21.2 Using the Cosmology unit

To include cosmological expansion in your FLASH executable, include the line

REQUESTS physics/Cosmology/

in your setup's Config file. At present the Cosmology unit in FLASH4 is built around the MatterLambdaKernel. This kernel assumes the contribution of radiation to be negligible in comparison with those of matter and the cosmological constant.

The runtime parameters available with the Cosmology unit are described in Table 21.1. Note that the total effective mass density is not explicitly specified but is inferred from the sum of the OmegaMatter, OmegaRadiation, and CosmologicalConstant parameters. The MaxScaleChange parameter sets the maximum allowed fractional change in the scale factor $a$ during a single timestep. This behavior is enforced by the Cosmology_computeDt routine. The default value is set to the system's HUGE value for a double precision real floating point value to avoid interfering with non-cosmological simulations.

Table 21.1: Runtime parameters used with the Cosmology unit.

Parameter	Type	Default	Description
useCosmology	BOOLEAN	.true.	True if cosmology is to be used in this simulation
OmegaMatter	REAL	0.3	Ratio of total mass density to critical density at the present epoch ($\Omega_m$)
OmegaBaryon	REAL	0.05	Ratio of baryonic (gas) mass density to critical density at the present epoch; must be $\le$ OmegaMatter ($\Omega_b$)
CosmologicalConstant	REAL	0.7	Ratio of the mass density equivalent in the cosmological constant to the critical density at the present epoch ( $\Omega_\Lambda$)
OmegaRadiation	REAL	$5\times 10^{-5}$	Ratio of the mass density equivalent in radiation to the critical density at the present epoch ($\Omega_r$)
HubbleConstant	REAL	$2.1065\times 10^{-18}$	Value of the Hubble constant $H_0$ in sec$^{-1}$
MaxScaleChange	REAL	HUGE(1.)	Maximum permitted fractional change in the scale factor during each timestep

The MatterLambdaKernel supplies a number of functions and routines that are helpful in initializing, performing, and analyzing cosmological simulations. They should be accessed through the wrapper functions shown below.

• Cosmology_cdmPowerSpectrum
  Return the present-day cold dark matter power spectrum as a function of a given wavenumber. The MatterLambdaKernel provides a fit to this power spectrum from Bardeen et al. (1986), which assumes baryons do not make a significant contribution to the mass density. Other fits are available; see e.g., Hu and Sugiyama (1996) or Bunn and White (1997).
• Cosmology_computeVariance
  Given an array of comoving length scales and a processed power spectrum, compute the linear variance $(\delta M/M)^2$ at the present epoch. A top-hat filter is applied in Fourier-space as a smoothing kernel.
• Cosmology_computeDeltaCrit
  This subroutine computes the linear overdensity at turnaround in the spherical collapse model. For more information, see the appendix of Lacey and Cole (1993).
• Cosmology_redshiftToTime
  Compute the age of the Universe corresponding to a cosmological redshift .
• Cosmology_massToLength
  Given a mass scale, return the corresponding comoving diameter of a sphere containing the given amount of mass.