abcmb.species module

class abcmb.species.BackgroundFluid(first_idx, specs)

Bases: Fluid

rho_delta(lna, y, args)

Compute density perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Density perturbation (units: eV cm^{-3})

rho_plus_P_sigma(lna, y, args)

Compute shear perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Shear perturbation (units: eV cm^{-3})

rho_plus_P_theta(lna, y, args)

Compute velocity perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Velocity perturbation (units: eV cm^{-3} Mpc^{-1})

y_ini(k, tau_ini, args)

Trivial initial condition vector for background.

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Trivial derivative vector for background.

class abcmb.species.Baryon(first_idx, specs)

Bases: StandardFluid

Baryon fluid species implementation.

Non-relativistic baryons with density and velocity perturbations.

Required input parameters: params[‘omega_b’], params[‘YHe’]

Required derived parameters: params[‘R_nu’], params[‘R_b’], params[‘om’]

Methods:

• rho :

  Compute baryon density (units: eV cm^{-3})

• P :

  Compute baryon pressure (units: eV cm^{-3})

• cs2 :

  Compute sound speed squared (units: dimensionless)

• mean_mass :

  Compute mean baryon mass (units: eV)

• y_ini :

  Compute initial perturbation conditions

• y_prime :

  Compute perturbation time derivatives

P(lna, args)

Compute baryon pressure.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Baryon pressure (units: eV cm^{-3})

Notes:

Baryon pressure is neglected, standard practice for SM baryons.

cs2(lna, args)

Compute sound speed squared.

Parameters:

• lna float

  Logarithm of scale factor

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

float

Sound speed squared (units: dimensionless)

Notes:

Adiabatic sound speed squared, taken from M&B Eq. (68). Although we can neglect the pressure, this term is important for perturbation growth during recombination. During reionization this cs2 is negative. This is not physical but it should not matter for cosmology.

mean_mass(lna, args)

Compute mean baryon mass at given redshift.

Parameters:

• lna float

  Logarithm of scale factor

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

float

Mean baryon mass (units: eV)

Notes:

Defined to be mu = rho_b / n_b = rho_b / (nH + nHe + ne)

output_perturbations(lna, modes, args)

Return named perturbation arrays for storage in PerturbationTable.

Each concrete species overrides this to select the physically meaningful subset of its modes. Species with no perturbations (e.g. dark energy) return an empty dict via this base implementation.

Parameters:

• lna array, shape (Nlna,)

  Logarithm of scale factor grid

• modes array, shape (Ny, Nlna, Nk)

  Full perturbation state, already transposed

• args tuple

  (BG, params) — background cosmology and cosmological parameters

Returns:

dict

{quantity_name: array(Nlna, Nk)}. Empty for background-only species.

rho(lna, args)

Compute baryon density.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Baryon density (units: eV cm^{-3})

y_ini(k, tau_ini, args)

Compute initial conditions for baryon perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• tau_ini float

  Initial conformal time (units: Mpc)

• args dict

  Cosmological parameters (params)

Returns:

array

Initial perturbation mode values (units: 1/Mpc for theta, else dimensionless)

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Compute time derivatives of baryon perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• lna float

  Logarithm of scale factor

• metric_h_prime float

  Derivative of metric h

• metric_eta_prime float

  Derivative of metric eta

• y array

  Current perturbation mode values

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

array

Time derivatives of perturbation modes (units: 1/Mpc for theta, else dimensionless)

class abcmb.species.ColdDarkMatter(first_idx, specs)

Bases: StandardFluid

Cold dark matter fluid species implementation.

Non-relativistic, pressureless dark matter with density perturbations but no velocity or shear modes.

Required input parameters: params[‘omega_cdm’].

Required derived parameters: params[‘om’].

Methods:

• rho :

  Compute cold dark matter density (units: eV cm^{-3})

• P :

  Compute cold dark matter pressure (units: eV cm^{-3})

• y_ini :

  Compute initial perturbation conditions

• y_prime :

  Compute perturbation time derivatives

P(lna, args)

Compute cold dark matter pressure.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Cold dark matter pressure (units: eV cm^{-3})

Notes:

Cold dark matter is pressureless, so this always returns zero.

output_perturbations(lna, modes, args)

Return named perturbation arrays for storage in PerturbationTable.

Each concrete species overrides this to select the physically meaningful subset of its modes. Species with no perturbations (e.g. dark energy) return an empty dict via this base implementation.

Parameters:

• lna array, shape (Nlna,)

  Logarithm of scale factor grid

• modes array, shape (Ny, Nlna, Nk)

  Full perturbation state, already transposed

• args tuple

  (BG, params) — background cosmology and cosmological parameters

Returns:

dict

{quantity_name: array(Nlna, Nk)}. Empty for background-only species.

rho(lna, args)

Compute cold dark matter density.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Cold dark matter density (units: eV cm^{-3})

y_ini(k, tau_ini, args)

Compute initial conditions for cold dark matter perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• tau_ini float

  Initial conformal time (units: Mpc)

• args dict

  Cosmological parameters (params)

Returns:

array

Initial density perturbation (units: dimensionless)

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Compute time derivatives of cold dark matter perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• lna float

  Logarithm of scale factor

• metric_h_prime float

  Derivative of metric h

• metric_eta_prime float

  Derivative of metric eta

• y array

  Current perturbation mode values

• args tuple

  Background cosmology and cosmological parameters (BG, params) - Note: BG parameter is unused in this implementation

Returns:

array

Time derivative of density perturbation (units: dimensionless)

class abcmb.species.DarkEnergy(first_idx, specs)

Bases: BackgroundFluid

Dark energy fluid species implementation.

Represents a constant energy density fluid with negative pressure.

Required input parameters: None.

Required derived parameters: params[‘omega_Lambda’]

Methods:

• rho :

  Compute dark energy density (units: eV cm^{-3})

• P :

  Compute dark energy pressure (units: eV cm^{-3})

P(lna, args)

Compute dark energy pressure.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Dark energy pressure (units: eV cm^{-3})

rho(lna, args)

Compute dark energy density.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Dark energy density (units: eV cm^{-3})

class abcmb.species.Fluid(first_idx, specs)

Bases: Module

Base class for fluid species.

Defines fluid properties.

Fields:

• first_idx int

  Default = 0 Position of the first perturbation equation in the Diffrax vector. For most fluids this is the density perturbation mode “delta”.

• num_equations int

  Default = 0 Number of equations that need to be simultaneously evolved in the perturbations module.

• name str

  Default = “” Name of the fluid, used to find fluid and refer to it later in the computation using species_dict[“name”].

• is_matter bool

  Default = False Whether the fluid is non-relativistic today and contributes towards the total matter power spectrum.

Methods:

• rho :

  Compute energy density (units: eV cm^{-3})

• P :

  Compute pressure (units: eV cm^{-3})

• w :

  Compute equation of state parameter (units: dimensionless)

• y_ini :

  Adiabatic initial conditions, in synchronous gauge

• y_prime :

  Perturbation derivatives, in synchronous gauge

• rho_delta :

  Perturbed density function δρ (units: eV cm^{-3})

• rho_plus_P_theta :

  Velocity perturbation (units: eV cm^{-3} Mpc^{-1})

• rho_plus_P_sigma :

  Compute standard shear perturbation (units: eV cm^{-3})

P(lna, args)

Compute pressure.

Calculates the pressure of the fluid species at a given cosmological epoch using the logarithm of the scale factor.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Pressure (units: eV cm^{-3})

output_perturbations(lna, modes, args)

Return named perturbation arrays for storage in PerturbationTable.

Each concrete species overrides this to select the physically meaningful subset of its modes. Species with no perturbations (e.g. dark energy) return an empty dict via this base implementation.

Parameters:

• lna array, shape (Nlna,)

  Logarithm of scale factor grid

• modes array, shape (Ny, Nlna, Nk)

  Full perturbation state, already transposed

• args tuple

  (BG, params) — background cosmology and cosmological parameters

Returns:

dict

{quantity_name: array(Nlna, Nk)}. Empty for background-only species.

rho(lna, args)

Compute energy density.

Calculates the energy density of the fluid species at a given cosmological epoch using the logarithm of the scale factor.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Energy density (units: eV cm^{-3})

rho_delta(lna, y, args)

Compute density perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Density perturbation (units: eV cm^{-3})

rho_plus_P_sigma(lna, y, args)

Compute shear perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Shear perturbation (units: eV cm^{-3})

rho_plus_P_theta(lna, y, args)

Compute velocity perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Velocity perturbation (units: eV cm^{-3} Mpc^{-1})

w(lna, args)

Compute equation of state parameter.

Calculates the ratio of pressure to energy density, representing the equation of state for the fluid species.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Equation of state parameter (units: dimensionless)

y_ini(k, tau_ini, args)

Compute initial conditions for perturbation modes.

Calculates the initial state of perturbation modes at early cosmological times.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• tau_ini float

  Initial conformal time (units: Mpc)

• args dict

  Cosmological parameters (params)

Returns:

array

Initial perturbation mode values

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Compute time derivatives of perturbation modes.

Calculates how perturbation modes evolve with cosmological time.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• lna float

  Logarithm of scale factor

• metric_h_prime float

  Derivative of metric h

• metric_eta_prime float

  Derivative of metric eta

• y array

  Current perturbation mode values

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

array

Time derivatives of perturbation modes

class abcmb.species.MassiveNeutrino(first_idx, specs)

Bases: Fluid

Massive neutrinos fluid species implementation.

Non-relativistic neutrinos with multiple angular momentum modes.

Required input parameters: params[‘N_nu_massive’], params[‘T_nu_massive’], params[‘m_nu_massive’], params[‘TCMB0’]

Required derived parameters: params[‘R_nu’], params[‘om’]

Attributes:

• num_ells_per_bin int

  Number of multipole moments per momentum bin for massive neutrino hierarchy

Methods:

• rho :

  Compute massive neutrino density (units: eV cm^{-3})

• P :

  Compute massive neutrino pressure (units: eV cm^{-3})

• y_ini :

  Compute initial perturbation conditions

• y_prime :

  Compute perturbation time derivatives

• rho_delta :

  Compute density perturbation (units: eV cm^{-3})

• rho_plus_P_theta :

  Compute velocity perturbation (units: eV cm^{-3} Mpc^{-1})

• rho_plus_P_sigma :

  Compute shear perturbation (units: eV cm^{-3})

P(lna, args)

Compute massive neutrino pressure.

Parameters:

• lna float or ArrayLike

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float or ArrayLike

Massive neutrino pressure (units: eV cm^{-3})

output_perturbations(lna, modes, args)

Return named perturbation arrays for storage in PerturbationTable.

Each concrete species overrides this to select the physically meaningful subset of its modes. Species with no perturbations (e.g. dark energy) return an empty dict via this base implementation.

Parameters:

• lna array, shape (Nlna,)

  Logarithm of scale factor grid

• modes array, shape (Ny, Nlna, Nk)

  Full perturbation state, already transposed

• args tuple

  (BG, params) — background cosmology and cosmological parameters

Returns:

dict

{quantity_name: array(Nlna, Nk)}. Empty for background-only species.

rho(lna, args)

Compute massive neutrino density.

Parameters:

• lna float or ArrayLike

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float or ArrayLike

Massive neutrino density (units: eV cm^{-3})

rho_delta(lna, y, args)

Compute massive neutrino density perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Density perturbation (units: eV cm^{-3})

rho_plus_P_sigma(lna, y, args)

Compute massive neutrino shear perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Shear perturbation (units: eV cm^{-3})

rho_plus_P_theta(lna, y, args)

Compute massive neutrino velocity perturbation.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Velocity perturbation (units: eV cm^{-3} Mpc^{-1})

y_ini(k, tau_ini, args)

Compute initial conditions for massive neutrino perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• tau_ini float

  Initial conformal time (units: Mpc)

• args dict

  Cosmological parameters (params)

Returns:

array

Initial perturbation mode values (units: 1/Mpc for kPsi1, else dimensionless)

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Compute time derivatives of massive neutrino perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• lna float

  Logarithm of scale factor

• metric_h_prime float

  Derivative of metric h

• metric_eta_prime float

  Derivative of metric eta

• y array

  Current perturbation mode values

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

array

Time derivatives of perturbation modes (units: 1/Mpc for kPsi1, else dimensionless)

class abcmb.species.MasslessNeutrino(first_idx, specs)

Bases: StandardFluid

Massless neutrinos fluid species implementation.

Represents relativistic neutrinos with multiple angular momentum modes.

Required input parameters: params[‘N_nu_massless’], params[‘T_nu_massless’], params[‘TCMB0’]

Required derived parameters: params[‘R_nu’], params[‘om’]

Methods:

• rho :

  Compute neutrino density (units: eV cm^{-3})

• P :

  Compute neutrino pressure (units: eV cm^{-3})

P(lna, args)

Compute neutrino pressure.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Neutrino pressure (units: eV cm^{-3})

output_perturbations(lna, modes, args)

Return named perturbation arrays for storage in PerturbationTable.

Each concrete species overrides this to select the physically meaningful subset of its modes. Species with no perturbations (e.g. dark energy) return an empty dict via this base implementation.

Parameters:

• lna array, shape (Nlna,)

  Logarithm of scale factor grid

• modes array, shape (Ny, Nlna, Nk)

  Full perturbation state, already transposed

• args tuple

  (BG, params) — background cosmology and cosmological parameters

Returns:

dict

{quantity_name: array(Nlna, Nk)}. Empty for background-only species.

rho(lna, args)

Compute neutrino density.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Neutrino density (units: eV cm^{-3})

y_ini(k, tau_ini, args)

Compute initial conditions for massless neutrino perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• tau_ini float

  Initial conformal time (units: Mpc)

• args dict

  Cosmological parameters (params)

Returns:

array

Initial perturbation mode values (units: 1/Mpc for theta, else dimensionless)

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Compute time derivatives of massless neutrino perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• lna float

  Logarithm of scale factor

• metric_h_prime float

  Derivative of metric h

• metric_eta_prime float

  Derivative of metric eta

• y array

  Current perturbation mode values

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

array

Time derivatives of perturbation modes (units: 1/Mpc for theta, else dimensionless)

class abcmb.species.Photon(first_idx, specs)

Bases: StandardFluid

Photon fluid species implementation.

Relativistic photons with temperature and polarization Boltzmann hierarchies.

Required input parameters: params[‘TCMB0’]

Required derived parameters: params[‘R_nu’], params[‘R_nu’], params[‘om’]

Attributes:

• num_F_ell_modes int

  Number of temperature multipole moments in Boltzmann hierarchy

• num_G_ell_modes int

  Number of polarization multipole moments in Boltzmann hierarchy

Methods:

• rho :

  Compute photon density (units: eV cm^{-3})

• P :

  Compute photon pressure (units: eV cm^{-3})

• y_ini :

  Compute initial perturbation conditions

• y_prime :

  Compute perturbation time derivatives

P(lna, args)

Compute photon pressure.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Photon pressure (units: eV cm^{-3})

output_perturbations(lna, modes, args)

Return named perturbation arrays for storage in PerturbationTable.

Each concrete species overrides this to select the physically meaningful subset of its modes. Species with no perturbations (e.g. dark energy) return an empty dict via this base implementation.

Parameters:

• lna array, shape (Nlna,)

  Logarithm of scale factor grid

• modes array, shape (Ny, Nlna, Nk)

  Full perturbation state, already transposed

• args tuple

  (BG, params) — background cosmology and cosmological parameters

Returns:

dict

{quantity_name: array(Nlna, Nk)}. Empty for background-only species.

rho(lna, args)

Compute photon density.

Parameters:

• lna float

  Logarithm of scale factor

• args dict

  Cosmological parameters (params)

Returns:

float

Photon density (units: eV cm^{-3})

y_ini(k, tau_ini, args)

Compute initial conditions for photon perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• tau_ini float

  Initial conformal time (units: Mpc)

• args dict

  Cosmological parameters (params)

Returns:

array

Initial perturbation mode values (units: 1/Mpc for theta, else dimensionless)

y_prime(k, lna, metric_h_prime, metric_eta_prime, y, args)

Compute time derivatives of photon perturbations.

Parameters:

• k float

  Wavenumber (units: Mpc^{-1})

• lna float

  Logarithm of scale factor

• metric_h_prime float

  Derivative of metric h

• metric_eta_prime float

  Derivative of metric eta

• y array

  Current perturbation mode values

• args tuple

  Background cosmology and cosmological parameters (BG, params)

Returns:

array

Time derivatives of perturbation modes (units: 1/Mpc for theta, else dimensionless)

class abcmb.species.StandardFluid(first_idx, specs)

Bases: Fluid

Standard implementation of perturbation methods for fluid species.

Provides default computations for perturbation-related methods used in this code.

Methods:

• rho_delta :

  Compute standard density perturbation (units: eV cm^{-3})

• rho_plus_P_theta :

  Compute standard velocity perturbation (units: eV cm^{-3} Mpc^{-1})

• rho_plus_P_sigma :

  Compute standard shear perturbation (units: eV cm^{-3})

get_delta(lna, y, args)

Getter method for density perturbation from perturbation equations vector

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Dimensionless density perturbation (units: None)

get_sigma(lna, y, args)

Getter method for shear perturbation from perturbation equations vector

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Dimensionless shear perturbation (units: None)

get_theta(lna, y, args)

Getter method for velocity divergence perturbation from perturbation equations vector

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Velocity divergence perturbation (units: 1/Mpc)

rho_delta(lna, y, args)

Compute energy density perturbation, contribution to metric perturbation evolution.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Energy density perturbation (units: eV cm^{-3})

rho_plus_P_sigma(lna, y, args)

Compute shear stress perturbation, needed for CMB

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Shear stress perturbation (units: eV cm^{-3})

rho_plus_P_theta(lna, y, args)

Compute velocity perturbation times the sum of energy density and pressure. {0, i} component of the perturbed stress energy tensor.

Parameters:

• lna float

  Logarithm of scale factor

• y array

  Perturbation mode values

• args dict

  Cosmological parameters (params)

Returns:

float

Velocity perturbation (units: eV cm^{-3} Mpc^{-1})