*** Cross-power spectrum of CMB lensing potential and the linear Integrated Sachs-Wolfe effect, Q(l) ***
April 6, 2012: E.Komatsu

This program reads in a linear power spectrum generated by CAMB, and calculates the cross-correlation power spectrum of the CMB lensing potential and the linear Integrated Sachs-Wolfe effect:

Q(l) = 2 \int_0^z* dz [r(z*)-r(z)]/[r(z*)r^3(z)] [dPpsi(k,z)/dz]_{k=l/r(z)}

where r(z) is the comoving distance, z*=1090 is the redshift of the photon decoupling epoch, and Ppsi(k,z) is the power spectrum of Newtonian gravitational potential.

This code reads in a linear power spectrum of density fluctuations (not potential) computed by CAMB. For this purpose we provide the sample data, "wmap5baosn_max_likelihood_matterpower.dat," which was generated using CAMB code for the maximum likelihood parameters given in Table I of Komatsu et al.(2008) [WMAP 5-year interpretation paper] with "WMAP5+BAO+SN". The input file for CAMB is also provided (wmap5baosn_max_likelihood_params.ini). NOTE THAT THIS POWER SPECTRUM IS COMPUTED AT Z=0.

Another power spectrum, evolved back to z=30, is provided as "wmap5baosn_max_likelihood_matterpower_at_z=30.dat".

- To compile and use the program, edit Makefile and simply "make"
- It will generate an executable called "compute_ql_linear"
- Running "compute_ql" generates a file called "ell_ql.txt", which contains:

(1st column) multipole, l
(2nd column) Q(l)