.. _physics-powerSpectrumNonlinear:

Nonlinear Power Spectrum
========================

Class providing non-linear matter power spectra :math:`P_\mathrm{NL}(k,t)`---the variance of the dark matter density field per unit logarithmic wavenumber interval, including the contributions from non-linear gravitational clustering that boost power on small scales beyond the linear prediction. Non-linear power spectra are essential for computing accurate two-point statistics, weak lensing observables, and halo model predictions at :math:`k \gtrsim 0.1` Mpc\ :math:`^{-1}`. Implementations include fitting formulae (e.g.\ halofit) and emulators trained on N-body simulations.

**Default implementation:** ``powerSpectrumNonlinearCosmicEmu``

Methods
-------

``value`` → ``double precision``
   Return the nonlinear power spectrum for :math:`k=`\ ``wavenumber`` [Mpc\ :math:`^{-1}`] at cosmic time :math:`t=`\ ``time`` [Gyr].

   * ``double precision, intent(in ) :: wavenumber, time``

.. _physics-powerSpectrumNonlinearCosmicEmu:

``powerSpectrumNonlinearCosmicEmu``
-----------------------------------

Provides a nonlinear power spectrum class in which the power spectrum is computed using the code of :cite:t:`moran_mira-titan_2023`. The CosmicEmu code will be downloaded, compiled and run as necessary if this option is utilized.

**(Default implementation)**

.. _physics-powerSpectrumNonlinearLinear:

``powerSpectrumNonlinearLinear``
--------------------------------

Provides a nonlinear power spectrum class in which the power spectrum equals the linear theory power spectrum. Intended primarily for testing purposes.

**Parameters**

* ``[coefficientConstant]`` (default ``1.67d0``) — The constant (zero-order) coefficient :math:`B_0` in the linear excursion-set barrier :math:`B(\sigma^2) = B_0 + B_1\,\sigma^2`; corresponds to the spherical collapse threshold :math:`\delta_\mathrm{c} \approx 1.686` in the simplest case.
* ``[coefficientLinear]`` (default ``0.0d0``) — The linear (first-order in :math:`\sigma^2`) coefficient :math:`B_1` in the excursion-set barrier :math:`B(\sigma^2) = B_0 + B_1\,\sigma^2`; a non-zero value produces a moving barrier that mimics ellipsoidal collapse corrections to the halo mass function.

.. _physics-powerSpectrumNonlinearPeacockDodds1996:

``powerSpectrumNonlinearPeacockDodds1996``
------------------------------------------

Provides a nonlinear power spectrum class in which the power spectrum is computed using the algorithm of :cite:t:`peacock_non-linear_1996`.

.. _physics-powerSpectrumNonlinearSmith2003:

``powerSpectrumNonlinearSmith2003``
-----------------------------------

Provides a nonlinear matter power spectrum computed using the halofit algorithm of :cite:t:`smith_stable_2003`, which models the transition from linear to nonlinear scales via contributions from quasi-linear modes and collapsed dark matter halos. Optional corrections from John Peacock's halofit web page can be included via ``[peacockCorrection]``.

**Methods**

* ``coefficients`` — Compute the fitting function coefficients at the given time.

**Parameters**

* ``[includePeacockCorrection]`` (default ``.true.``) — If true, include the correction proposed on John Peacock's `web page <https://www.roe.ac.uk/~jap/haloes/>`_.
* ``[includeQuasiLinearPower]`` (default ``.true.``) — If true, include quasi-linear contribution to the power spectrum.
* ``[includeHaloPower]`` (default ``.true.``) — If true, include halo contribution to the power spectrum.