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/*
effective sigma8 calculation
Copyright (C) 2016, 2017 Boud Roukema, Jan Ostrowski
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; if not, write to the Free Software Foundation,
Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
See also http://www.gnu.org/licenses/gpl.html
*/
#include <stdio.h>
#include <sys/types.h>
#include "config.h"
#include <math.h>
#include "lib/inhomog.h"
/** effective sigma8 calculation
Given sigma_8 inferred from observations under
FLRW and assuming LCDM, calculate sigma_8
for an EdS model with the LCDM proxy H_1^bg value
(see arXiv:1608.06004).
*/
int main(void){
/* https://arxiv.org/abs/1502.01589 Table 4 column 6 */
const double sigma_8_LCDM = 0.8159; /* pm 0.0086 */
double sigma_8_init;
double sigma_8_EdS_bg; /* EdS background model that matches at high redshifts */
double sigma_8_EdS_bg_t0eff;
/* initial redshift, time */
const double z_init = 1000.0;
double t_init;
const double t_0_LCDM = 13.80; /* Gyr */
double t_0_EdS_bg;
int want_verbose = 1;
struct background_cosm_params_s bg_cosm_params_LCDM,
bg_cosm_params_EdS_bg;
bg_cosm_params_LCDM.EdS = 0;
bg_cosm_params_LCDM.flatFLRW = 1;
bg_cosm_params_LCDM.H_0 = 67.74; /* pm 0.46 */
bg_cosm_params_LCDM.OmLam_0 = 0.6911; /* pm 0.0062 */
bg_cosm_params_LCDM.Omm_0 = 1.0 - bg_cosm_params_LCDM.OmLam_0;
bg_cosm_params_LCDM.recalculate_t_0 = 1;
bg_cosm_params_LCDM.inhomog_a_scale_factor_initial = 1.0/201.0;
bg_cosm_params_LCDM.inhomog_a_d_scale_factor_initial = 1.0/201.0;
bg_cosm_params_LCDM.inhomog_a_scale_factor_now = 1.0;
bg_cosm_params_EdS_bg.EdS = 1;
bg_cosm_params_EdS_bg.flatFLRW = 1; /* superfluous */
bg_cosm_params_EdS_bg.H_0 = 37.7;
bg_cosm_params_EdS_bg.Omm_0 = 1.0;
bg_cosm_params_EdS_bg.OmLam_0 = 0.0;
bg_cosm_params_EdS_bg.recalculate_t_0 = 1;
bg_cosm_params_EdS_bg.inhomog_a_scale_factor_initial = 1.0/201.0;
bg_cosm_params_EdS_bg.inhomog_a_d_scale_factor_initial = 1.0/201.0;
bg_cosm_params_EdS_bg.inhomog_a_scale_factor_now = 1.0;
t_init = t_flatFLRW(&bg_cosm_params_LCDM,
1.0/(z_init+1.0),
want_verbose);
/* Within the LCDM proxy, calculate the initial epoch sigma_8. */
sigma_8_init = sigma_8_LCDM *
growth_FLRW(&bg_cosm_params_LCDM,
t_init,
want_verbose) /
growth_FLRW(&bg_cosm_params_LCDM,
t_0_LCDM,
want_verbose);
/* Evolve the initial epoch sigma_8 forward with the EdS background
model to the *EdS background* unity scale factor epoch t_0_EdS_bg. */
t_0_EdS_bg = t_EdS(&bg_cosm_params_EdS_bg,
1.0,
want_verbose);
sigma_8_EdS_bg = sigma_8_init *
growth_FLRW(&bg_cosm_params_EdS_bg,
t_0_EdS_bg,
want_verbose) /
growth_FLRW(&bg_cosm_params_EdS_bg,
t_init,
want_verbose);
sigma_8_EdS_bg_t0eff = sigma_8_init *
growth_FLRW(&bg_cosm_params_EdS_bg,
t_0_LCDM,
want_verbose) /
growth_FLRW(&bg_cosm_params_EdS_bg,
t_init,
want_verbose);
printf("\n");
printf("z_init = %g\n", z_init);
printf("t_init,t_0_LCDM,t_0_EdS_bg = %g %g %g\n",
t_init, t_0_LCDM, t_0_EdS_bg);
printf("sigma_8_init, sigma_8_LCDM, sigma_8_EdS_bg_t0eff, ");
printf("sigma_8_EdS_bg = %g %g %g %g\n",
sigma_8_init, sigma_8_LCDM,
sigma_8_EdS_bg_t0eff, sigma_8_EdS_bg);
printf("\n");
return 0;
}
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