Model Utilities¶

The objects contained in the models_utils module can be used to facilitate the creation of model files.

A detailed discussion of this module can be found in the reference section. Here, we highlight some of its most useful functionalities.

Several handy constants expressed in natural units are pre-defined in models_utils. A complete list can be found here.
The effective number of relativistic degrees of freedom contributing to the Universe's energy and entropy densities is parametrized in the functions g_rho and g_s. These functions, derived by interpolating the tabulated data in Saikawa et al., can be evaluated both as a functions of temperature (in GeV), or as a functions of frequency (in Hz). In the latter case, they will return the value of these functions at the time of the cosmological evolution when GWs with comoving wavenumber \(k=2\pi a_0 f\) re-entered the horizon. (1)
1. Here \(a_0\) denotes the value of the cosmological scale factor today. In our convention, \(a_0=1\).
The function spec_importer allows the user to define the spectrum of a stochastic signal by using tabulated data. This is useful if the spectrum you are interested in is only evaluated numerically without a closed analytical expression for the stochastic signal amplitude \(h^2 \Omega_{\textrm{GW}}\). spec_importer expects the path to an HDF5 file containing the spectrum as a function of frequency and eventual other parameters. It returns a callable function of the frequency \(f\) and any other relevant parameters. In the example below, we interpolate a spectrum parametrized by frequency and one additional parameter \(p\).
```
import os
from ptarcade.models_utils import spec_importer

path = "/This/Is/A/Path/to/the/HDF5/File/spectrum.h5"

log_spectrum = spec_importer(path)

def spectrum(f, p):
    return 10**log_spectrum(np.log10(f), p = p)
```
In this example, the HDF5 file was generated from a plain-text file with the following formatting:
```
p    f          spectrum
-1   -10.000000 -19.000000
-1    -9.950000 -18.900000
-1    -9.900000 -18.800000
...
-0.9 -10.000000 -19.100000
-0.9  -9.950000 -19.000000
-0.9  -9.900000 -18.900000
...
```
PTArcade provides fast_interpolate.reformat to convert such plain-text files to an HDF5 file that fast_interpolate.interp will use to quickly interpolate tabulated data. The plain-text files must meet the following requirements:
- The file has a header with at least spectrum and f present
- Each column is evenly spaced
- The f column must be last if spectrum is not. If spectrum is last, f must be the second-to-last column.
fast_interpolate.reformat will convert the supplied plain-text file to an HDF5 file at a specified destination with the the following HDF5 datasets:
- parameter_names - this dataset contains the parameter names from the header other than spectrum
- spectrum - this dataset contains the spectrum data from the original file
- There will be one additional dataset for each parameter other than spectrum. These datasets will contain two values: the minimum value the parameter can take and the step size. The example file above would generate such datasets for f and p. Assuming the HDF5 file has been read into memory as data, then you would have the following:
```
print(data["p"])
[-1.0, 0.1]

print(data["f"]
[-10.0, 0.05]
```