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cosmoratio.c
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Fri, Nov 29, 09:22

cosmoratio.c
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#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<structure.h>
#include "lt.h"
#include "gsl/gsl_integration.h"
#include "errors.h"
/****************************************************************/
/* nom: cosmoratio */
/* auteur: Jean-Paul Kneib */
/* date: 10/02/92 */
/* place: Toulouse */
/****************************************************************/
static double gg(double z);
static double sk(double x, double k);
static double chi1(double z);
static double chi2(double z1, double z2);
static double chiz_gsl(double z, void* param);
static double integral_chiz_ab(double a, double b);
/**************************************************************/
double distcosmo1(double z)
/* Return the angular distance DA(observator(z=0),object(z)) (no unit)
* Multiply discosmo1(z) by c/H0 to get the true value in Mpc.
* distcosmo1(z) * c/H0 = DA(0,z) = 1/(1+z) * Sk( integral( 0,z,c*dz/H(z) ) )
*
* Global variables used :
* - C
*/
{
const extern struct g_cosmo C;
double g;
if (C.omegaX == 0.)
{
g = gg(z);
// Reformulation of the Mattig relation of OL = OK = 0 (De Sitter)
return(2.*((1. - C.omegaM - g)*(1. - g)) / C.omegaM / C.omegaM / (1. + z) / (1. + z));
}
else
{
if (C.kcourb != 0.)
return(sk(chi1(z)*sqrt(fabs(C.kcourb)), C.kcourb)
/ (1 + z) / sqrt(fabs(C.kcourb)));
else
return(chi1(z) / (1 + z));
}
}
/**************************************************************/
/* Return the angular distance DA(object(z1),object(z2)) divided by c/H0
* distcosmo2(z1,z2) * c/H0 = DA(z1,z2) = 1/(1+z2) * Sk( integral( z1,z2,c*dz/H(z) ) )
*
* Global variables used :
* - C
* - in gg() : C
* - in chi2() : C
*/
double distcosmo2(double z1, double z2)
{
const extern struct g_cosmo C;
double g1, g2;
if ( z1 >= z2 )
return 0.;
if (C.omegaX == 0.)
{
g1 = gg(z1);
g2 = gg(z2);
// Mattig relation for a De Sitter Universe
return(2.*((1. - C.omegaM - g1*g2)*(g1 - g2))
/ C.omegaM / C.omegaM / (1. + z1) / (1. + z2) / (1. + z2));
}
else
{
if ( C.kcourb != 0. )
return(sk(chi2(z1, z2)*sqrt(fabs(C.kcourb)), C.kcourb)
/ (1 + z2) / sqrt(fabs(C.kcourb)));
else
return(chi2(z1, z2) / (1 + z2));
}
}
/****************************************************************/
/* Return the lens efficacity E=DA(LS) / DA(OS)
*
* If zl > zs, return 0.
*
* Global variables used :
* - in distcosmo1() : C
* - in distcosmo2() : C
*/
double dratio(double zl, double zs)
{
if ( zl >= zs )
return (0.);
else
return (distcosmo2(zl, zs) / distcosmo1(zs));
}
/* Same as dratio() but for arclet structures
*/
void dratio_gal(struct galaxie *arclet, double zl)
{
if( zl < arclet->z )
arclet->dl0s = distcosmo2(zl, arclet->z);
else
arclet->dl0s = 0.;
arclet->dos = distcosmo1(arclet->z);
arclet->dr = arclet->dl0s / arclet->dos;
}
/**************************************************************
* Return the luminosity distance DL(0,z) = (1+z)^2 * DA(0,z)
*/
double dlumcosmo1(double z)
{
return(distcosmo1(z)*(1. + z)*(1. + z));
}
/**************************************************************/
double distprime1(double z)
{
const extern struct g_cosmo C;
double g;
if (C.omegaX == 0.)
{
g = 1. / (1. + z);
return(g*(g / gg(z) - distcosmo1(z)*2.*g));
}
else
{
return((distcosmo1(z + 0.1) - distcosmo1(z)) / 0.1);
}
}
/**************************************************************
* Global variables used :
* - in gg() : C
* - in chi2() : C
*/
double distprime2(double z1, double z2)
{
const extern struct g_cosmo C;
double g2; //g1
if (C.omegaX == 0.)
{
g2 = 1. / (1. + z2);
return(g2*(g2 / gg(z2) - distcosmo2(z1, z2)*2.*g2));
}
else
{
return((distcosmo2(z1, z2 + 0.1) - distcosmo2(z1, z2)) / 0.1);
}
}
/**************************************************************/
double dratioprime(double zl, double zs)
{
double ds;
ds = distcosmo1(zs);
return( (distprime2(zl, zs) - distcosmo2(zl, zs)*distprime1(zs) / ds) / ds );
}
/**************************************************************/
/* Global variables used :
* - in chiz() : C
* */
static double gg(double z)
{
const extern struct g_cosmo C;
return(sqrt(1. + C.omegaM*z));
}
/**************************************************************
* Global variables used :
* - none
*/
static double sk(double x, double k)
{
if (k > 0)
return(sin(x));
else if (k < 0)
return(sinh(x));
else
return(x);
}
/**************************************************************
* Return 1 / H(z) multiplied by H0
* chiz(z) / H0 = 1 / H(z) = 1/H0/(1+z)/sqrt( sum(i, Omega_i*(1+z)^(3*(w_i + 1) ) )
* with w_M = 0 and w_k = -1/3
*
* Global variables used :
* - C
* */
double chiz(double z)
{
const extern struct g_cosmo C;
double x;
double yy, yyy, y4;
double r0, e1, e2, frac;
x = 1 + z;
switch (C.model) //TV CPL Model
{
case(1):
x = -x * x * C.kcourb + x * x * x * C.omegaM + C.omegaX * pow(x, 3 * (1 + C.wX + C.wa)) * exp(-3 * C.wa * z / x);
break;
case(2): //TV Cardassian (wx is q, wa is n)
yy = pow ( (1.+C.kcourb)/C.omegaM ,C.wX);
yyy = (yy - 1.) * pow( x,3.*C.wX*(C.wa-1.) );
y4 = pow(1.+yyy,1./C.wX);
x = -x * x * C.kcourb + x * x * x * C.omegaM*y4;
break;
case(3): //TV Interacting DE Model (wa is delta)
yy = C.omegaX*pow( x,3.*(1.+C.wX) );
yyy = ( C.omegaM/(C.wa+3.*C.wX) ) * ( C.wa*pow(x,3.*(1.+C.wX)) + 3.*C.wX*pow(x,(3.-C.wa)) );
x = -x * x * C.kcourb + yy +yyy;
break;
case(4): //TV Holographic Ricci Scale with CPL
r0 = C.omegaM/(1.-C.omegaM);
e1 = (3./2.)*( (1.+r0+C.wX+4*C.wa)/(1.+r0+3.*C.wa) );
e2 = (-1./2.)*( (1.+r0-3.*C.wX)/(1.+r0+3.*C.wa) ) ;
frac = ( 1.+r0+3.*C.wa*(x-1.)/x )/(1.+r0) ;
yy = pow(x,e1);
yyy = pow(frac,e2);
x = (yy*yyy)*(yy*yyy);
break;
default:
fprintf(stderr, "ERROR: Unknown cosmological model %d\n", C.model);
exit(E_COSMO_MODEL);
break;
}
if ( x <= 0 )
{
fprintf( stderr, "ERROR : H^2(z)<=0 produced (z,omegaM,omegaX,wX,wa) = (%.3lf,%.3lf,%.3lf,%.3lf,%.3lf)\n",
z, C.omegaM, C.omegaX, C.wX, C.wa );
exit(-1);
}
return( 1. / sqrt(x) );
}
/**************************************************************
* Return the proper distance Dp(0,z) divided by c/H0
* chi1(z) * c/H0 = Dp(0,z) = integral( 0, z, c*dz / H(z) )
*
* Global variables used :
* - in chiz() : C
* */
static double chi1(double z)
{
double rez;
rez = integral_chiz_ab(0., z);
return rez;
}
/**************************************************************
* Return the proper distance Dp(z1,z2) divided by c/H0
* chi2(z) * c/H0 = Dp(z1,z2) = integral( z1, z2, c*dz / H(z) )
*
* Global variables used :
* - in chiz() : C
*/
static double chi2(double z1, double z2)
{
double rez;
rez = integral_chiz_ab(z1, z2);
return rez;
}
static double chiz_gsl(double z, void* param)
{
return chiz(z);
}
static double integral_chiz_ab(double a, double b)
{
gsl_function f;
f.function = &chiz_gsl;
const int limit = 10;
gsl_integration_workspace * w1 = gsl_integration_workspace_alloc(limit);
double rez, err;
gsl_integration_qag(&f, a, b, 0, 1e-6, limit, GSL_INTEG_GAUSS15, w1 , &rez ,&err);
gsl_integration_workspace_free(w1);
return rez;
}

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