CMB constraints

Overview

The Theory class contains functions for computing CMB limits and \(f_{\mathrm{eff}}\) for dark matter models. Other useful constants and functions are also available.

Computing CMB limits

Theory.cmb_limit(x_kd=0.0001, p_ann=3.5e-31)

Computes the CMB limit on <sigma v>.

This is derived by requiring that

\[f_{\mathrm{eff}} \langle \sigma v \rangle / m_{\chi} < p_{\mathrm{ann}},\]

where \(f_{\mathrm{eff}}\) is the efficiency with which dark matter annihilations around recombination inject energy into the plasma and \(p_{\mathrm{ann}}\) is derived from CMB observations.

Parameters:

• x_kd (float) – T_kd / m_x, where T_kd is the dark matter’s kinetic decoupling temperature. This will be computed self-consistently in future versions of hazma.
• p_ann (float) – Constraint on energy release per DM annihilation in cm^3 s^-1 MeV^-1.

Returns:

<sigma v> – Upper bound on <sigma v>, in cm^3 s^-1.

Return type:

float

Functions and constants

Theory.f_eff(x_kd=0.0001)

Computes \(f_{\mathrm{eff}}\) the efficiency with which dark matter annihilations around recombination inject energy into the thermal plasma.

hazma.cmb.p_ann_planck_temp_pol = 3.5e-31

Planck 2018 95% upper limit on p_ann from temperature + polarization measurements, in cm^3 s^-1 MeV^-1

hazma.cmb.p_ann_planck_temp_pol_lensing = 3.3e-31

Planck 2018 95% upper limit on p_ann from temperature + polarization + lensing measurements, in cm^3 s^-1 MeV^-1

hazma.cmb.p_ann_planck_temp_pol_lensing_bao = 3.2e-31

Planck 2018 95% upper limit on p_ann from temperature + polarization + lensing + BAO measurements, in cm^3 s^-1 MeV^-1

hazma.cmb.vx_cmb(mx, x_kd)

Computes the DM relative velocity at CMB using eq. 28 from this reference.

Parameters:

• mx (float) – Dark matter mass in MeV.
• x_kd (float) – T_kd / m_x, where T_kd is the dark matter’s kinetic decoupling temperature.

Returns:

v_x – The DM relative velocity at the time of CMB formation.

Return type:

float