primordial.equations package

Subpackages

• primordial.equations.N package
  • Submodules
  • primordial.equations.N.cosmology module
  • primordial.equations.N.inflation module
  • primordial.equations.N.mukhanov_sasaki module
  • Module contents
• primordial.equations.t package
  • Submodules
  • primordial.equations.t.cosmology module
  • primordial.equations.t.inflation module
  • primordial.equations.t.mukhanov_sasaki module
  • Module contents

Submodules

primordial.equations.cosmology module

class primordial.equations.cosmology.Equations(H0, Omega_r, Omega_m, Omega_k, Omega_l)

Bases: primordial.equations.equations.Equations

Cosmology equations

Solves background variables in cosmic time for curved and flat universes using the Friedmann equation.

Independent variable:

N: efolds

Variables:

t: cosmic time

Methods

H(t, y)	Hubble parameter
H2(t, y)	The square of the Hubble parameter, computed using the Friedmann equation
__call__(t, y)	Vector of derivatives
add_variable(*args)	Add dependent variables to the equations
set_independent_variable(name)	Set name of the independent variable
sol(sol, **kwargs)	Post-process solution of solve_ivp

H(t, y)

Hubble parameter

H2(t, y)

The square of the Hubble parameter, computed using the Friedmann equation

sol(sol, **kwargs)

Post-process solution of solve_ivp

primordial.equations.equations module

class primordial.equations.equations.Equations

Bases: object

Base class for equations.

Allows one to compute derivatives and derived variables. Most of the other classes take ‘equations’ as an object.

Attributes:

i : dict

dictionary mapping variable names to indices in the solution vector

independent_variable : string

name of independent variable

Methods

__call__(t, y)	Vector of derivatives
add_variable(*args)	Add dependent variables to the equations
set_independent_variable(name)	Set name of the independent variable
sol(sol, **kwargs)	Amend solution from from solve_ivp

add_variable(*args)

Add dependent variables to the equations

• creates an index for the location of variable in y
• creates a class method of the same name with signature name(self, t, y) that should be used to extract the variable value in an index-independent manner.

Parameters:

*args : str

Name of the dependent variables

set_independent_variable(name)

Set name of the independent variable

Parameters:

name : str

Name of the independent variable

sol(sol, **kwargs)

Amend solution from from solve_ivp

primordial.equations.events module

class primordial.equations.events.Collapse(equations, direction=0, terminal=False, value=0)

Bases: primordial.equations.events.Event

Tests if H^2 is positive

Methods

__call__

class primordial.equations.events.Event(equations, direction=0, terminal=False, value=0)

Bases: object

Base class for events.

Gives a more usable wrapper to

Derived classes must define:

__call__(self, t, y)

Scalar root function for determining event

equations: Equations

The equations for computing derived variables.

direction: [-1, 0, +1]

The direction of the root finding (if any)

terminal: bool

Whether to stop at this root

class primordial.equations.events.Inflation(equations, direction=0, terminal=False, value=0)

Bases: primordial.equations.events.Event

Inflation entry/exit

Methods

__call__

class primordial.equations.events.ModeExit(equations, direction=0, terminal=False, value=0)

Bases: primordial.equations.events.Event

When mode exits the horizon

Methods

__call__

class primordial.equations.events.UntilN(equations, direction=0, terminal=False, value=0)

Bases: primordial.equations.events.Event

Stop at N

Methods

__call__

primordial.equations.inflation module

Base classes for inflationary solvers

class primordial.equations.inflation.Equations(K, potential)

Bases: primordial.equations.equations.Equations

Methods

H(t, y)	Hubble parameter
V(t, y)	Potential
__call__(t, y)	Vector of derivatives
add_variable(*args)	Add dependent variables to the equations
dVdphi(t, y)	Potential derivative
set_independent_variable(name)	Set name of the independent variable
sol(sol, **kwargs)	Post-process solution of solve_ivp

H(t, y)

Hubble parameter

V(t, y)

Potential

dVdphi(t, y)

Potential derivative

sol(sol, **kwargs)

Post-process solution of solve_ivp

primordial.equations.inflation_potentials module

class primordial.equations.inflation_potentials.ChaoticPotential(m=1)

Bases: primordial.equations.inflation_potentials.Potential

Methods

__call__
d
dd

d(phi)

dd(phi)

class primordial.equations.inflation_potentials.Potential

Bases: object

Module contents