gf=geff(X); Sum/=gf*gf;}
/*
exit(1);
*/
return Sum;
}
