Lambda |
Omega |
K |
Zmax |
WMtype |
Model name |
T |
-0.10 | 0.28 | -0.82 | | 2 | |
-0.10 | 1.10 | 0.00 | | 3 | |
-0.10 | 1.50 | 0.40 | | 4 | |
0.00 | 1.28 | 0.28 | | 5 | Misner-Thorne-Wheeler | |
0.00 | 0.00 | -1.00 | | 7 | Milne |
0.00 | 0.28 | -0.72 | | 8 | |
0.00 | 1.00 | 0.00 | | 9 | Einstein-de Sitter | |
0.72 | 0.00 | -0.28 | | 10 | |
0.72 | 0.10 | -0.18 | | 11 | |
1.00 | 0.00 | 0.00 | | 12 | de Sitter |
0.72 | 0.28 | 0.00 | | 13 | Flat |
2.20 | 0.67 | 1.87 | | 14 | Lemaitre | 0.0120 | |
2.20 | 0.66 | 1.86 | * | 17 | Eddington | 0.0032 |
2.20 | 0.656321 | 1.856321 | * | 18 | Bounce | -0.00000026 |
1.20 | 0.00 | 0.00 | * | 19 | de Sitter |
The first 3 columns show the parameters Lambda, Omega and K.
However this are not Cosmological Constants Lambda, Omega and K as part of the Friedmann equation. See The equations but the density parameters Omega(L), Omega(M) and Omega(K). See: Density parameter
The current interpretation is that the sum of those three (four) parameters is 1. That means Omega(L) + Omega(M) + Omega(K) = 1
In the Fortran program the following equation is used: K = OMEGA + LAMBDA - 1. See program INICOS.
The density equivalent is: Omega(M) + Omega(L) - Omega(K) = 1
The subroutine QQ uses the equation QQ = OMEGA * V ^ 3 - K * V ^ 2 + LAMBDA
What this means is that the sign of the parameter K is opposite of the standard implementation.
WMtype = 13 Flat
WMtype = 13 represents the current most accepted model. In that case OMEGA and LAMBDA are greater than zero and K = 0. That means Omega(L) + Omega(M) = 1 and Omega(K) = 0.
The most current accepted density values are: Omega(L) = 0.72 Omega(M) = 0.28 and Omega(K)= 0 Flat Universe. See specific
SEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE (WMAP1) OBSERVATIONS: POWER SPECTRA AND WMAP-DERIVED PARAMETERS Figure 14, page 15.
The parameter EPS and WMtype = 17
The parameter EPS is used to distinquish between the WMtype models 14, 17 and 18.
- In the case of WMtype = 17 the parameter T has to be smaller than parameter EPS and larger than zero.
- In the case of WMtype = 14 the parameter T has to be larger than parameter EPS.
- In the case of WMtype = 18 the parameter T has to be smaller than zero.
The FORTRAN program uses EPS = 0.000001.
To test typeWM = 17 you need LAMBA = 2.2 and OMEGA = .656321 (T = 0.00000026) or OMEGA = .656322 (T = 0.00000063).
In the case of WMtype = 17 Zmax is greater than zero.
IMO WMtype 17 is an artificial model. WMtype is the boundary between the WMtypes 14 and 18.
To calculate this boundary a new subroutine BOUNDARY is used. This subroutine calculates the omega value of this boundary without the parameter EPS.
When you test typeWM for the above mentioned values you will see that the values for ZMAX and for Zrange do not match. That means the program INICOS is in error. For WMtype = 17 ZMAX should be 1 smaller.
In the latest issue of the program this error is solved.
A similar problem also exists for WMtype = 15. There are also two indications of WMtype = 12. Maybe one of those should be WMtype = 16.
The parameter TINY
The parameter TINY is used to test the results of the calls to the subroutine QQ(V).
In 4 cases the following code is used G=SQRT(QQ(V)) and then a test is done if G is smaller than TINY.
The problem is that QQ(V) can be smaller than zero.
The following code is sufficienct : IF QQ(V) < 0 then display ERROR = 11 and RETURN (Exit sub)
Specific the RETURN is missing. This will cause the program to hold.
The parameter ZMAX and the program ZRANGE.
In order to calculate ZMAX also the artificial parameter EPS is used.
To circumvent this problem the program ZRANGE is written which is independent of PC or computer used.
The subroutines ANGSIZ and BNGSIZ
In order to test ANGSIZ and BNGSIZ the parameter Zmax has to be greater than zero. This is only the case for World Model types 17, 18 and 19.
I did not succeed to calculate the output parameters: D12, D14, D34 and D32.
- Input parameters for the subroutine ANGSIZ are Z1 and Z2
- Input parameters for the subroutine BNGSIZ are Ystart(1) and Ystart(2)
WMtype 18 and 19 are what is called bouncing models. I expect a different name for those models is cyclic. Roger Penrose is in favour of this model. The reason why those models are tested is not clear because they do not reflect the current accepted mainstream view. See For Example: No evidence of time before Big Bang
The subroutines LOWLVL and BSSTEP use the artificial parameter EPS. The meaning is not clear.