def rates(self):
forward_integral = numpy.vectorize(lambda p0: p0**2 / (2 * numpy.pi)**3
* self.integrate(p0, self.F_A)[0])
backward_integral = numpy.vectorize(lambda p0: p0**2 / (2 * numpy.pi)**3
* self.integrate(p0, self.F_B)[0])
grid = self.particle.grid
forward_rate, _ = integrators.integrate_1D(forward_integral,
(grid.MIN_MOMENTUM, grid.MAX_MOMENTUM))
backward_rate, _ = integrators.integrate_1D(backward_integral,
(grid.MIN_MOMENTUM, grid.MAX_MOMENTUM))
return -forward_rate, backward_rate
def pressure(particle):
""" \begin{equation}
P = \int dp I_P
\end{equation}
"""
pressure, _ = integrators.integrate_1D(
lambda p: pressure_integrand(p, particle), (0, 20 * particle.T))
return pressure
def energy_density(particle):
""" \begin{equation}
\rho = \int dp I_\rho
\end{equation}
"""
energy_density, _ = integrators.integrate_1D(
lambda p: energy_density_integrand(p, particle), (0, 20 * particle.T))
return energy_density
def pressure(particle):
""" \begin{equation}
P = \int dp I_P
\end{equation}
"""
pressure, _ = integrators.integrate_1D(
lambda p: pressure_integrand(p, particle),
(0, 20 * particle.T)
)
return pressure
def energy_density(particle):
""" \begin{equation}
\rho = \int dp I_\rho
\end{equation}
"""
energy_density, _ = integrators.integrate_1D(
lambda p: energy_density_integrand(p, particle),
(0, 20 * particle.T)
)
return energy_density
def density(particle):
""" ## Particle density
\begin{equation}
g \int \frac{p^2 dp}{2 \pi^2} f\left( \frac{p}{T} \right)
\end{equation}
"""
density, _ = integrators.integrate_1D(
lambda p: (particle.equilibrium_distribution_function(
particle.energy(p) / particle.T) * p**2 * particle.dof / 2. / numpy
.pi**2), (0, 20 * particle.T))
return density
def density(particle):
""" ## Particle density
\begin{equation}
g \int \frac{p^2 dp}{2 \pi^2} f\left( \frac{p}{T} \right)
\end{equation}
"""
density, _ = integrators.integrate_1D(
lambda p: (
particle.equilibrium_distribution_function(particle.energy(p) / particle.T)
* p**2 * particle.dof / 2. / numpy.pi**2
), (0, 20 * particle.T)
)
return density
def integrate(self, p0, fau=None, bounds=None):
if p0 == 0:
return self.rest_integral(fau)
if bounds is None:
bounds = (self.grids[0].MIN_MOMENTUM, self.grids[0].MAX_MOMENTUM)
def prepared_integrand(p1):
return self.integrand(p0, p1, fau)
integral, error = integrators.integrate_1D(prepared_integrand,
bounds=bounds)
constant = self.particle.params.a / 16. / math.pi
return constant * integral
def baryonic_rates(_a):
global a
a = _a
grid = particles.neutrino.grid
data = []
for integrand, bounds in [(_rate1, (grid.MIN_MOMENTUM, grid.MAX_MOMENTUM)),
(_rate2, (grid.MIN_MOMENTUM, grid.MAX_MOMENTUM)),
(_rate3, (grid.MIN_MOMENTUM, (q - m_e) * a)),
(_rate4, (grid.MIN_MOMENTUM, (q - m_e) * a)),
(_rate5, ((q + m_e) * a, grid.MAX_MOMENTUM)),
(_rate6, ((q + m_e) * a, grid.MAX_MOMENTUM))]:
if bounds[0] < bounds[1]:
data.append(CONST.rate_normalization /
particles.neutrino.params.a**5 *
integrate_1D(integrand, bounds=bounds)[0])
else:
data.append(0.)
return data
def Int(particle, y_power=2):
if environment.get('LAGUERRE_GAUSS_FOR_MASSIVE_EQUILIBRIUM_PARTICLES'):
aT = particle.params.aT
mat = particle.conformal_mass / aT
laguerre = (
particle.dof / 2. / numpy.pi**2 * aT**(y_power + 1) *
numpy.exp(-mat) * gauss_laguerre.integrate_1D(lambda eps: (
(eps + mat) * (eps * (eps + 2. * mat))**((y_power - 1.) / 2.) /
(numpy.exp(-eps - mat) + particle.eta)**2))[0])
return laguerre
else:
legendre = particle.dof / 2. / numpy.pi**2 * integrators.integrate_1D(
lambda y:
(y**y_power * numpy.exp(
particle.conformal_energy(y) / particle.params.aT) /
(numpy.exp(particle.conformal_energy(y) / particle.params.aT) +
particle.eta)**2),
(particle.grid.MIN_MOMENTUM, particle.grid.MAX_MOMENTUM))[0]
return legendre
def baryonic_rates(_a):
global a
a = _a
grid = particles.neutrino.grid
data = []
for integrand, bounds in [
(_rate1, (grid.MIN_MOMENTUM, grid.MAX_MOMENTUM)),
(_rate2, (grid.MIN_MOMENTUM, grid.MAX_MOMENTUM)),
(_rate3, (grid.MIN_MOMENTUM, (q - m_e)*a)),
(_rate4, (grid.MIN_MOMENTUM, (q - m_e)*a)),
(_rate5, ((q + m_e)*a, grid.MAX_MOMENTUM)),
(_rate6, ((q + m_e)*a, grid.MAX_MOMENTUM))]:
if bounds[0] < bounds[1]:
data.append(CONST.rate_normalization / a**5
* integrate_1D(integrand, bounds=bounds)[0])
else:
data.append(0.)
return data
def Int(particle, y_power=2):
if environment.get('LAGUERRE_GAUSS_FOR_MASSIVE_EQUILIBRIUM_PARTICLES'):
aT = particle.params.aT
mat = particle.conformal_mass / aT
laguerre = (
particle.dof / 2. / numpy.pi**2 * aT**(y_power + 1) * numpy.exp(-mat)
* gauss_laguerre.integrate_1D(lambda eps: (
(eps + mat) * (eps * (eps + 2. * mat))**((y_power - 1.) / 2.)
/ (numpy.exp(-eps - mat) + particle.eta)**2
))[0]
)
return laguerre
else:
legendre = particle.dof / 2. / numpy.pi**2 * integrators.integrate_1D(
lambda y: (
y**y_power * numpy.exp(particle.conformal_energy(y) / particle.params.aT)
/ (numpy.exp(particle.conformal_energy(y) / particle.params.aT) + particle.eta)**2
),
(particle.grid.MIN_MOMENTUM, particle.grid.MAX_MOMENTUM)
)[0]
return legendre