Cosmological Model

EMRI event-rate cosmological model and H₀ evaluation orchestration.

This module contains two conceptual layers:

1. Cosmological model — Model1CrossCheck samples EMRI events from a cosmological rate model; LamCDMScenario and DarkEnergyScenario define the parameter spaces.

2. Pipeline B (production) — BayesianStatistics loads saved Cramér-Rao bounds and orchestrates the full Hubble-constant posterior evaluation using the real GLADE galaxy catalog, KDE-based DetectionProbability, full Fisher-matrix covariance, and multiprocessing. Invoked via main.py:evaluate() / --evaluate CLI flag. Extracted to master_thesis_code.bayesian_inference.bayesian_statistics and master_thesis_code.bayesian_inference.detection_probability. Re-exported here for backward compatibility.

A simpler, self-contained cross-check pipeline exists as Pipeline A (BayesianInference), which uses a synthetic galaxy catalog, erf-based detection probability, and a hardcoded 10 % σ(d_L). See bayesian_inference/bayesian_inference.py.

class master_thesis_code.cosmological_model.CosmologicalParameter(symbol: str, unit: str, lower_limit: float, upper_limit: float, value: float = 0.0, derivative_epsilon: float = 1e-06, is_fixed: bool = False, randomize_by_distribution: collections.abc.Callable[[float, float, numpy.random._generator.Generator], float] = <function uniform at 0x7fb42a5c8fe0>, fiducial_value: float = 1.0)

Bases: Parameter

Parameters:

• symbol (str)

• unit (str)

• lower_limit (float)

• upper_limit (float)

• value (float)

• derivative_epsilon (float)

• is_fixed (bool)

• randomize_by_distribution (Callable[[float, float, Generator], float])

• fiducial_value (float)

fiducial_value: float = 1.0

class master_thesis_code.cosmological_model.DarkEnergyScenario

Bases: object

Omega_DE: float = 0.75

Omega_m: float = 0.25

de_equation(z)

Parameters:

z (float)

Return type:

float

h: float = 0.73

w_0: CosmologicalParameter

w_a: CosmologicalParameter

class master_thesis_code.cosmological_model.LamCDMScenario

Bases: object

https://arxiv.org/pdf/2102.01708.pdf

Omega_m: CosmologicalParameter

h: CosmologicalParameter

w_0: float = -1.0

w_a: float = 0.0

master_thesis_code.cosmological_model.MBH_spin_distribution(lower_limit, upper_limit)

https://iopscience.iop.org/article/10.1088/0004-637X/762/2/68/pdf

Parameters:

• lower_limit (float)

• upper_limit (float)

Return type:

float

class master_thesis_code.cosmological_model.Model1CrossCheck(rng=None)

Bases: object

cross check of Model M1 in PHYSICAL REVIEW D 95, 103012 (2017)

Parameters:

rng (Generator | None)

static R_emri(M)

Parameters:

M (float)

Return type:

float

static dN_dz_of_mass(mass, redshift)

Parameters:

• mass (float)

• redshift (float)

Return type:

float

emri_distribution(M, redshift)

Parameters:

• M (float)

• redshift (float)

Return type:

float

emri_rate: int = 294

parameter_space: ParameterSpace

sample_emri_events(number_of_samples)

Parameters:

number_of_samples (int)

Return type:

list[ParameterSample]

setup_emri_events_sampler()

Return type:

None

setup_simplified_event_sampler()

Return type:

None

simplified_event_mass_dependency(mass)

Parameters:

mass (float)

Return type:

float

snr_threshold: int = 15

master_thesis_code.cosmological_model.gaussian(x, mu, sigma, a)

Parameters:

• x (float | ndarray[tuple[Any, ...], dtype[float64]])

• mu (float)

• sigma (float)

• a (float)

Return type:

float | ndarray[tuple[Any, …], dtype[float64]]

master_thesis_code.cosmological_model.polynomial(x, a, b, c, d, e, f, g, h, i)

Parameters:

• x (float | ndarray[tuple[Any, ...], dtype[float64]])

• a (float)

• b (float)

• c (float)

• d (float)

• e (float)

• f (float)

• g (float)

• h (float)

• i (float)

Return type:

float