primpy.time package

Calculations for the primordial Universe w.r.t. time t.

primpy.time.inflation module

Differential equations for inflation w.r.t. time t.

class primpy.time.inflation.InflationEquationsT(K, potential, track_eta=False, verbose=False)

Bases: InflationEquations

Background equations during inflation w.r.t. time t.

Solves background variables in cosmic time for curved and flat universes using the Klein-Gordon and Friedmann equations.

Independent variable:

t: cosmic time

Dependent variables:

• _N: number of e-folds

• phi: inflaton field

• dphidt: d(phi)/dt

• eta: conformal time (optional)

Methods

H2(x, y)	Hubble parameter squared.
__call__(x, y)	System of coupled ODEs for underlying variables.
get_H2(N, dphi, V, K)	Get the Hubble parameter squared from the background equations.
get_d2H(N, H, dH, dphi, d2phi, K)	Get the 2nd time derivative of the Hubble parameter from the background equations.
get_d2phi(H2, dH_H, dphi, dV)	Get the 2nd time derivative of the inflaton field from the background equations.
get_d3H(N, H, dH, d2H, dphi, d2phi, d3phi, K)	Get the 3rd time derivative of the Hubble parameter from the background equations.
get_d3phi(H, dH, d2H, dphi, d2phi, dV, d2V)	Get the 3rd time derivative of the inflaton field from the background equations.
get_d4phi(H, dH, d2H, d3H, dphi, d2phi, ...)	Get the 4th time derivative of the inflaton field from the background equations.
get_dH(N, H, dphi, K)	Get the 1st time derivative of the Hubble parameter from the background equations.
inflating(x, y)	Inflation diagnostic for event tracking.
sol(sol, **kwargs)	Post-processing of scipy.integrate.solve_ivp() solution.
w(x, y)	Equation of state parameter.

get_dH_H

__call__(x, y)

System of coupled ODEs for underlying variables.

static get_H2(N, dphi, V, K)

Get the Hubble parameter squared from the background equations.

Returns:

H2float or array_like

static get_dH(N, H, dphi, K)

Get the 1st time derivative of the Hubble parameter from the background equations.

Returns:

dHfloat or array_like

static get_dH_H(N, H2, dphi, K)

static get_d2H(N, H, dH, dphi, d2phi, K)

Get the 2nd time derivative of the Hubble parameter from the background equations.

Returns:

d2Hfloat or array_like

static get_d3H(N, H, dH, d2H, dphi, d2phi, d3phi, K)

Get the 3rd time derivative of the Hubble parameter from the background equations.

Returns:

d3Hfloat or array_like

static get_d2phi(H2, dH_H, dphi, dV)

Get the 2nd time derivative of the inflaton field from the background equations.

Returns:

d2phifloat or array_like

static get_d3phi(H, dH, d2H, dphi, d2phi, dV, d2V)

Get the 3rd time derivative of the inflaton field from the background equations.

Returns:

d3phifloat or array_like

static get_d4phi(H, dH, d2H, d3H, dphi, d2phi, d3phi, dV, d2V, d3V)

Get the 4th time derivative of the inflaton field from the background equations.

Returns:

d4phifloat or array_like

H2(x, y)

Hubble parameter squared.

w(x, y)

Equation of state parameter.

inflating(x, y)

Inflation diagnostic for event tracking.

sol(sol, **kwargs)

Post-processing of scipy.integrate.solve_ivp() solution.

primpy.time.perturbations module

Curvature perturbations with respect to time t.

class primpy.time.perturbations.PerturbationT(background, k, **kwargs)

Bases: Perturbation

Curvature perturbation for wavenumber k with respect to time t.

Solves the Mukhanov–Sasaki equations w.r.t. cosmic time for curved universes.

Parameters:

backgroundBunch object same as returned by scipy.integrate.solve_ivp()

Background solution as returned by primpy.time.inflation.InflationEquationsT.sol().

kfloat

wavenumber

class primpy.time.perturbations.ScalarModeT(background, k, **kwargs)

Bases: ScalarMode

Template for scalar modes.

Methods

__call__(x, y)	Vector of derivatives.
get_vacuum_ic_HD()	Get initial conditions for scalar modes for HD vacuum w.r.t.
get_vacuum_ic_RST()	Get initial conditions for scalar modes for RST vacuum w.r.t.
get_vacuum_ic_k()	Get initial conditions for scalar modes for HD approximation w.r.t.
mukhanov_sasaki_frequency_damping()	Frequency and damping term of the Mukhanov-Sasaki equations for scalar modes.

__call__(x, y)

Vector of derivatives.

mukhanov_sasaki_frequency_damping()

Frequency and damping term of the Mukhanov-Sasaki equations for scalar modes.

Frequency and damping term of the Mukhanov-Sasaki equations for the comoving curvature perturbations R w.r.t. time t, where the e.o.m. is written as ddR + 2 * damping * dR + frequency**2 * R = 0.

get_vacuum_ic_k()

Get initial conditions for scalar modes for HD approximation w.r.t. cosmic time t.

get_vacuum_ic_HD()

Get initial conditions for scalar modes for HD vacuum w.r.t. cosmic time t.

get_vacuum_ic_RST()

Get initial conditions for scalar modes for RST vacuum w.r.t. cosmic time t.

class primpy.time.perturbations.TensorModeT(background, k, **kwargs)

Bases: TensorMode

Template for tensor modes.

Methods

__call__(x, y)	Vector of derivatives.
get_vacuum_ic_HD()	Get initial conditions for tensor modes for HD vacuum w.r.t.
get_vacuum_ic_RST()	Get initial conditions for tensor modes for RST vacuum w.r.t.
get_vacuum_ic_k()	Get initial conditions for tensor modes for HD approximation w.r.t.
mukhanov_sasaki_frequency_damping()	Frequency and damping term of the Mukhanov-Sasaki equations for tensor modes.

__call__(x, y)

Vector of derivatives.

mukhanov_sasaki_frequency_damping()

Frequency and damping term of the Mukhanov-Sasaki equations for tensor modes.

Frequency and damping term of the Mukhanov-Sasaki equations for the tensor perturbations h w.r.t. time t, where the e.o.m. is written as ddh + 2 * damping * dh + frequency**2 * h = 0.

get_vacuum_ic_k()

Get initial conditions for tensor modes for HD approximation w.r.t. cosmic time t.

get_vacuum_ic_HD()

Get initial conditions for tensor modes for HD vacuum w.r.t. cosmic time t.

get_vacuum_ic_RST()

Get initial conditions for tensor modes for RST vacuum w.r.t. cosmic time t.