Parameter space
On this page we describe the native emulator parameter space with the supported range of values, as well as the various cosmological and bias parameters that can be specified.
Ranges of emulated parameters
Since COMET employs the evolution mapping approach, its parameter space consists of a set of shape parameters, in addition to \(\sigma_{12}\) and the growth rate \(f\), which capture the dependence on redshift and evolution parameters. The following table lists the ranges for each emulated parameter.
Parameter |
Minimum |
Maximum |
|---|---|---|
\(\omega_c\) |
0.085 |
0.155 |
\(\omega_b\) |
0.0205 |
0.02415 |
\(n_s\) |
0.92 |
1.01 |
\(\sigma_{12}\) |
0.2 |
1.0 |
\(f\) |
0.5 |
1.05 |
All predictions from COMET are limited to the range of scales \(k \in [6.95 \times 10^{-4}, 0.35028]\,\mathrm{Mpc}^{-1}\) (note that the range is defined in units of \(\mathrm{Mpc}\), opposed to \(h^{-1}\,\mathrm{Mpc}\)!).
Note
Note that for values of \(k\) beyond 0.35 \(\mathrm{Mpc}^{-1}\) COMET returns a power-law extrapolation of the power spectrum multipoles. This is mainly intended for performing the convolution with the survey window function. Direct evaluation of the multipoles should always be kept within the supported range above.
Cosmological parameters
The table below lists all available cosmological parameters and the corresponding keys by which they are identified in the parameter dictionary that is given as an argument to the function returning the power spectrum multipoles (see Tutorials).
Note
The three shape parameters \((\omega_c,\, \omega_b,\, n_s)\) always need
to be specified in the dictionary, while the remaining required parameters
are determined by the option de_model. If de_model = None (default),
the native emulator parameter space is assumed and we need to provide values
for \(\sigma_{12}\) and \(f\). For de_model = lambda, w0, or
w0wa different sets of parameters are required. The curvature density
is always optional and if not explicitly included in the parameter dictionary
a flat cosmology is assumed.
Parameter |
Description |
Key |
Option |
|---|---|---|---|
\(\omega_c\) |
Phys. cold dark matter density |
|
|
\(\omega_b\) |
Phys. baryon density |
|
|
\(n_s\) |
Scalar spectral index |
|
|
\(\sigma_{12}\) |
RMS of fluctuations in spheres of 12 Mpc |
|
|
\(f\) |
Growth rate |
|
|
\(A_s\) |
Amplitude of scalar fluctuations |
|
|
\(h\) |
Hubble rate |
|
|
\(w_0\) |
Const. DE equation of state parameter |
|
|
\(w_a\) |
Time evolving DE equation of state parameter |
|
|
\(\Omega_K\) |
Curvature density |
|
|
Bias parameters
Finally we list all bias parameters that can be specified in the models that COMET implements. All of them are optional and assumed to be zero if they are not explicitly included in the parameter dictionary.
Parameter |
Description |
Key |
|---|---|---|
\(b_1\) |
Linear bias |
|
\(b_2\) |
Quadratic non-linear bias |
|
\(\gamma_2\) |
Second-order tidal bias |
|
\(\gamma_{21}\) |
Third-order tidal bias |
|
\(c_0\) |
Counterterm parameter, in units of \(L^2\) |
|
\(c_2\) |
Counterterm parameter, prop. to \({\cal L}_2(\mu)\), in units of \(L^2\) |
|
\(c_4\) |
Counterterm parameter, prop. to \({\cal L}_4(\mu)\), in units of \(L^2\) |
|
\(c_{\mathrm{nlo}}\) |
Next-to-leading order counterterm parameter, in units of \(L^4\) |
|
\(N^P_0\) |
Constant shot noise, in units of \(L^3\) |
|
\(N^P_{20}\) |
Scale-dependent shot noise, in units of \(L^5\) |
|
\(N^P_{22}\) |
Scale-dependent shot noise, prop. to \({\cal L}_2(\mu)\), in units of \(L^5\) |
|
where \(L\) either stands for \(\mathrm{Mpc}\) or \(h^{-1}\,\mathrm{Mpc}\), depending on the unit configuration of COMET, see Tutorials.