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 double darkOmega1(double * Xf,double Z1,double dZ1,int Fast,double Beps)
{
double X = *Xf;
double CCX=(Z1-1)*(Z1+1);
double dCCX=(Z1-1+dZ1)*(Z1+1+dZ1)-CCX;
double ddY;
double dCC1,dCC2,X1,X2;
sigma= (Fast)?sigma_gauss:sigma_simpson;
if(Beps>=1) Beps=0.999;
vSigmaGrid.pow=0;
ddY=dY(X,Beps,Fast); if(FError || ddY==0) return -1;
if(fabs(CCX-ddY)<dCCX) { *Xf=X; MassCut=Mcdm*(2-log(Beps)/X); return Yeq(X)*sqrt(1+ddY);}
dCC1=dCC2=ddY-CCX; ;X1=X2=X;
while(dCC2>0)
{
X1=X2;
dCC1=dCC2;
X2=X2/XSTEP;
X=X2;
dCC2=-CCX+dY(X,Beps,Fast);
}
while (dCC1<0)
{
X2=X1;
dCC2=dCC1;
X1=X1*XSTEP;
X=X1;
dCC1=-CCX+dY(X,Beps,Fast);
}
for(;;)
{ double dCC;
if(fabs(dCC1)<dCCX)
{*Xf=X1; MassCut=Mcdm*(2-log(Beps)/X1); return Yeq(X1)*sqrt(1+CCX+dCC1);}
if(fabs(dCC2)<dCCX || fabs(X1-X2)<0.0001*X1)
{*Xf=X2; MassCut=Mcdm*(2-log(Beps)/X2); return Yeq(X2)*sqrt(1+CCX+dCC2);}
X=0.5*(X1+X2);
dCC=-CCX+dY(X,Beps,Fast);
if(dCC>0) {dCC1=dCC;X1=X;} else {dCC2=dCC;X2=X;}
}
}
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);
}
}
double darkOmega(double * Xf, int Fast, double Beps)
{
double Yt,Yi,Xt=25;
double Z1=1.1;
double Z2=10;
int i;
double Xf1;
if(Xf)*Xf=Xt;
assignVal("Q",2*M);
if(Beps>=1) Beps=0.999;
if(Z1<=1) Z1=1.1;
fast_=Fast;
Yt= darkOmega1(&Xt, Z1, (Z1-1)/5,Fast, Beps);
if(Yt<0||FError) return -1;
Xf1=Xt;
for(i=0; ;i++)
{ double X2=vSigmaGrid.xtop*pow(XSTEP,i+1);
double y;
if(Yt>=Z2*Yeq(Xt)) break;
if(Xt>X2*0.999999) continue;
while(vSigmaGrid.pow<=i+1)
{ double X;
if(vSigmaGrid.pow==vSigmaGrid.size)
{ vSigmaGrid.size+=10;
vSigmaGrid.data=(double*)realloc(vSigmaGrid.data,sizeof(double)*vSigmaGrid.size);
}
X=vSigmaGrid.xtop*pow(XSTEP,vSigmaGrid.pow);
MassCut=M*(2-log(Beps)/X);
vSigmaGrid.data[vSigmaGrid.pow++]=aRate(X,0,Fast,NULL);
if(FError) return -1;
}
y=log(Yt);
odeint(&y,1 , Xt , X2 , 1.E-3, (X2-Xt)/2, &XderivLn);
Yt=exp(y);
Xt=X2;
}
if(Xf) *Xf=0.5*(Xf1+Xt);
Yi=1/( (M/Xt)*sqrt(M_PI/45)*MPlank*aRate(Xt,1,Fast,NULL) );
if(!finite(Yi)||FError) return -1;
return 2.742E8*M/(1/Yt + 1/Yi); /* 2.828-old 2.755-new,2.742 -newnew */
}
double darkOmega(double * Xf, int Fast, double Beps)
{
double Yt,Yi,Xt=25;
double Z1=1.1;
double Z2=10;
int i;
double Xf1;
if(Xf)*Xf=Xt;
assignVal("Q",2*Mcdm);
if(Beps>=1) Beps=0.999;
Beps_=Beps; Fast_=Fast;
if(Z1<=1) Z1=1.1;
Yt= darkOmega1(&Xt, Z1, (Z1-1)/5,Fast, Beps);
if(Yt<0||FError) {return -1;}
Xf1=Xt;
for(i=0; ;i++)
{ double X2=vSigmaGrid.xtop*pow(XSTEP,i+1);
double y;
if(Yt>=Z2*Yeq(Xt)) break;
if(Xt>X2*0.999999) continue;
y=Yt;
if(odeint(&y,1 , Xt , X2 , 1.E-3, (X2-Xt)/2, &XderivLn)){return -1;}
Yt=y;
Xt=X2;
}
if(Xf) *Xf=0.5*(Xf1+Xt);
Yi=1/( (Mcdm/Xt)*sqrt(M_PI/45)*MPlank*aRate(Xt,1,Fast,NULL,NULL));
if(!finite(Yi)||FError) return -1;
if(deltaY==0.)
{ dmAsymm=0;
return 2.742E8*Mcdm/(1/Yt + 1/Yi); /* 2.828-old 2.755-new,2.742 -newnew */
} else
{ double a,f,z0,Y0;
a=fabs(deltaY);
f= (sqrt(Yt*Yt+a*a)-a)/
(sqrt(Yt*Yt+a*a)+a)*exp(-2*a/Yi);
z0=sqrt(f)*2*a/(1-f);
Y0=sqrt(z0*z0+a*a);
dmAsymm=log((Y0+deltaY)/(Y0-deltaY));
return 2.742E8*Mcdm*Y0;
}
}
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;}
}
}