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How to calculate basic cosmological parameters

last edited by 13 years, 4 months ago

How to calculate basic comological parameters

Once IDL and iCosmo are set up, you can calculate most cosmological parameters in 2 simple steps (an explanation is given below):

; (1) set fiducial parameters:

fid=set_fiducial(cosmo_in={omega_m:.25d},calc_in={fit_tk:2},expt_in={sv1_n_zbin:2,sv1_zerror:0.02d})

; (2) create cosmology parameters structure:

cosmo=mk_cosmo(fid)

How to plot basic cosmological parameters

Once these cosmological parameters are calculated, you can easily plot them.  To plot the angular diameter distance and the linear power spectrum at redshift z=0.5 for example:

; (3) To plot the angular diameter distance as a function of z, for a given cosmology

plt_cosmo, cosmo, 'z', 'da', linestyle=2

; (4) To plot the linear power spectrum at redshift z = 0.5, P(k, z=0.5):

plt_pk, cosmo, z=0.5, /linear

Explanation: calculating basic cosmological parameters

(1) Set Fiducial Parameters

Create a structure that contains all the fiducial values that are used in iCosmo.  At this stage users can input options here.  For this there are three input structures: cosmo_in, calc_in and expt_in:

cosmo_in: input cosmological parameter, the options are -

H, Omega_B, Omega_m, Omega_L, w0, wa, n, Tau, Sigma8 and Curv

calc_in: Input calculation parameter. Here you can decide which transfer function to use (using the fit_tk key word) and the nonlinear correction to use (the fit_nl key word). In the example fit_nl is set to 2 (Smith et al) and fit_tk is set to 0 (E&H).  The options are -

fit_NL, fit_TK, verbose, delta, n_l, l_ran, speed, linear, k_ran, n_k, n_lbin, nz_fn, nz_crs, ran_z and err

fit_nl: fitting formula for the non-linear powerspectrum

(default 0:Peacock & Dodds, 1: Ma et al., 2: Smith et al.)

fit_tk: fitting function for transfer function to use:

0: E&H without wiggles (default)

1: E&H with wiggles (UNSTABLE w/ NON-LINEAR CORRECTION)

2: BBKS as summarised by Peacock & Dodds (1997)

expt_in: Input experiment parametersproperties of a survey. The options are:

sv1_N_ZBIN, sv1_ZERROR, sv1_Z_MED, sv1_NG,  sv1_A_SURVEY, sv1_EFF, sv1_SIG_INT, sv1_DNDZTYPE, sv1_DNDZP, sv1_DNDZZ, sv1_BIASTYPE, sv1_NS, sv1_SIGMAM, sv1_DELM, sv1_SNE_ZRAN, sv1_NAME, sv1_PROBES  (sv1 can also be changed to sv2 and sv3)

a_survey: survey area  [deg^2]

ng: galaxy surface density (without binning) [gals amin^-2]

z_m: galaxy median redshift (without binning)

sig_int: intrinsic rms shear per component

n_zbin: number of redshift slices

;at the moment the BAO calculation does not take into account photometric errors

gerror: Gaussian photo-z error (sigz=gerror*(1+z))

f_cat: fraction of catastrophic failures

z_delta: off set of a catastrophic failure

To see the cosmological parameters:  help,fid.cosmo,/st

To see the calculation parameters:  help,fid.calc,/st

To see the parameters for survey:  help,fid.expt.sv1,/st

(2) Create a Cosmology Structure

Calculates the basic cosmology parameters using the setting in the fiducial structure.  This routine produces a structure which in turn contains three structure (help,cosmo,/st):

cosmo.const - cosmological constants such as Omega_m and sigma8

cosmo.evol   - cosmological parameters that evolve with redshift such as co-moving distance

cosmo.pk     - 3D matter powerspectrum (both linear and non-linear) for a set of redshift.

To see the const parameters: help,cosmo.const,/st

To see the evol parameters:   help,cosmo.evol,/st

To see the pk parameters:      help,cosmo.pk,/st

Explanation: plotting basic cosmological parameters

To plot the basic cosmological parameters you can either use the routines plt_cosmo or plt_pk.

3) Plotting cosmological parameters - apart from the power spectrum

To plot any cosmological parameter that evolves with redshift (expect the power spectrum), you can use the plt_cosmo routine in the following way: plt_cosmo, cosmo, 'x', 'y', where 'x' corresponds to the parameter you want on the x axis (here either 'z' or 'a'), 'y' corresponds to the parameter you want on the y axis (type icosmo_help, plt_cosmo for details).

All the usual IDL plotting commands are accepted. For example, to plot the angular diameter distance as a function of z:

plt_cosmo, cosmo, 'z', 'da', linestyle=2, thick=3

You can also overplot the angular diameter distance for a different cosmology:

plt_cosmo, cosmo2, 'z', 'da', /over

(4) Plotting the power spectrum

When the 'cosmo' structure is created, the power spectrum is calculated and stored in 'cosmo.pk'.

To plot the power spectrum, simply type:

plt_pk, cosmo

To overplot the linear power spectrum at redshift z=0.5:

plt_pk, cosmo, /linear, z=0.5, /over

Again, all the usual IDL plotting commands are accepted.

Key

• red - Commands you can type into IDL
• green - What IDL print
• blue - other, e.g. keywords