cobi.simulation.CMB

class CMB(libdir, nside, model='iso', beta=None, mass=None, Acb=None, lensing=False, Acb_sim_config=None, verbose=True)

CMB map generator with cosmic birefringence support.

This class handles the generation of CMB temperature and polarization maps with optional cosmic birefringence rotation. Supports three birefringence models:

• iso: Isotropic (constant) rotation angle β

• iso_td: Time-dependent isotropic model with axion mass parameter

• aniso: Anisotropic (spatially-varying) rotation from patchy reionization

Parameters:

• libdir (str) – Directory for caching simulation products and power spectra.

• nside (int) – HEALPix resolution parameter (nside = 2^n).

• model ({'iso', 'iso_td', 'aniso'}, default 'iso') – Birefringence model type.

• beta (float, optional) – Isotropic rotation angle in degrees (required for model=’iso’).

• mass (float, optional) – Axion mass parameter in units of 10^-22 eV. Must be 1, 1.5, or 6.4 (required for model=’iso_td’).

• Acb (float, optional) – Amplitude of anisotropic birefringence power spectrum (required for model=’aniso’).

• lensing (bool, default False) – Whether to include CMB lensing effects.

• Acb_sim_config (dict, optional) – Configuration for anisotropic simulation batches with keys: - ‘alpha_vary_index’: [start, end] indices for varying α - ‘alpha_cons_index’: [start, end] indices for constant α - ‘null_alpha_index’: [start, end] indices for null test (α=0)

• verbose (bool, default True) – Enable logging output.

nside

HEALPix resolution.

Type:

int

lmax

Maximum multipole (3*nside - 1).

Type:

int

model

Birefringence model type.

Type:

str

beta

Isotropic rotation angle in degrees.

Type:

float or None

lensing

Whether lensing is enabled.

Type:

bool

cls

CMB power spectra (TT, EE, BB, TE).

Type:

dict

Examples

Generate isotropic birefringence simulation:

cmb = CMB(
    libdir='./cmb_sims',
    nside=512,
    model='iso',
    beta=0.35,
    lensing=True
)

# Get rotated CMB map
cmb_map = cmb.get_map(idx=0, apply_beta=True)

Generate anisotropic birefringence:

cmb = CMB(
    libdir='./cmb_sims',
    nside=512,
    model='aniso',
    Acb=1e-6,
    lensing=True
)

# Get map with spatially-varying rotation
cmb_map = cmb.get_map(idx=0, apply_beta=True)

Notes

• Uses CAMB for power spectrum generation

• Supports efficient caching of realizations

• MPI-aware for parallel simulation generation

• Lensing implemented via lenspyx

__init__(libdir, nside, model='iso', beta=None, mass=None, Acb=None, lensing=False, Acb_sim_config=None, verbose=True)

Parameters:

• libdir (str)

• nside (int)

• model (str)

• beta (float | None)

• mass (float | None)

• Acb (float | None)

• lensing (bool | None)

• Acb_sim_config (Dict[str, List[int]] | None)

• verbose (bool | None)

Methods

__init__(libdir, nside[, model, beta, mass, ...])
alpha_alm(idx)	Generate the alpha alm for the anisotropic model.
alpha_map(idx)	Generate a map of the rotation angle alpha for the anisotropic model.
cl_aa()	Compute the Cl_AA power spectrum for the anisotropic model.
cl_pp()
compute_powers()	compute the CMB power spectra using CAMB.
get_aniso_gauss_lensed_QU(idx)
get_aniso_model_cb_lensed_QU(idx)
get_aniso_real_lensed_QU(idx)
get_cb_lensed_QU(idx)
get_cb_lensed_mass_spectra([dl, dtype, new])
get_cb_lensed_spectra([beta, dl, dtype, new])	Calculate the cosmic birefringence (CB) lensed spectra with a given rotation angle beta.
get_cb_unlensed_mass_spectra([dl, dtype, new])
get_cb_unlensed_spectra([beta, dl, dtype, new])	Calculate the cosmic birefringence (CB) unlensed spectra with a given rotation angle beta.
get_iso_const_cb_gaussian_lensed_QU(idx)	Generate or retrieve the Q and U Stokes parameters after applying cosmic birefringence.
get_iso_const_cb_real_lensed_QU(idx)
get_iso_model_cb_gaussian_lensed_QU(idx)
get_iso_model_cb_lensed_QU(idx)
get_iso_model_cb_real_lensed_QU(idx)
get_iso_td_cb_gaussian_lensed_QU(idx)
get_iso_td_cb_real_lensed_QU(idx)
get_lensed_spectra([dl, dtype])	Retrieve the lensed scalar spectra from the power spectrum data.
get_power([dl])	Get the CMB power spectra.
get_unlensed_spectra([dl, dtype])	Retrieve the unlensed scalar spectra from the power spectrum data.
grad_phi_alm(idx)
phi_alm(idx)
scale_invariant(Acb)

__init__(libdir, nside, model='iso', beta=None, mass=None, Acb=None, lensing=False, Acb_sim_config=None, verbose=True)

Parameters:

• libdir (str)

• nside (int)

• model (str)

• beta (float | None)

• mass (float | None)

• Acb (float | None)

• lensing (bool | None)

• Acb_sim_config (Dict[str, List[int]] | None)

• verbose (bool | None)

scale_invariant(Acb)

__validate_Acb_sim_config__()

Validate the Acb_sim_config dictionary structure.

Return type:

None

__get_alpha_mode__(idx)

Determine which alpha mode to use for a given index.

Parameters: idx (int): The realization index.

Returns: str: One of ‘vary’, ‘constant’, or ‘null’

Parameters:

idx (int)

Return type:

str

__set_seeds__()

Sets the seeds for the simulation.

Return type:

None

__set_workspace__()

Set the workspace for the CMB simulations.

Return type:

None

__dl2cl__(arr, unit_only=False)

Convert Dl to Cl.

Parameters:

arr (numpy.ndarray)

Return type:

numpy.ndarray

__td_eb__(dl=True)

Read the E and B mode power spectra from the CMB power spectra data.

Return type:

numpy.ndarray

compute_powers()

compute the CMB power spectra using CAMB.

Return type:

Dict[str, Any]

get_power(dl=True)

Get the CMB power spectra.

Parameters: dl (bool): If True, return the power spectra with dl factor else without dl factor.

Returns: Dict[str, np.ndarray]: A dictionary containing the CMB power spectra.

Parameters:

dl (bool)

Return type:

Dict[str, numpy.ndarray]

get_unlensed_spectra(dl=True, dtype='d')

Retrieve the unlensed scalar spectra from the power spectrum data.

Parameters: dl (bool, optional): If True, returns Dl (C_l * l * (l + 1) / 2π). Defaults to True. dtype (str, optional): Specifies the format of the returned spectra.

• ‘d’ returns a dictionary with keys ‘tt’, ‘ee’, ‘bb’, ‘te’.

• ‘a’ returns the full array of power spectra.

Defaults to ‘d’.

Returns: Union[Dict[str, Any], np.ndarray]:

• A dictionary containing individual power spectra for ‘tt’, ‘ee’, ‘bb’, ‘te’ if dtype is ‘d’.

• The full array of unlensed scalar power spectra if dtype is ‘a’.

Raises: ValueError: If dtype is not ‘d’ or ‘a’.

Parameters:

• dl (bool)

• dtype (str)

Return type:

Dict[str, Any] | numpy.ndarray

get_lensed_spectra(dl=True, dtype='d')

Retrieve the lensed scalar spectra from the power spectrum data.

Parameters: dl (bool, optional): If True, returns Dl (C_l * l * (l + 1) / 2π). Defaults to True. dtype (str, optional): Specifies the format of the returned spectra.

• ‘d’ returns a dictionary with keys ‘tt’, ‘ee’, ‘bb’, ‘te’.

• ‘a’ returns the full array of power spectra.

Defaults to ‘d’.

Returns: Union[Dict[str, Any], np.ndarray]:

• A dictionary containing individual power spectra for ‘tt’, ‘ee’, ‘bb’, ‘te’ if dtype is ‘d’.

• The full array of lensed scalar power spectra if dtype is ‘a’.

Raises: ValueError: If dtype is not ‘d’ or ‘a’.

Parameters:

• dl (bool)

• dtype (str)

Return type:

Dict[str, Any] | numpy.ndarray

get_cb_unlensed_spectra(beta=0.0, dl=True, dtype='d', new=False)

Calculate the cosmic birefringence (CB) unlensed spectra with a given rotation angle beta.

Parameters: beta (float, optional): The rotation angle in degrees for the cosmic birefringence effect. Defaults to 0.3 degrees. dl (bool, optional): If True, returns Dl (C_l * l * (l + 1) / 2π). Defaults to True. dtype (str, optional): Specifies the format of the returned spectra.

• ‘d’ returns a dictionary with keys ‘tt’, ‘ee’, ‘bb’, ‘te’, ‘eb’, ‘tb’.

• ‘a’ returns an array of power spectra.

Defaults to ‘d’.

new (bool, optional): Determines the ordering of the spectra in the array if dtype is ‘a’.

If True, returns [TT, EE, BB, TE, EB, TB]. If False, returns [TT, TE, TB, EE, EB, BB]. Defaults to False.

Returns: Union[Dict[str, np.ndarray], np.ndarray]:

• A dictionary containing individual CB unlensed power spectra for ‘tt’, ‘ee’, ‘bb’, ‘te’, ‘eb’, ‘tb’ if dtype is ‘d’.

• An array of CB unlensed power spectra with ordering determined by the new parameter if dtype is ‘a’.

Raises: ValueError: If dtype is not ‘d’ or ‘a’.

Notes: The method applies a rotation by alpha degrees to the E and B mode spectra to account for cosmic birefringence.

Parameters:

• beta (float)

• dl (bool)

• dtype (str)

• new (bool)

Return type:

Dict[str, numpy.ndarray] | numpy.ndarray

get_cb_unlensed_mass_spectra(dl=True, dtype='d', new=False)

Parameters:

• dl (bool)

• dtype (str)

• new (bool)

Return type:

Dict[str, numpy.ndarray] | numpy.ndarray

get_cb_lensed_spectra(beta=0.0, dl=True, dtype='d', new=False)

Calculate the cosmic birefringence (CB) lensed spectra with a given rotation angle beta.

Parameters: beta (float, optional): The rotation angle in degrees for the cosmic birefringence effect. Defaults to 0.3 degrees. dl (bool, optional): If True, returns Dl (C_l * l * (l + 1) / 2π). Defaults to True. dtype (str, optional): Specifies the format of the returned spectra.

• ‘d’ returns a dictionary with keys ‘tt’, ‘ee’, ‘bb’, ‘te’, ‘eb’, ‘tb’.

• ‘a’ returns an array of power spectra.

Defaults to ‘d’.

new (bool, optional): Determines the ordering of the spectra in the array if dtype is ‘a’.

If True, returns [TT, EE, BB, TE, EB, TB]. If False, returns [TT, TE, TB, EE, EB, BB]. Defaults to False.

Returns: Union[Dict[str, np.ndarray], np.ndarray]:

• A dictionary containing individual CB lensed power spectra for ‘tt’, ‘ee’, ‘bb’, ‘te’, ‘eb’, ‘tb’ if dtype is ‘d’.

• An array of CB lensed power spectra with ordering determined by the new parameter if dtype is ‘a’.

Raises: ValueError: If dtype is not ‘d’ or ‘a’.

Notes: The method applies a rotation by alpha degrees to the E and B mode spectra to account for cosmic birefringence.

Parameters:

• beta (float)

• dl (bool)

• dtype (str)

• new (bool)

Return type:

Dict[str, numpy.ndarray] | numpy.ndarray

get_cb_lensed_mass_spectra(dl=True, dtype='d', new=False)

Parameters:

• dl (bool)

• dtype (str)

• new (bool)

Return type:

Dict[str, numpy.ndarray] | numpy.ndarray

cl_aa()

Compute the Cl_AA power spectrum for the anisotropic model.

cl_pp()

get_iso_const_cb_real_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_iso_td_cb_real_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_iso_model_cb_real_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_iso_const_cb_gaussian_lensed_QU(idx)

Generate or retrieve the Q and U Stokes parameters after applying cosmic birefringence.

Parameters: idx (int): Index for the realization of the CMB map.

Returns: List[np.ndarray]: A list containing the Q and U Stokes parameter maps as NumPy arrays.

Notes: The method applies a rotation to the E and B mode spherical harmonics to simulate the effect of cosmic birefringence. If the map for the given idx exists in the specified directory, it reads the map from the file. Otherwise, it generates the Q and U maps, applies the birefringence, and saves the resulting map to a FITS file.

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_iso_td_cb_gaussian_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_iso_model_cb_gaussian_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_iso_model_cb_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

alpha_alm(idx)

Generate the alpha alm for the anisotropic model.

Parameters: idx (int): Index for the realization of the CMB map.

Returns: np.ndarray: The alpha alm as a NumPy array.

Notes: The method generates the alpha alm for the anisotropic model. The alpha alm is generated as a random realization of the Cl_AA power spectrum. The behavior depends on Acb_sim_config: - ‘vary’: Each idx gets a unique seed (default) - ‘constant’: All indices in this range use the same fixed seed - ‘null’: Returns zeros (no rotation)

Parameters:

idx (int)

Return type:

numpy.ndarray

phi_alm(idx)

Parameters:

idx (int)

Return type:

numpy.ndarray

grad_phi_alm(idx)

Parameters:

idx (int)

Return type:

numpy.ndarray

alpha_map(idx)

Generate a map of the rotation angle alpha for the anisotropic model.

Parameters: idx (int): Index for the realization of the CMB map.

Returns: np.ndarray: A map of the rotation angle alpha as a NumPy array.

Notes: The method generates a map of the rotation angle alpha for the anisotropic model. The map is generated as a random realization of the Cl_AA power spectrum.

Parameters:

idx (int)

Return type:

numpy.ndarray

get_aniso_real_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_aniso_gauss_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_aniso_model_cb_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]

get_cb_lensed_QU(idx)

Parameters:

idx (int)

Return type:

List[numpy.ndarray]