CosmoCoffee

It seems that the default pivot scale k_0 of cosmomc is 0.005/Mpc, while the WMAP team set it to 0.002/Mpc. any particular reason for such choices?

I think cosmomc default is 0.05/Mpc.

If the pivot scale is much larger (smaller k) there are big degeneracies between the spectral index and amplitude when you have running (basically because the data is pinning things at a scale much smaller than 0.002/Mpc). The likelihood is easier to explore using a pivot choice where the parameters are more independent; 0.05/Mpc is however not an optimized choice, but inherited as a default from CMBFAST (I think).

On the other hand the tensor ratio is effectively measured on a larger scale.

See Table 4 and section 5.5 of Komatsu et al. for a little discussion about this.

There is actually a very nice paper by Cortes, Liddle, and Mukherjee
(http://arxiv.org/abs/astro-ph/0702170) in which they determine the pivot scale at which spectrum degeneracies are minimized, k = 0.017 h Mpc^-1. Their analysis was done for WMAP3.