Parameter Reference
Physical inputs
| Symbol | Code name | Unit | Description |
|---|---|---|---|
Nshells |
self.Nshells |
— | Number of shells |
g |
self.g |
— | Yukawa coupling constant |
m_phi |
self.m_phi |
eV | Mediator (scalar field) mass |
m_nu |
self.m_nu |
eV | Neutrino mass |
T_nu |
self.T_nu |
eV | Present-day neutrino temperature |
H0 |
self.H0 |
eV | Hubble constant |
r_phi |
self.r_phi |
eV⁻¹ | Yukawa range = 1/m_phi |
Dimensionless ratios
| Symbol | Code name | Definition | Description |
|---|---|---|---|
alpha |
self.alpha |
\(g^2 T_{\nu,0}^2 / m_\phi^2\) | Yukawa force strength |
beta |
self.beta |
\(T_{\nu, 0}^4 / (m_\phi^2 m_{\rm pl}^2)\) | Gravity force strength |
eta |
self.eta |
\(\beta/\alpha\) | Gravity-to-Yukawa ratio |
m0 |
self.m0 |
\(m_\nu / T_{\nu, 0}\) | Dimensionless bare neutrino mass |
m_phi_hat |
self.m_phi_hat |
\(m_\phi / H_0\) | Dimensionless mediator mass; sets scale factor evolution |
Scale factors & time
| Symbol | Code name | Definition | Description |
|---|---|---|---|
a |
self.a |
— | Current scale factor |
a_ini |
self.a_ini |
kappa * a_NR |
Initial scale factor |
a_NR |
— | 1 / m0 |
Scale factor at NR transition |
a_end |
self.a_end |
kappa2 / Rmin |
Final scale factor; Yukawa range shrinks below Rmin |
dt |
self.dt |
— | Current timestep (adaptive, Courant condition) |
dt_frac |
self.dt_frac |
— | Courant safety factor multiplying sqrt(soft/F) |
kappa |
— | — | Sets a_ini as fraction of a_NR (default 0.75) |
kappa2 |
— | — | Sets a_end as fraction of 1/Rmin (default 0.75) |
Grid & force
| Symbol | Code name | Unit | Description |
|---|---|---|---|
Rmin |
self.Rmin |
1/m_phi |
Inner radial boundary = 0.01 * lambda_phi(a_ini) |
Rmax |
self.Rmax |
1/m_phi |
Outer radial boundary = 50 * max(lambda_phi, lambda_FS) |
soft |
self.soft |
1/m_phi |
Softening length; used as reflecting boundary threshold |
lambda_phi |
— | 1/m_phi |
Yukawa range = 1/a at a given scale factor |
lambda_FS |
— | 1/m_phi |
Free-streaming scale; sets minimum resolved clustering scale |
Per-shell fields
| Symbol | Code name | Definition | Description |
|---|---|---|---|
R |
self.R |
1/m_phi |
Dimensionless radial position = r * m_phi |
q |
self.q |
— | Radial momentum = q_r / T_nu |
ell |
self.ell |
— | Angular momentum = r * q_perp / T_nu * H0 |
w |
self.w |
— | Phase-space weight (dimensionless) |
phi |
self.phi |
— | Scalar field = hat_phi / T_nu |
m |
self.m |
— | Effective mass = m0 + phi |
eps |
self.eps |
— | Energy = sqrt(q^2 + ell^2/R^2 + a^2 m^2) |
F_fs |
self.F_fs |
— | Free-streaming acceleration = ell^2 / (eps * R^3) |
F_lr |
self.F_lr |
— | Yukawa (long-range) acceleration |
F_g |
self.F_g |
— | Gravitational acceleration |
Initial condition parameters
| Symbol | Code name | Description |
|---|---|---|
ic_type |
self.ic_type |
Initial perturbation profile |
Psi0 |
— | Amplitude of initial perturbation |
R0 |
self.R0 |
Scale of initial perturbation (default: lambda_phi at a_ini) |
w_min |
— | Floor on shell weights after normalisation (default: 1e-3) |
Solver parameters
| Symbol | Code name | Description |
|---|---|---|
iter_m |
self.iter_m |
Method for solvePhi: 'anderson' or 'naive' |
iter_tol |
self.iter_tol |
Convergence tolerance for solvePhi |