CAMB: minimum value of k for calculating angular power spectrum

[Hassan Mohm]

For a cosmological model, I have data for the power spectrum corresponding to each k. I am feeding CAMB code with this set of data as:

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# computing the TT power spectrum by feeding camb code!
pars1 = camb.CAMBparams()
pars1.set_cosmology(H0= 67.36, ombh2=0.02237, omch2=0.1200, mnu=0.06, omk=0, tau=0.0544)
lmax=2500
pars1.set_for_lmax(lmax,lens_potential_accuracy=0)
pars1.set_initial_power_table(k_final, Ps_values, pk_tensor=None, effective_ns_for_nonlinear=None)
results1 = camb.get_results(pars1)
cl1=results1.get_total_cls(CMB_unit ='muK')
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The resulting plot for the angular power spectrum is well fit for larger l and very off for small l.

Before asking my question, let me explain the situation a little.
The created data includes a wide k range as k=[10^-7, 10]. For the small value of k, the power spectrum is large. For example, for k=10^-6, the power spectrum is of the order of 10^-3, however, for the observable range of k, as k= [10^-4, 1] specially around the k_pivot, the values of power spectrum can be consistent with the data.
As I have checked the CAMB doc, there is no lower k limit for the function “set_initial_power_table”. So, I fed all the data to CAMB. The resulting Cl is well fit for large l, but way off for small l. regarding this, I have a couple of questions, and I would appreciate it if anyone could help me out:

a)Should I stick to the observable k range and cut my data? By cutting it and sticking to the observable range, I can reproduce the result of the paper I am reading.

b)Is the calculated transfer function in the CAMB code possibly getting divergent because of low values of k and high values of Ps? Due to this divergence in the transfer function, I am getting this kind of result for low values of l.

c)If it is not required to limit the lower limit of k in the code above, could the problem be because of the large value of the power spectrum which we have for small k?

[Antony Lewis]

The low multipoles should converge as long as P(k) doesn't diverge too badly towards zero, but of course default accuracy settings assume nearly scale invariant, so you may need to explore settings. If your P(k) does diverge, then obviously not surprising that you get strange behaviour at low L (and you probably need to then calculate something else, like the C_l conditional on the CMB monopole to remove locally-unobservable dependence on superhorizon modes).