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));
}
static double dY(double X, double Beps,double fast)
{ double d, dYdX,Yeq0X, sqrt_gStar, vSig,cFactor=sqrt(M_PI/45)*MPlank*Mcdm;
double epsY;
d=X*0.001; MassCut=Mcdm*(2-log(Beps)/X); dYdX=(Yeq(X+d)-Yeq(X-d))/(2*d);
Yeq0X=Yeq(X);
epsY=deltaY/Yeq0X;
Yeq0X/=X;
termod(Mcdm/X,&sqrt_gStar,NULL);
vSig=vSigmaI(X,Beps, fast);
if(vSig==0){ FError=1; return 0;}
return -dYdX/(vSig*cFactor*sqrt_gStar*Yeq0X*Yeq0X)/sqrt(1+epsY*epsY);
}
static void XderivLn(double x, double *Y, double *dYdx)
{
double y=Y[0];
double yeq, sqrt_gStar;
termod(Mcdm/x,&sqrt_gStar,NULL);
MassCut=Mcdm*(2-log(Beps_)/x); yeq=Yeq(x);
if(y<yeq) *dYdx=0; else
{
double epsY=deltaY/y;
*dYdx=-(Mcdm/x/x)*MPlank*sqrt_gStar*sqrt(M_PI/45)*vSigmaI(x,Beps_,Fast_)*(y*y-yeq*yeq)*sqrt(1+epsY*epsY);
}
}
static void XderivLn(double x, double *Y, double *dYdx)
{
double y=exp(Y[0]);
double yeq=Yeq(x);
double sqrt_gStar;
int i=log(x/vSigmaGrid.xtop)/log(XSTEP)-0.00001;
double X1=vSigmaGrid.xtop*pow(XSTEP,i); double sigmav1=vSigmaGrid.data[i];
double X2=vSigmaGrid.xtop*pow(XSTEP,i+1); double sigmav2=vSigmaGrid.data[i+1];
double sigmav;
sigmav1=log(sigmav1); sigmav2=log(sigmav2);
if(i>0)
{ double X0=vSigmaGrid.xtop*pow(XSTEP,i-1); double sigmav0=vSigmaGrid.data[i-1];
sigmav0=log(sigmav0);
sigmav=sigmav0*(x-X1)*(x-X2)/(X0-X1)/(X0-X2)
+sigmav1*(x-X0)*(x-X2)/(X1-X0)/(X1-X2)
+sigmav2*(x-X0)*(x-X1)/(X2-X0)/(X2-X1);
}else if(i+2<vSigmaGrid.pow)
{ double X0=vSigmaGrid.xtop*pow(XSTEP,i+2); double sigmav0=vSigmaGrid.data[i+2];
sigmav0=log(sigmav0);
sigmav=sigmav0*(x-X1)*(x-X2)/(X0-X1)/(X0-X2)
+sigmav1*(x-X0)*(x-X2)/(X1-X0)/(X1-X2)
+sigmav2*(x-X0)*(x-X1)/(X2-X0)/(X2-X1);
} else sigmav=(sigmav1*(x-X2)-sigmav2*(x-X1))/(X1-X2);
/*printf("sigmav=%e\n");*/
sigmav=exp(sigmav);
termod(M/x,&sqrt_gStar,NULL);
*dYdx=-(M/x/x)*MPlank*sqrt_gStar*sqrt(M_PI/45)*sigmav*(y-yeq*yeq/y);
/*printf("x=%e dydx=%e\n",x,*dYdx);*/
}
static double darkOmega1(double * Xf,double Z1,double dZ1,int Fast,double Beps)
{
double X = *Xf;
double sqrt_gStar;
double CCX=(Z1-1)*(Z1+1);
double dCCX=(Z1-1+dZ1)*(Z1+1+dZ1)-CCX;
double d, dYdX,Yeq0X;
double dCC,dCC1,dCC2,X1,X2,vSigma,vSigma1,vSigma2;
double cFactor=sqrt(M_PI/45)*MPlank*M;
int i;
if(vSigmaGrid.data==NULL)
{ vSigmaGrid.data=(double*)malloc(20*sizeof(double));
vSigmaGrid.size=20;
}
sigma= (Fast)?sigma_gauss:sigma_simpson;
if(Beps>=1) Beps=0.999;
MassCut=M*(2-log(Beps)/X);
d=X*0.01; dYdX=(Yeq(X+d)-Yeq(X-d))/(2*d);
Yeq0X=Yeq(X)/X;
termod(M/X,&sqrt_gStar,NULL);
vSigma=aRate(X,0,Fast,NULL); if(FError) return -1;
if(vSigma ==0)
{ printf("ERROR:Zero annihilation rate,\n");
return -1;
}
dCC=-CCX-dYdX/(vSigma*cFactor*sqrt_gStar*Yeq0X*Yeq0X);
vSigmaGrid.data[0]=vSigma;
vSigmaGrid.xtop=X;
vSigmaGrid.pow=1;
if(fabs(dCC)<dCCX) { *Xf=X; return Yeq(X)*sqrt(1+dCC+CCX);}
dCC1=dCC;dCC2=dCC;X1=X;X2=X; vSigma1=vSigma;vSigma2=vSigma;
while(dCC2>0)
{
X1=X2;
dCC1=dCC2;
vSigma1=vSigma2;
X2=X2/XSTEP;
X=X2;
MassCut=M*(2-log(Beps)/X);
termod(M/X,&sqrt_gStar,NULL);
d=0.01*X; dYdX= (Yeq(X+d)-Yeq(X-d))/(2*d);
Yeq0X=Yeq(X)/X;
vSigma2=aRate(X,0,Fast,NULL); if(FError) return -1;
dCC2=-CCX-dYdX/(vSigma2*cFactor*sqrt_gStar*Yeq0X*Yeq0X);
if(vSigmaGrid.pow==vSigmaGrid.size)
{ vSigmaGrid.size+=10;
vSigmaGrid.data=(double*)realloc(vSigmaGrid.data,sizeof(double)*vSigmaGrid.size);
}
for(i=vSigmaGrid.pow;i;i--) vSigmaGrid.data[i]=vSigmaGrid.data[i-1];
vSigmaGrid.xtop=X; vSigmaGrid.data[0]=vSigma2; vSigmaGrid.pow++;
}
while (dCC1<0)
{
X2=X1;
dCC2=dCC1;
vSigma2=vSigma1;
X1=X1*XSTEP;
X=X1;
MassCut=M*(2-log(Beps)/X);
termod(M/X,&sqrt_gStar,NULL);
d=0.01*X; dYdX=(Yeq(X+d)-Yeq(X-d))/(2*d);
Yeq0X=Yeq(X)/X;
vSigma1=aRate(X,0,Fast,NULL); if(FError) return -1;
dCC1=-CCX-dYdX/(vSigma1*cFactor*sqrt_gStar*Yeq0X*Yeq0X);
if(vSigmaGrid.pow==vSigmaGrid.size)
{ vSigmaGrid.size+=10;
vSigmaGrid.data=(double*)realloc(vSigmaGrid.data,sizeof(double)*vSigmaGrid.size);
}
vSigmaGrid.data[vSigmaGrid.pow++]=vSigma1;
}
for(;;)
{
if(fabs(dCC1)<dCCX) { *Xf=X1; return Yeq(X1)*sqrt(1+dCC1+CCX);}
if(fabs(dCC2)<dCCX) { *Xf=X2; return Yeq(X2)*sqrt(1+dCC2+CCX);}
X=(X1*dCC2 - X2*dCC1)/(dCC2-dCC1);
MassCut=M*(2-log(Beps)/X);
termod(M/X,&sqrt_gStar,NULL);
d=0.01*X; dYdX= (Yeq(X+d)-Yeq(X-d))/(2*d);
Yeq0X=Yeq(X)/X;
vSigma= (vSigma1*(X2-X) - vSigma2*(X1-X))/(X2-X1);
dCC=-CCX-dYdX/(vSigma*cFactor*sqrt_gStar*Yeq0X*Yeq0X);
if(dCC*dCC1>0) {dCC1=dCC;X1=X;vSigma1=vSigma;} else {dCC2=dCC;X2=X;vSigma2=vSigma;}
}
}
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;
}
