primordial 0.0.13

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('$N$')

Cosmology

• Slow roll initial conditions

• Mukhanov Sazaki evolution in \(N\)

• add \(\eta\) as independent variable

• add \(\phi\) as independent variable

Code

• Documentation

• Tests

  • 100% coverage

  • interpolation

  • cosmology