Functions for mapping from one arbitrary cosmological parameter to another. This includes the provision of a generic interpolation function and another exact value lookup.
cosmapval(val=50, cosparam="CoVol", H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR, OmegaR=0,
w0=-1, wprime=0, Sigma8=0.8, fSigma8=FALSE, zrange=c(-0.99,100), res=100, iter=8,
out='cos', degen='lo', ref)
cosmapfunc(cosparamx="CoVol", cosparamy="z", H0=100, OmegaM=0.3, OmegaL=1-OmegaM-OmegaR,
OmegaR=0, w0=-1, wprime=0, Sigma8=0.8, fSigma8=FALSE, zrange=c(0,20), step='z', res=100,
degen='lo', ref)The value/s to be mapped from parameter cosparamx to parameter cosparamy (this can be a vector or a single number).
Cosmological parameter, must be one of: z, a, CoDist, LumDist, CoDistTran, DistMod, CoVol, UniAgeAtz, TravelTime (see cosdist help for further description of these) H, CoVel, OmegaM, OmegaL, OmegaK, Factor, Rate, RhoCrit (see cosgrow help for further description of these). Note that AngDist and AngSize are not an option for cosparam due to degenerate redshift solutions causing problems with the approxfun mapping.
Cosmological parameter, must be one of: z, a, CoDist, LumDist, CoDistTran, DistMod, CoVol, UniAgeAtz, TravelTime (see cosdist help for further description of these) H, CoVel, OmegaM, OmegaL, OmegaK, Factor, Rate, RhoCrit (see cosgrow help for further description of these). Note that AngDist and AngSize are not an option for cosparamx due to degenerate redshift solutions causing problems with the approxfun mapping.
Hubble constant as defined at z=0 (default is H0=100 (km/s)/Mpc).
Omega matter (default is 0.3).
Omega Lambda (default is for a flat Universe with OmegaL = 1-OmegaM = 0.7).
Omega Radiation (default is 0, but OmegaM/3400 is typical).
The value of dark energy equation of state at z=0. See cosgrow for more details.
The evolution term that governs how the dark energy equation of state evolves with redshift. See cosgrow for more details.
The value of Sigma8 to use if fsigma8=TRUE (by default this is a reasonable 0.8 for simplicity).
Logical to express whether the growth rate of structure calculated by cosgrow, cosgrowRate or cosgrowRateApprox is given as f*Sigma8 (TRUE) or simply f (FALSE). This is useful for redshift space distortion comparisons (RSD), since RSD strictly measures f*Sigma8.
Lower and upper z limits that the approxfun mapping is generated over (increase range if default is not sufficient, and decrease if it is wasteful, i.e. the possible redshift window is known to be quite narrow).
The type of stepping used. Allowed values are 'z' (uniform stepping in z), 'logz' (uniform stepping in log10(1+z) and expansion factor 'a' (uniform stepping in a=1/(1+z)). Default is z. For mappings using time (UniAgeNow, UniAgeAtz, TravelTime) or comoving quantities (CoDist, CoDistTran, CoVol) or distance modulus (DistMod) 'a' or 'logz' map the numeric range more uniformly. This is because a and log10(1+z) are approximately linear in light travel time (positive and negative correlation respectively), and typically they have better behaviour than stepping uniformly in z directly.
The resolution of steps. Larger numbers will be more accurate, but will be slower to compute.
The number of iterations to make when calculating the exact location of a given cosmological parameter when using cosmapval.
In cases where solutions are degenerate (multiple y solutions for a single x), this specifies whether to calculate the lower y solution (degen='lo'), or the higher y solutions (degen='hi').
The name of a reference cosmology to use, one of 137 / 737 / Planck / Planck13 / Planck15 / Planck18 / WMAP / WMAP9 / WMAP7 / WMAP5 / WMAP3 / WMAP1 / Millennium / GiggleZ. Planck = Planck18 and WMAP = WMAP9. The usage is case insensitive, so wmap9 is an allowed input. See cosref for details. This overrides any other settings for H0/ OmegaM and OmegaL. If ref=137 or ref=737 no specific Sigma8 is assumed, instead Sigma8 is set to whatever the input value is set to (by default this is 0.8).
If out='cos', cosmapval contains the concatenation of the cosdist (with age=TRUE and error=TRUE) and cosgrow functions for parameter 'cosparam' at value 'val'. The 'z' and 'a' columns are only included once (from the output of cosdist). See cosdist and cosgrow for information on the cosdist and cosgrow outputs. If out='z', then cosmapval merely returns the corresponding redshifts.
The cosmapval output (when out='cos') includes an additional final column named 'MapError' which gives the approximate relative error of the values returned compared to the desired lookup location. Smaller is obviously better, but at the cost of computational time.
cosmapfunc uses base R approxfun to map cosparamx onto cosparamy between zrange[1] and zrange[2] in uniform steps of expansion factor (a=1/(1+z)). cosmofunc returns the output function created by approxfun.
The default zrange and res should be sufficient for most reasonable cosmologies if the approximate redshift location of the region to be mapped is entirely unknown.
Predictions into the future are possible if val is set to negative (distance and volume parameters) or below their present day value (age and growth parameters). However, many potential values are outside of the asymptotic limits, e.g. using the default 737 cosmology H is tending to 83.666, i.e. it will fail if you request H=83 but work if your resuest H=84.
The default res and iter for cosmapval is appropriate for most mappings with -0.99 < z < 100 using a fiducial 737 cosmology. If this proves insufficient (this should be obvious from error column) then increase both of these. Overall accuracy goes as res^iter.
Based on the equations in:
Hogg D.W., 1999, arXiv, 9905116
Wright E.L., 2006, PASP, 118, 1711
# NOT RUN {
tempfunc=cosmapfunc('CoVol', 'UniAgeAtz')
tempfunc(50)
cosmapval(50:60, 'CoVol')
#A future prediction:
cosmapval(59, 'H', H0=70)
# }
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