Nonlinear Power Spectrum

Class providing non-linear matter power spectra \(P_\mathrm{NL}(k,t)\)—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 \(k \gtrsim 0.1\) Mpc\(^{-1}\). 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 \(k=\)wavenumber [Mpc\(^{-1}\)] at cosmic time \(t=\)time [Gyr].

  • double precision, intent(in ) :: wavenumber, time

powerSpectrumNonlinearCosmicEmu

Provides a nonlinear power spectrum class in which the power spectrum is computed using the code of Moran et al. (2023). The CosmicEmu code will be downloaded, compiled and run as necessary if this option is utilized.

(Default implementation)

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 \(B_0\) in the linear excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2\); corresponds to the spherical collapse threshold \(\delta_\mathrm{c} \approx 1.686\) in the simplest case.

  • [coefficientLinear] (default 0.0d0) — The linear (first-order in \(\sigma^2\)) coefficient \(B_1\) in the excursion-set barrier \(B(\sigma^2) = B_0 + B_1\,\sigma^2\); a non-zero value produces a moving barrier that mimics ellipsoidal collapse corrections to the halo mass function.

powerSpectrumNonlinearPeacockDodds1996

Provides a nonlinear power spectrum class in which the power spectrum is computed using the algorithm of Peacock and Dodds (1996).

powerSpectrumNonlinearSmith2003

Provides a nonlinear matter power spectrum computed using the halofit algorithm of Smith et al. (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.

  • [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.