These functions allows comoving, angular size and luminosity distances to be calculated for a given redshift, it can also return look back time. They use curvature correctly, calculated internally using the relation OmegaM+OmegaL+OmegaK=1, but by default they assume a flat Universe where only OmegaM needs to be specified.
cosgrow(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, Sigma8=0.8, fSigma8=FALSE, ref)
cosgrowz(z = 1)
cosgrowa(z = 1)
cosgrowH(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosgrowOmegaM(z=1, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosgrowOmegaL(z=1, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosgrowOmegaK(z=1, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosgrowFactor(z=1, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosgrowRate(z=1, OmegaM=0.3, OmegaL=1-OmegaM, Sigma8=0.8, fSigma8=FALSE, ref)
cosgrowSigma8(z=1, OmegaM=0.3, OmegaL=1-OmegaM, Sigma8=0.8, ref)
cosgrowFactorApprox(z=1, OmegaM=0.3, OmegaL=1-OmegaM, ref)
cosgrowRateApprox(z=1, OmegaM=0.3, OmegaL=1-OmegaM, Sigma8=0.8, fSigma8=FALSE, ref)
cosgrowSigma8Approx(z=1, OmegaM=0.3, OmegaL=1-OmegaM, Sigma8=0.8, ref)
cosgrowRhoCrit(z=1, H0=100, OmegaM=0.3, OmegaL=1-OmegaM, ref)Redshift, where z must be > -1 (can be a vector).
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).
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.
The name of a reference cosmology to use, one of 137 / 737 / Planck / WMAP9 / WMAP7 / WMAP5 / WMAP3 / WMAP1 / Millennium / GiggleZ. 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).
cosgrow function returns a data.frame (even if only 1 redshift if requested) with the following parameters evaluated at the respective redshift/s:
| z | Requested redshift |
| a | Universe expansion factor, as given by a=1/(1+z) |
| H | Hubble value in units of (km/s)/Mpc |
| OmegaM | Omega matter |
| OmegaL | Omega lambda |
| OmegaK | Omega curvature |
| Factor | Exact growth factor (g, see cosgrowFactor below for details) |
| Rate | Exact growth rate (f or f*Sigma8, see cosgrowRate below for details) |
| Sigma8 | Power spectrum fluctuation amplitude on the scale 8 Mpc/z |
| RhoCrit | critical mass density of the Universe at z, in units of Msol/Mpc^3 |
cosgrowz function returns the input redshift (only included for clarity).
cosgrowa function returns the Universe expansion factor, as given by a=1/(1+z).
cosgrowH function returns the value of the Hubble constant at z, in units of km/s/Mpc.
cosgrowOmegaM function returns the value of Omega matter at z.
cosgrowOmegaL function returns the value of Omega lambda at z.
cosgrowOmegaK function returns the value of Omega curvature at z.
cosgrowFactor function returns the exact value of the growth factor (typically referred to as 'g' in the astronomy literature), at z.
cosgrowRate function returns either the true (typically referred to as 'f' in the astronomy literature) or RSD type (f*Sigma8) value of the growth rate of structure, at z.
cosgrowSigma8 function returns the power spectrum fluctuation amplitude on the scale 8 Mpc/z at z, and is unitless.
cosgrowFactorApprox function returns the approximate value of the growth factor (typically referred to as 'g' in the astronomy literature), at z.
cosgrowRateApprox function returns either the approximate true (typically referred to as 'f' in the astronomy literature) or approximate RSD type (f*Sigma8) value of the growth rate of structure, at z.
cosgrowSigma8Approx function returns the approximate power spectrum fluctuation amplitude on the scale 8 Mpc/z at z, and is unitless.
cosgrowRhoCrit function returns the critical mass density of the Universe at z, in units of Msol/Mpc^3.
The above functions are heavily based on the equations in Hamilton A.J.S., 2001, MNRAS 322 419 and Lahav O., et al., 1991, MNRAS, 251, 136.
Negative value of z> -1 are allowed, which produces future predictions based on present day cosmology.
The approximation routines are generally accurate to sub 1 percent, and since they do not involve numericla integration they are substantially faster when computing large grids of numbers, i.e. they are recommended for plots, since the accuracy is sub the line width.
Based on the equations in Hamilton A.J.S., 2001, MNRAS 322 419 and Lahav O., et al., 1991, MNRAS, 251, 136
# NOT RUN {
cosgrow(0.3)
cosgrow(0.3,ref='Planck')
cosgrowz(0.3)
cosgrowa(0.3)
cosgrowH(0.3)
cosgrowOmegaM(0.3)
cosgrowOmegaL(0.3)
cosgrowOmegaK(0.3)
sum(cosgrowOmegaM(0.3)+cosgrowOmegaL(0.3)+cosgrowOmegaK(0.3)) #Still 1.
cosgrowFactor(0.3)
cosgrowFactorApprox(0.3) #The approximation better than 1% for reasonable cosmologies.
cosgrowRate(0.3)
cosgrowRateApprox(0.3) #The approximation better than 1% for reasonable cosmologies.
cosgrowRhoCrit(0.3)
# }
Run the code above in your browser using DataLab