nbodykit.cosmology.background

Classes

PerturbationGrowth(cosmo[, a]) Perturbation Growth coefficients at several orders.
class nbodykit.cosmology.background.PerturbationGrowth(cosmo, a=None)[source]

Perturbation Growth coefficients at several orders.

2-LPT is implemented. This implements the single fluid model of Boltamann equations. Therefore it is accurate only in a matter dominated universe. When background includes the radation contribution, the first order result is tuned to agree at sub-percent level comparing to a true multi-fluid boltzmann code under Planck15 cosmology.

All derivatives are against lna.

Note

Formulas are derived from Yin Li’s notes on 2LPT.

Parameters:
  • cosmo (Cosmology) – a astropy Cosmology like object.
  • a (array_like) – a list of time steps where the factors are exact. other a values are interpolated.

Methods

D1(a[, order]) Linear order growth function.
D2(a[, order]) Second order growth function.
E(a[, order]) Hubble function and derivatives against log a.
Gf(a) FastPM growth factor function, eq, 20
Gp(a) FastPM growth factor function, eq, 19
Hfac(a)
Om(a)
f1(a) Linear order growth rate
f2(a) Second order growth rate.
gf(a) Similarly, the derivative is against ln a, so
gp(a) Notice the derivative of D1 is against ln a but gp is d D1 / da, so
ode(y, lna)
D1(a, order=0)[source]

Linear order growth function.

Parameters:
  • a (float, array_like) – scaling factor
  • order (int) – order of differentation; 1 for first derivative against log a.
Returns:

array_like
Return type:

linear order growth function.
D2(a, order=0)[source]

Second order growth function.

Parameters:
  • a (float, array_like) – scaling factor
  • order (int) – order of differentation; 1 for first derivative against log a.
Returns:

array_like
Return type:

second order growth function.
E(a, order=0)[source]

Hubble function and derivatives against log a.

Gf(a)[source]

FastPM growth factor function, eq, 20

Gp(a)[source]

FastPM growth factor function, eq, 19

f1(a)[source]

Linear order growth rate

Parameters:
  • a (float, array_like) – scaling factor
  • order (int) – order of differentation; 1 for first derivative against log a.
Returns:

array_like
Return type:

linear order growth rate.
f2(a)[source]

Second order growth rate.

Parameters:
  • a (float, array_like) – scaling factor
  • order (int) – order of differentation; 1 for first derivative against log a.
Returns:

array_like
Return type:

second order growth rate.
gf(a)[source]

Similarly, the derivative is against ln a, so gf = Gf(a, order=1) / a

gp(a)[source]

Notice the derivative of D1 is against ln a but gp is d D1 / da, so gp = D1(a, order=1) / a