API¶

The power spectrum classes are:

`HaloZeldovichP00`(cosmo, z)	The dark matter auto-spectrum P00 using Halo-Zel’dovich Perturbation Theory
`HaloZeldovichP01`(cosmo, z)	The dark matter density - radial momentum cross correlation P01 using HZPT
`HaloZeldovichP11`(cosmo, z)	The mu4 contribution to the radial momentum auto spectrum P11, using HZPT
`HaloZeldovichPhm`(cosmo, z)	The halo-matter cross-correlation Phm, using HZPT

Each of these objects provides three main functions to compute the various HZPT terms:

`__call__`(k)	Return the total power at the specified k
`zeldovich`(k)	Return the Zel’dovich power term at the specified k
`broadband`(k)	The broadband power in units of \((\mathrm{Mpc}/h)^3\)

The correlation function classes are:

`HaloZeldovichCF00`(cosmo, z)	The dark matter correlation function using Halo-Zel’dovich Perturbation Theory
`HaloZeldovichCFhm`(cosmo, z)	The dark matter - halo correlation function using Halo-Zel’dovich Perturbation Theory

Similary, the three main functions to compute the various HZPT terms are:

`__call__`(r)	Return the total correlation function
`zeldovich`(r)	Return the Zel’dovich correlation at the specified r
`broadband`(r)	The correlation function broadband correction term

HZPT Classes¶

class pyRSD.rsd.hzpt.HaloZeldovichP00(cosmo, z)¶

The dark matter auto-spectrum P00 using Halo-Zel’dovich Perturbation Theory

__call__(k)¶

Return the total power at the specified k

The total power is equal to the Zel’dovich power + broadband term

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

__init__(cosmo, z)¶

Parameters:

cosmo : cosmology.Cosmology, pygcl.Cosmology

the cosmology instance

z : float

the redshift; this determines the values of sigma8(z) to use in the HZPT equations

broadband(k)¶

The broadband power in units of \((\mathrm{Mpc}/h)^3\)

The functional form is given by:

\[P_\mathrm{BB} = A_0 F(k) \left[ \frac{1 + (k R_1)^2}{1 + (k R_{1h})^2 + (k R_{2h})^4} \right],\]

as given by Eq. 1 in arXiv:1501.07512.

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

zeldovich(k)¶

Return the Zel’dovich power term at the specified k

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

class pyRSD.rsd.hzpt.HaloZeldovichP01(cosmo, z)¶

The dark matter density - radial momentum cross correlation P01 using HZPT

__call__(k)¶: Return the full Halo Zeldovich P01

__init__(cosmo, z)¶

Parameters:

cosmo : cosmology.Cosmology, pygcl.Cosmology

the cosmology instance

z : float

the redshift; this determines the values of sigma8(z) to use in the HZPT equations

broadband(k)¶

The broadband power correction for P01 in units of (Mpc/h)^3

This is the derivative of the broadband band term for P00, taken with respect to lna

zeldovich(k)¶

Return the Zel’dovich power term at the specified k

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

class pyRSD.rsd.hzpt.HaloZeldovichP11(cosmo, z)¶

The mu4 contribution to the radial momentum auto spectrum P11, using HZPT

Notes

The 1-loop SPT model for the vector contribution to P11[mu4] should be added to the power returned by this class to model the full P11[mu4]

__call__(k)¶: Return the total power

__init__(cosmo, z)¶

Parameters:

cosmo : cosmology.Cosmology, pygcl.Cosmology

the cosmology instance

z : float

the redshift; this determines the values of sigma8(z) to use in the HZPT equations

broadband(k)¶

The broadband power correction in units of (Mpc/h)^3

Modeled with a Pade function,

\[P_{BB} = F(k) A_0 / (1 + (k R_{1h})^2)\]

zeldovich(k)¶

Return the Zel’dovich power term at the specified k

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

class pyRSD.rsd.hzpt.HaloZeldovichPhm(cosmo, z)¶

The halo-matter cross-correlation Phm, using HZPT

__call__(b1, k)¶

Return the total power, equal to the b1 * Zeldovich power + broadband correction

Parameters:

b1 : float

the linear bias to compute the bias at

k : array_like

the wavenumbers in \(h/\mathrm{Mpc}\) to compute the power at

__init__(cosmo, z)¶

Parameters:

cosmo : cosmology.Cosmology, pygcl.Cosmology

the cosmology instance

z : float

the redshift; this determines the values of sigma8(z) to use in the HZPT equations

broadband(k)¶

The broadband power in units of \((\mathrm{Mpc}/h)^3\)

The functional form is given by:

\[P_\mathrm{BB} = A_0 F(k) \left[ \frac{1 + (k R_1)^2}{1 + (k R_{1h})^2 + (k R_{2h})^4} \right],\]

as given by Eq. 1 in arXiv:1501.07512.

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

zeldovich(k)¶

Return the Zel’dovich power term at the specified k

Parameters:

k : float, array_like

the wavenumber in units of \(h/\mathrm{Mpc}\)

class pyRSD.rsd.hzpt.HaloZeldovichCF00(cosmo, z)¶

The dark matter correlation function using Halo-Zel’dovich Perturbation Theory

__call__(r)¶: Return the total correlation function

__init__(cosmo, z)¶

Parameters:

cosmo : cosmology.Cosmology, pygcl.Cosmology

the cosmology instance

z : float

the redshift; this determines the values of sigma8(z) to use in the HZPT equations

broadband(r)¶

The correlation function broadband correction term

This is given by the Fourier transform of the Pade function

Parameters:

r : float, array_like

the separation array, in units of \(\mathrm{Mpc}/h\)

zeldovich(r)¶

Return the Zel’dovich correlation at the specified r

Parameters:

r : float, array_like

the separation array, in units of \(\mathrm{Mpc}/h\)

class pyRSD.rsd.hzpt.HaloZeldovichCFhm(cosmo, z)¶

The dark matter - halo correlation function using Halo-Zel’dovich Perturbation Theory

__call__(b1, r)¶

Return the total correlation

Parameters:

b1 : float

the linear bias to compute correlation at

r : array_like

the separations in \(\mathrm{Mpc}/h\) to correlation at

__init__(cosmo, z)¶

Parameters:

cosmo : cosmology.Cosmology, pygcl.Cosmology

the cosmology instance

z : float

the redshift; this determines the values of sigma8(z) to use in the HZPT equations

broadband(r)¶

The correlation function broadband correction term

This is given by the Fourier transform of the Pade function

zeldovich(r)¶: Return the Zel’dovich correlation at the specified r