|Code based on CMBFAST4.5.1 by Seljak & Zaldarriaga|
Welcome to CROSS_CMBFAST
This code is an extension of CMBFAST4.5.1 to compute the ISW-correlation power spectrum and the 2-point angular ISW-correlation function for a given galaxy window function. It includes dark energy models specified by a constant equation of state (w) or a linear parameterization in the scale factor (w0,wa) and a constant sound speed (c2de). For reference see astro-ph/0504115, while for a detailed description of the ISW-correlation equations implemented see astro-ph/0506396. The ISW computation is limited to flat geometry. Differently from the original CMBFAST4.5 version dark energy perturbations are implemented for a general dark energy fluid specified by w(z) and c2de in synchronous gauge (see for instance Eq.7-9 in Bean and Dore astro-ph/0307100). For time varying dark energy models it is suggested not to cross the w=-1 line, as Dr. Wenkman says: "never cross the streams", bad things can happen.
Galaxy Selection Function
The code allows to specify the galaxy window function. Two possibilities are implemented: 1) a standard window function ( A z^m exp[-(z/z0)^beta] ) normalized to unity with input parameters median redshift zmed (=1.41 z0) and the slopes m and beta. A bit of care is necessary for the normalization (see remarks); 2) Luminous Red Galaxies window function from SDSS.
The output consists of two files, the angular ISW-correlation function in microK (theta,C_Tg(theta)) and the power spectra in multipole space, the second column is the ISW-correlation power spectrum l(l+1)/2pi C_l(Tg) and the last column is the matter-matter angular power spectrum l(l+1)/2pi C_l(gg), in order to get the galaxy-galaxy power spectrum you need to multiply by your preferred constant bias value or you need to implement the model bias in the ISW-correlation computation (see remarks). Other columns are standard CMB spectra as in CMBFAST. Output data are normalized as WMAP3 at k=0.002 Mpc^-1 (A_s is an input parameter).
The code can be easily modified for studying ISW-correlation
in more complicate models (modified gravity, time varying neutrino mass,
coupled quintessence, etc..). In order to implement a scale and time
dependent bias you need to modify the ISW-correlation computation in
cmbcrossflat.F. If you want to use a non-standard selection function
you can modify it in subcross.F. and change the normalization
accordingly, you can use a numerical integration which I left for such
a case. On the other hand if you want to use a very broad standard
selection function be careful with the value of beta you plug in, if
beta ~ 0 remember that the Gamma function blows up, while you are just using
a power low selection function whose integral depends on the maximmum
redshift of the survey.