WCDM model: SNIa

declaration of variables:

In[]:=
Ωr=8
-5
10
;(*ΩrisdensityofradiationDependedetypedemodule*)​​
In[]:=
c=299792.458;(*Speedoflight*)​​

Friedman equation: EE

In[]:=
​
In[]:=
H[z_?NumberQ,Ωm_?NumberQ,ωd_?NumberQ,h_?NumberQ]:=100h
Ωr
4
(1+z)
+Ωm
3
(1+z)
+(1-Ωm-Ωr)
3(1+ωd)
(1+z)
​​​​(*EquationdetatdeBIGRIPestPd=ωd*ρd*)​​​​H[zz[22],0.33,-1.01,0.5]
Out[]=
50.4378

the luminosity distance dl

In[]:=
​
In[]:=
DLL[z_,Ωm_,ωd_,h_]:=100h(1+z)NIntegrate
1
H[Z,Ωm,ωd,h]
,{Z,0,z}​​DLL[0.04,0.33,-1.01,0.2]
Out[]=
0.0411933

Chi square X

In[]:=
DATA=Import["C:\\Users\\USER\\Desktop\\BIG RIP SNIA\\gold.txt","Table"]​​
Out[]=
{{0.04,36.38,0.19},{0.05,36.84,0.21},{0.0307,35.9,0.2},{0.056,37.31,0.18},{0.0331,35.54,0.2},{0.0141,34.13,0.25},{0.046,36.35,0.21},{0.0265,35.64,0.2},{0.101,38.73,0.2},{0.075,37.77,0.19},{0.061,37.3,0.22},{0.0141,34.12,0.25},{0.0262,35.06,0.24},{0.043,36.53,0.19},{0.045,36.97,0.18},{0.036,36.17,0.19},{0.058,37.13,0.19},{0.063,37.67,0.19},{0.0186,34.96,0.22},{0.079,37.94,0.18},{0.088,38.07,0.28},{0.0178,34.7,0.23},{0.071,37.78,0.19},{0.0251,35.09,0.21},{0.052,37.16,0.18},{0.0286,35.53,0.21},{0.049,36.9,0.2},{0.05,37.08,0.19},{0.018,34.29,0.23},{0.0244,35.09,0.2},{0.029,35.7,0.19},{0.0161,34.5,0.24},{0.036,36.01,0.2},{0.478,42.48,0.23},{0.45,42.13,0.21},{0.48,42.37,0.2},{0.615,42.85,0.23},{0.4,42.04,0.19},{0.049,36.52,0.2},{0.0219,34.7,0.22},{0.388,42.07,0.19},{0.0152,34.11,0.25},{0.0276,35.9,0.2},{0.425,41.7,0.4},{0.62,43.11,0.3},{0.57,42.81,0.25},{0.3,41.01,0.25},{0.38,42.02,0.22},{0.43,42.33,0.34},{0.124,39.2,0.22},{0.0165,33.82,0.27},{0.0167,34.21,0.23},{0.0348,36.17,0.19},{0.828,43.96,0.46},{0.495,42.25,0.19},{0.0132,34.02,0.26},{0.58,43.04,0.21},{0.526,42.56,0.18},{0.172,39.79,0.18},{0.18,39.98,0.18},{0.472,42.46,0.19},{0.43,41.99,0.18},{0.657,43.27,0.2},{0.0166,34.54,0.23},{0.45,42.1,0.23},{0.32,41.45,0.18},{0.581,42.63,0.19},{0.44,42.57,0.4},{0.508,41.64,0.35},{0.416,42.1,0.19},{0.83,43.85,0.19},{0.579,42.86,0.19},{0.42,41.76,0.23},{0.518,42.83,0.3},{0.334,40.92,0.3},{0.0175,34.52,0.25},{0.5,42.74,0.2},{0.44,42.08,0.19},{0.0297,36.12,0.2},{0.0104,33.73,0.33},{0.778,43.81,0.35},{0.86,44.03,0.3},{0.538,42.66,0.18},{1.755,45.53,0.35},{0.886,42.91,0.81},{0.828,43.61,0.61},{0.63,42.62,0.24},{0.017,34.47,0.23},{0.46,41.83,0.4},{0.74,43.35,0.3},{0.43,42.36,0.25},{0.0104,33.21,0.32},{0.0171,34.68,0.24},{0.0327,36.08,0.19},{0.053,36.97,0.18},{0.017,34.18,0.23},{0.0234,35.36,0.2},{0.46,42.56,0.27},{0.5,42.75,0.19},{0.0257,35.41,0.2},{0.0157,34.58,0.24},{0.0316,35.85,0.19},{0.0104,33.56,0.31},{0.0141,34.43,0.26},{0.0136,33.73,0.26},{0.038,36.67,0.18},{0.278,41.,0.41},{1.056,44.25,0.23},{0.949,43.99,0.25},{0.815,43.76,0.33},{0.455,42.29,0.28},{1.19,44.19,0.34},{0.477,42.38,0.21},{0.026,35.62,0.2},{0.0193,34.59,0.23},{0.0266,35.36,0.21},{0.036,36.39,0.18},{0.0233,35.14,0.21},{0.0164,34.41,0.24},{0.5,42.75,0.24},{0.49,42.41,0.25},{0.47,42.74,0.23},{0.54,41.96,0.41},{0.47,42.77,0.21},{0.543,42.68,0.19},{0.0218,35.06,0.21},{0.0162,34.13,0.23},{0.873,43.75,0.38},{0.771,43.12,0.17},{0.811,43.97,0.35},{0.798,43.88,0.31},{0.832,43.55,0.29},{0.882,43.9,0.3},{0.34,40.71,0.27},{0.397,40.89,0.3},{0.57,42.88,0.31},{0.71,43.05,0.32},{0.528,42.77,0.25},{0.884,44.23,0.19},{0.815,44.09,0.28},{0.977,43.91,0.26},{0.475,42.14,0.19},{0.95,44.06,0.26},{1.3,45.27,0.19},{0.526,43.01,0.27},{1.305,44.7,0.22},{0.735,43.09,0.19},{1.14,44.84,0.3},{1.265,45.2,0.2},{1.551,45.3,0.22},{0.67,43.19,0.28},{0.64,43.07,0.21},{1.34,45.05,0.25},{0.954,44.28,0.31},{0.839,43.86,0.22},{0.899,43.64,0.25},{0.94,43.87,0.2}}
In[]:=
LN=Length[DATA](*LNnombredesDATA*)
Out[]=
157
In[]:=
zz[i_]:=DATA[[i,1]](*lesDatadez*)
In[]:=
μob[i_]:=DATA[[i,2]](*lesDatadeμ*)
In[]:=
σ[i_]:=DATA[[i,3]](*lesDatadeσ*)
In[]:=
zz[2]
Out[]=
0.05
In[]:=
σ[22]
Out[]=
0.23
In[]:=
μob[33]
Out[]=
36.01
In[]:=
chi[Ωm_,ωd_,h_]:=
LN
∑
i=1
2
(μob[i]-43.3-5Log10[DLL[zz[i],Ωm,ωd,h]])
2
(σ[i])
​​chi[0.34,-1.01,0.7]​​
Out[]=
186.925

The minimum value of chic

In[]:=
fminL=FindMinimum[chi[Ωm,ωd,h],{Ωm,0.32,0.321},{ωd,-1.1,-0.99},{h,0.7,0.71}]//AbsoluteTiming​​
NIntegrate
:The integrand
1
H[Z,Ωm,ωd,h]
has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,0.04}}.
NIntegrate
:The integrand
1
H[Z,Ωm,ωd,h]
has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,0.04}}.
NIntegrate
:The integrand
1
H[Z,Ωm,ωd,h]
has evaluated to non-numerical values for all sampling points in the region with boundaries {{0,0.04}}.
General
:Further output of NIntegrate::inumr will be suppressed during this calculation.
FindMinimum
:Unable to bracket a minimum along the direction {0,0,0.01} from the point {0.300207,-1.13137,0.7}.
FindMinimum
:Unable to bracket a minimum along the direction {0,0,0.01} from the point {0.300207,-1.13137,0.7}.
FindMinimum
:Unable to bracket a minimum along the direction {0,0,0.01} from the point {0.300207,-1.13137,0.7}.
General
:Further output of FindMinimum::lsbrak will be suppressed during this calculation.
Out[]=
{81.7552,FindMinimum[chi[Ωm,ωd,h],{Ωm,0.32,0.321},{ωd,-1.1,-0.99},{h,0.7,0.71}]}