geff.utility.cosmo

This module defines constants and functions which are often times encountered in cosmology. These are primarily used in GEFF.tools.gw

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 1r"""
 2This module defines constants and functions which are often times encountered in cosmology. These are primarily used in `GEFF.tools.gw`
 3"""
 4import natpy as nat
 5import numpy as np
 6import pandas as pd
 7import os
 8
 9basepath = os.path.dirname(os.path.abspath(__file__))
10
11nat.set_active_units("HEP")
12
13#constants
14G : float = 6.67430e-11 * nat.convert(nat.m**3 * nat.kg**(-1) * nat.s**(-2), nat.GeV**(-2)) 
15"""Newtons constant in GeV."""
16M_pl : float = (8*np.pi*G)**(-1/2) # reduced Planck mass in GeV
17"""The reduced Planck mass in GeV."""
18
19#Conversions
20gev_to_hz : float = nat.convert(nat.GeV, nat.Hz)
21"""The conversion factor between Hz and GeV."""
22
23#Planck results
24T_0 : float = 2.7255 * nat.convert(nat.K, nat.GeV)
25"""The temperatur of CMB photons today (in GeV)."""
26h : float = 0.674
27"""The reduced Hubble parameter $h$ (from [Planck 2018](https://arxiv.org/abs/1807.06209))."""
28H0 : float = h*100*nat.convert(nat.km * nat.s**(-1) * nat.Mpc**(-1), nat.GeV)
29"""The Hubble rate today (in GeV)."""
30
31gtab = pd.read_table(os.path.join(basepath, "../data/eff_dof.dat"), sep=" ", comment="#").values.T
32gdic = {"T":gtab[0,:],"f":gtab[1,:],"grho":gtab[2,:], "gs":gtab[3,:]}
33
34def g_rho(T : float) -> float:
35    """
36    Effective number of relativistic degrees of freedom as a function of temperature, $g_{*}(T)$.
37
38    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
39    """
40    return np.interp(T, gdic["T"], gdic["grho"])
41
42def g_s(T : float) -> float:
43    """
44    Effective number of entropic degrees of freedom as a function of temperature, $g_{*,S}(T)$.
45
46    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
47    """
48    return np.interp(T, gdic["T"], gdic["gs"])
49
50def g_rho_freq(f : float) -> float:
51    """
52    Effective number of relativistic degrees of freedom as a function of frequency, $g_{*}(T(f))$.
53
54    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
55    """
56    return np.interp(f, gdic["f"], gdic["grho"])
57
58def g_s_freq(f : float) -> float:
59    """
60    Effective number of entropic degrees of freedom as a function of frequency, $g_{*,S}(T(f))$.
61
62    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
63    """
64    return np.interp(f, gdic["f"], gdic["gs"])
65
66
67
68g_rho_0 : float = g_rho(T_0)
69"""The effective number of relativistic degrees of freedom today, $g_{*}(T_0)$."""
70g_s_0 : float = g_s(T_0)
71"""The effective number of entropic degrees of freedom today, $g_{*,S}(T_0)$."""
72omega_r : float = np.pi**2*g_rho_0/(90*M_pl**2*H0**2)*T_0**4
73"""The density parameter for radiation today, $\Omega_r$."""
74
75feq = 2.1e-17
76"""Frequency corresponding to mattter-radiation equality"""

G: float = np.float64(6.708830746231456e-39)

Newtons constant in GeV.

M_pl: float = np.float64(2.4353234600842885e+18)

The reduced Planck mass in GeV.

gev_to_hz: float = np.float64(1.519267447878626e+24)

The conversion factor between Hz and GeV.

T_0: float = np.float64(2.348654180597668e-13)

The temperatur of CMB photons today (in GeV).

h: float = 0.674

The reduced Hubble parameter $h$ (from Planck 2018).

H0: float = np.float64(1.4377226630738714e-42)

The Hubble rate today (in GeV).

def g_rho(T: float) -> float: View Source

35def g_rho(T : float) -> float:
36    """
37    Effective number of relativistic degrees of freedom as a function of temperature, $g_{*}(T)$.
38
39    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
40    """
41    return np.interp(T, gdic["T"], gdic["grho"])

Effective number of relativistic degrees of freedom as a function of temperature, $g_{*}(T)$.

Data is taken from 2005.03544.

def g_s(T: float) -> float: View Source

43def g_s(T : float) -> float:
44    """
45    Effective number of entropic degrees of freedom as a function of temperature, $g_{*,S}(T)$.
46
47    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
48    """
49    return np.interp(T, gdic["T"], gdic["gs"])

Effective number of entropic degrees of freedom as a function of temperature, $g_{*,S}(T)$.

Data is taken from 2005.03544.

def g_rho_freq(f: float) -> float: View Source

51def g_rho_freq(f : float) -> float:
52    """
53    Effective number of relativistic degrees of freedom as a function of frequency, $g_{*}(T(f))$.
54
55    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
56    """
57    return np.interp(f, gdic["f"], gdic["grho"])

Effective number of relativistic degrees of freedom as a function of frequency, $g_{*}(T(f))$.

Data is taken from 2005.03544.

def g_s_freq(f: float) -> float: View Source

59def g_s_freq(f : float) -> float:
60    """
61    Effective number of entropic degrees of freedom as a function of frequency, $g_{*,S}(T(f))$.
62
63    Data is taken from [2005.03544](https://arxiv.org/abs/2005.03544).
64    """
65    return np.interp(f, gdic["f"], gdic["gs"])

Effective number of entropic degrees of freedom as a function of frequency, $g_{*,S}(T(f))$.

Data is taken from 2005.03544.

g_rho_0: float = np.float64(3.38308)

The effective number of relativistic degrees of freedom today, $g_{*}(T_0)$.

g_s_0: float = np.float64(3.93094)

The effective number of entropic degrees of freedom today, $g_{*,S}(T_0)$.

omega_r: float = np.float64(9.208359428041601e-05)

The density parameter for radiation today, $\Omega_r$.

feq = 2.1e-17

Frequency corresponding to mattter-radiation equality