Cosmology Functions

A class that provides various cosmological functions. The background cosmology describes the evolution of an isotropic, homogeneous Universe within which our calculations are carried out. For the purposes of Galacticus, the background cosmology is used to relate expansion factor/redshift to cosmic time and to compute the density of various components (e.g. dark matter, dark energy, etc.) at different epochs.

Default implementation: cosmologyFunctionsMatterLambda

Methods

epochValidate → void

Check the given cosmic epoch is valid (aborting otherwise) and, optionally, return time or expansion factor associated with the epoch.

• double precision, intent(in ), optional :: timeIn

• double precision, intent(in ), optional :: expansionFactorIn

• logical , intent(in ), optional :: collapsingIn

• double precision, intent( out), optional :: timeOut

• double precision, intent( out), optional :: expansionFactorOut

• logical , intent( out), optional :: collapsingOut

cosmicTime → double precision

Return the cosmological age (in Gyr) of the universe at the given expansion factor \(a\), computed by integrating the Friedmann equation from \(a=0\) to the specified value.

• double precision, intent(in ) :: expansionFactor

• logical , intent(in ), optional :: collapsingPhase

timeBigCrunch → double precision

Return the cosmological age at Big Crunch (or a negative value if no Big Crunch occurs).

expansionFactor → double precision

Returns the expansion factor at cosmological time time.

• double precision, intent(in ) :: time

expansionRate → double precision

Returns the cosmological expansion rate, \(\dot{a}/a\) at expansion factor expansionFactor.

• double precision, intent(in ) :: expansionFactor

hubbleParameterEpochal → double precision

Returns the Hubble parameter at the requested cosmological time, time, or expansion factor, expansionFactor.

• double precision, intent(in ), optional :: time,expansionFactor

• logical , intent(in ), optional :: collapsingPhase

hubbleParameterRateOfChange → double precision

Returns the rate of change of the Hubble parameter at the requested cosmological time, time, or expansion factor, expansionFactor.

• double precision, intent(in ), optional :: time,expansionFactor

• logical , intent(in ), optional :: collapsingPhase

densityScalingEarlyTime → void

Compute the scaling of density with expansion factor at early times in the universe.

• double precision, intent(in ) :: dominateFactor

• double precision, intent( out) :: densityPower , expansionFactorDominant

• double precision, intent( out), optional :: OmegaDominant

omegaMatterEpochal → double precision

Return the matter density parameter at expansion factor expansionFactor.

• double precision, intent(in ), optional :: time , expansionFactor

• logical , intent(in ), optional :: collapsingPhase

omegaMatterRateOfChange → double precision

Return the rate of change of the matter density parameter at expansion factor expansionFactor.

• double precision, intent(in ), optional :: time , expansionFactor

• logical , intent(in ), optional :: collapsingPhase

omegaDarkEnergyEpochal → double precision

Return the dark energy density parameter at expansion factor expansionFactor.

• double precision, intent(in ), optional :: time , expansionFactor

• logical , intent(in ), optional :: collapsingPhase

equationOfStateDarkEnergy → double precision

Return the equation of state parameter, \(w\), for the dark energy component.

• double precision, intent(in ), optional :: time, expansionFactor

exponentDarkEnergy → double precision

Return the exponent of the dark energy density with expansion factor, i.e. \(\gamma\) in \(\rho_\mathrm{DE}(a) \propto a^\gamma\).

• double precision, intent(in ), optional :: time, expansionFactor

equalityEpochMatterDarkEnergy → double precision

Return the epoch of matter-dark energy magnitude equality (either expansion factor or cosmic time).

• integer, intent(in ), optional :: requestType

equalityEpochMatterCurvature → double precision

Return the epoch of matter-curvature magnitude equality (either expansion factor or cosmic time).

• integer, intent(in ), optional :: requestType

equalityEpochMatterRadiation → double precision

Return the epoch of matter-radiation magnitude equality (either expansion factor or cosmic time).

• integer, intent(in ), optional :: requestType

dominationEpochMatter → double precision

Compute the epoch at which matter dominates over other forms of energy by a given factor.

• double precision, intent(in ) :: dominateFactor

temperatureCMBEpochal → double precision

Return the temperature of the cosmic microwave background at expansionFactor.

• double precision, intent(in ), optional :: time , expansionFactor

• logical , intent(in ), optional :: collapsingPhase

distanceParticleHorizonComoving → double precision

Return the comoving distance to the particle horizon at the given time.

• double precision, intent(in ) :: time

distanceComoving → double precision

Return the comoving distance to the given cosmic time.

• double precision, intent(in ) :: time

distanceLuminosity → double precision

Return the luminosity distance to the given cosmic time.

• double precision, intent(in ) :: time

distanceAngular → double precision

Return the angular diameter distance to the given cosmic time.

• double precision, intent(in ) :: time

• double precision, intent(in ), optional :: timeOrigin

timeAtDistanceComoving → double precision

Return the cosmic time corresponding to the given comovingDistance.

• double precision, intent(in ) :: comovingDistance

distanceComovingConvert → double precision

Convert between different measures of comoving distance (luminosity distance, distance modulus, or k-corrected distance modulus) given an input distance or redshift, returning the requested output distance measure.

• integer , intent(in ) :: output

• double precision, intent(in ), optional :: distanceLuminosity, distanceModulus, distanceModulusKCorrected, redshift

redshiftFromExpansionFactor → double precision

Returns the cosmological redshift, typically \(z = 1/a - 1\), corresponding to the given expansion factor \(a\), where \(a=1\) corresponds to the present day (\(z=0\)).

• double precision, intent(in ) :: expansionFactor

expansionFactorFromRedshift → double precision

Returns the cosmological expansion factor, typically \(a = 1/(1+z)\), corresponding to the given redshift \(z\), where \(a=1\) at the present day and \(a\rightarrow 0\) at the Big Bang.

• double precision, intent(in ) :: redshift

comovingVolumeElementRedshift → double precision

Returns the differential comoving volume element \(\mathrm{d}V/\mathrm{d}z = r_\mathrm{c}^2(t) \mathrm{c} H^{-1}(t)\) (where \(r_\mathrm{c}\) is the comoving distance to time \(t\) and \(H(t)\) is the Hubble parameter at that time) for unit solid angle at the specified time.

• double precision, intent(in ) :: time

comovingVolumeElementTime → double precision

Returns the differential comoving volume element \(\mathrm{d}V/\mathrm{d}t = r_\mathrm{c}^2(t) \mathrm{c} a(t)\) (where \(r_\mathrm{c}\) is the comoving distance to time \(t\) and \(a(t)\) is the expansion at that time) for unit solid angle at the specified time.

• double precision, intent(in ) :: time

epochTime → double precision

Convenience function that returns the time corresponding to an epoch specified by time or expansion factor.

• double precision, intent(in ), optional :: time , expansionFactor

• logical , intent(in ), optional :: collapsingPhase

matterDensityEpochal → double precision

Convenience function that returns the matter density at the specified epoch.

• double precision, intent(in ), optional :: time , expansionFactor

• logical , intent(in ), optional :: collapsingPhase

cosmologyFunctionsMatterDarkEnergy

Cosmological relations are computed assuming a universe that contains only collisionless matter and dark energy with an equation of state \(w(a)=w_0+w_1a(1-a)\) (Jassal et al., 2005), with \(w_0=\)[darkEnergyEquationOfStateW0], and \(w_1=\)[darkEnergyEquationOfStateW1].

Methods

• targetSelf — Set a module-scope pointer to self.

• exponentDarkEnergyDerivative — Return the derivative of the dark energy exponent with respect to expansion factor.

Parameters

• [darkEnergyEquationOfStateW0] (default -1.0d0) — The equation of state parameter for dark energy, \(w_0\), defined such that \(P=\rho^w\) with \(w(a)=w_0+w_1 a (1-a)\).

• [darkEnergyEquationOfStateW1] (default 0.0d0) — The equation of state parameter for dark energy, \(w_1\), defined such that \(P=\rho^w\) with \(w(a)=w_0+w_1 a (1-a)\).

cosmologyFunctionsMatterLambda

Cosmological relations are computed assuming a universe that contains only collisionless matter and a cosmological constant.

(Default implementation)

Methods

• distanceTabulate — Tabulate comoving distance as a function of cosmic time.

• expansionFactorTabulate — Tabulate expansion factor as a function of cosmic time.

cosmologyFunctionsStaticUniverse

A cosmology functions class for static universes. Intended for testing purposes. Time is arbitrary (as there is no Big Bang), and expansion factor is fixed at \(1\). Attempts to compute time from expansion factor will cause fatal errors. Expansion rates and the Hubble constant are set to zero.