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Description:

primordial 0.0.13

primordial:
inflationary equation solver

Author:
Will Handley
Version:
0.0.13
Homepage:
https://github.com/williamjameshandley/primordial

Documentation:
http://primordial.readthedocs.io/

Description
primordial is a python package for solving cosmological inflationary equations.
It is very much in beta stage, and currently being built for research purposes.

Example Usage

Plot Background evolution
import numpy
import matplotlib.pyplot as plt
from primordial.solver import solve
from primordial.equations.inflation_potentials import ChaoticPotential
from primordial.equations.t.inflation import Equations, KD_initial_conditions
from primordial.equations.events import Inflation, Collapse

fig, ax = plt.subplots(3,sharex=True)
for K in [-1, 0, +1]:
m = 1
V = ChaoticPotential(m)
equations = Equations(K, V)

events= [Inflation(equations), # Record inflation entry and exit
Inflation(equations, -1, terminal=True), # Stop on inflation exit
Collapse(equations, terminal=True)] # Stop if universe stops expanding

N_p = -1.5
phi_p = 23
t_p = 1e-5
ic = KD_initial_conditions(t_p, N_p, phi_p)
t = numpy.logspace(-5,10,1e6)

sol = solve(equations, ic, t_eval=t, events=events)

ax[0].plot(sol.N(t),sol.phi(t))
ax[0].set_ylabel(r'$\phi$')

ax[1].plot(sol.N(t),sol.H(t))
ax[1].set_yscale('log')
ax[1].set_ylabel(r'$H$')

ax[2].plot(sol.N(t),1/(sol.H(t)*numpy.exp(sol.N(t))))
ax[2].set_yscale('log')
ax[2].set_ylabel(r'$1/aH$')

ax[-1].set_xlabel('$N$')

Plot mode function evolution
import numpy
import matplotlib.pyplot as plt
from primordial.solver import solve
from primordial.equations.inflation_potentials import ChaoticPotential
from primordial.equations.t.mukhanov_sasaki import Equations, KD_initial_conditions
from primordial.equations.events import Inflation, Collapse, ModeExit

fig, axes = plt.subplots(3,sharex=True)
for ax, K in zip(axes, [-1, 0, +1]):
ax2 = ax.twinx()
m = 1
V = ChaoticPotential(m)
k = 100
equations = Equations(K, V, k)

events= [
Inflation(equations), # Record inflation entry and exit
Collapse(equations, terminal=True), # Stop if universe stops expanding
ModeExit(equations, +1, terminal=True, value=1e1*k) # Stop on mode exit
]

N_p = -1.5
phi_p = 23
t_p = 1e-5
ic = KD_initial_conditions(t_p, N_p, phi_p)
t = numpy.logspace(-5,10,1e6)

sol = solve(equations, ic, t_eval=t, events=events)

N = sol.N(t)
ax.plot(N,sol.R1(t), 'k-')
ax2.plot(N,-numpy.log(sol.H(t))-N, 'b-')

ax.set_ylabel('$\mathcal{R}$')
ax2.set_ylabel('$-\log aH$')

ax.text(0.9, 0.9, r'$K=%i$' % K, transform=ax.transAxes)

axes[-1].set_xlabel('$N$')

To do list
Eventually would like to submit this to JOSS. Here are things to do before then:

Cosmology

Slow roll initial conditions
Mukhanov Sazaki evolution in N
add η as independent variable
add ϕ as independent variable

Code

Documentation

Tests

100% coverage
interpolation
cosmology