Particle Physics & Cosmology Posters
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2
ω Ω r 1 , M1
M1
ω Ω r 2 , M2
M2
5
9
.
r2 r1
9
St ω
dgE
Mag. of Hubble Cons. vs. Cosm. Age
EGM 1
The Cosmological Evolution Process 2.5 .10
Derived From Particle-Physics
42
Max. Cosmological Temp. Line: 3.2x1031(K)
t1
Hα
2
H = HβHα
Primordial Inflation
Thermal Inflation 42 2 .10 dH dt H β
dH dt e
M1
ω Ω r 2, M 2
M2
2
Hα
Region of positive Hubble gradient
t4
t1
0
42
0
Region of negative Hubble gradient
η 84 1 .10
FOR MORE INFO...
1
dH dt e
4
2
1
2
1 .10
42
84 2 .10
1 dH dt e
2 2 5 .µ . 5 .µ
1 84 3 .10
2 2 5 .µ . 5 .µ
2 1
5 .µ
dH dt e
2
4
2 2 2 5 .µ . 5 .µ . 5 .µ
1
2
84 4 .10
St T
H α
λ x 4.
http://www.deltagroupen gineering.com/public ations.htm
π
Hα ≈ 0.37ωh
λ x
5 .10
µ
λ x .ω h 4 .µ . µ π ( 4 .µ ) .c
ω h
1 .10
2 .µ
2
41
2 2 .µ
0 43 1 .10
1 .10
42
1 .10
41
1 .10
Big-Bang: 0(K)
40
1 .10
39
1 .10
t = (ΗβηΗα)-1
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
38
1 .10
37
1 .10 1
36
Gr ap h 15 dgE
Cosmological Expansion
Cosmological Inflation
Max. Cosmological Temp. Line: 3.2x1031(K)
84 7 .10
G .h
1
84 1 .10
84 5 .10
5
H
1
2 2 2 5 .µ . 5 .µ . 5 .µ
c
. 2
. H5 µ
Hα Hγ . 5 .ln 1 .µ 2 2 Hγ 5 .µ Hγ
dH dt H γ
84 6 .10
ω h
Hα
1st Derivative of the Hubble Constant
(Hz^2)
(Hz)
T U2( H ) K W . St T . ln 2.
1
dH dt H β
2 2 5 .µ . 5 .µ dH dt e
→
84 2 .10
1 2 2 5 .µ . 5 .µ
St ω
Hγ = Ηβη
t4
1
9
r1
Hubble Expansion 1.5 .10
dH dt e
r2
.
Hubble Inflation
η
1 5 .µ
ω Ω r 1, M 1
5
9
43
1 .10
1 .10
35
42
1 .10
1 .10
η H β .H α Cosmological Age (s)
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
41
34
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
1 .10
33
39
1 .10
1 .10
32
38
1 .10
1 .10
37
31
1 .10
36
1 .10
30
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
1st Derivative of the Hubble Constant
EGM
2 .10
84 1
The Cosmological Evolution Process
Hα
Derived From Particle-Physics 1 .10
Region of positive Hubble gradient
t4
t1
84
0 0 2nd Derivative of the Hubble Constant 8 .10
t5
η
dH dt H β
84 1 .10
6 .10
2
1 2 .10
dH2 dt2 H β
84
dH dt e
2 2 5 .µ . 5 .µ
1
dH2 dt2 e
4
dH dt e
η 125 5 .10
5 .µ
2
1
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH2 dt2 e
2 2 2 5 .µ . 5 .µ . 5 .µ
4 .10
125
3 .10
125
2 .10
125
2
1 .10
125
2 2 2 5 .µ . 5 .µ . 5 .µ
1
2
84 4 .10
ω h
St T
H α
2
1
0 0
1 .10
Hγ = Ηβ
1
2
4
2 1
3 2 H α .H γ . 5 .µ 2 . ln 1 . 5 .µ 2 2 Hγ 5 .µ Hγ
dH2 dt2 H γ
1
84 3 .10 2 2 5 .µ . 5 .µ
125
1 dH2 dt2 e
1 (Hz^3)
(Hz^2)
5 .µ
125 7 .10
Region of negative Hubble gradient
1 dH dt e
125
125
η 5 .10
c
5
G .h
λ x
ω h
π 2
µ
Cosmological Inflation 6 .10
84
7 .10
84
42
1 .10 η H β .H α
Cosmological Expansion
41
1 .10
40
1
Cosmological Age (s)
2 2 .µ
Hα ≈ 0.37ωh
λ x
1 .10
2 .µ
4.
λ x .ω h 4 .µ . µ π ( 4 .µ ) .c
84
Max. Cosmological Temp. Line: 3.2x1031(K)
1 .10
43
1 .10
42
Big-Bang: 0(K)
1 .10
41
1 .10
t = (ΗβηΗα)-1
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
40
1 .10
39
1 .10
38
1 .10
37
1 .10
36
1
η H β .H α Cosmological Age (s)
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
Av. Cosmological Temperature vs. Age
EGM
2
1
The Cosmological Evolution Process
t1
Hα
Derived From Particle-Physics
H = HβHα
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
5
9
.
r2 r1
9
St ω
TU2(H) → TU3(Hβ) t1
71 8 .10
t2
K W .St T .
dT dt ( t )
2 5 .ln H α .t .µ 5 .µ
2
2.5 .10
31
2 .10
31
1.5 .10
31
1 .10
31
5 .10
30
1
.t
71 4 .10
2 5 .µ
71 2 .10 dT dt
2 10 .µ
1
2 2 5 .µ . 5 .µ
H β .H α
1
dT dt t 1 (K/s)
0 5 .10
t2
dT dt t 3
1
2nd Derivative of Av. Cosmological Temp.
113
dT dt t 2 2 .10
71
4 .10
71
t3
0
dT2 dt2( t )
t
t2
H β .H α
3
2
8 .10
5 .µ
2
1
2
1
.t2
t3
1 114 1 .10
1 .10156
dT2 dt2 t 1 dT2 dt2 t 2 dT2 dt2 t 3
1.5 .10114
dT3 dt3 (K/s^3)
2 2 2 5 .µ . 5 .µ . 5 .µ
71 6 .10
2
2
2 2 5 .µ . ln H α .t . 5 .µ
3rd Derivative of Av. Cosmological Temp.
1 .10157
dT2 dt2
2 2 15 .µ . 5 .µ
K W .St T .
5 .10113
(K/s^2)
Av. Cosmological Temperature (K)
31
71 6 .10
1
T U3 e
3 .10
. 2
. H5 µ
H
t
T U3 H β
T U3 e
Hα
T U2( H ) K W . St T . ln
31
1st Derivative of Av. Cosmological Temp.
72 1 .10
T U3 e
→
3.5 .10
H β .H α
1 .10155 1
dT3 dt3 t 1 dT3 dt3 t 2 1 .10154
71
114 2 .10
1 .10153
dT3 dt3( t )
114 2.5 .10
1 .10
72
1.2 .10
72
3 .10114 42 2 .10
Hγ = Ηβη
42 1 .10
K W .St T .
2 2 2 5 .µ .ln H α .t . 5 .µ . 5 .µ
t 1 .10152 42 2 .10
3 .10
42
4 .10
42
41 1 .10
5 .10
42
6 .10
42
3 .10
7 .10
42
42
42
5 .10
8 .10
42
4 .10
42
6 .10
42
7 .10
42
8 .10
42
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
1.1 .10
41
1.1 .10
1.2 .10
41
1.2 .10
41
41
3 5 .µ
2
2
1.3 .10
2 2 15.µ . 5 .µ
2
2
.t 3
1.3 .10
41
41
1.4 .10
41
1.4 .10
1.5 .10
41
40 1 .10
41
1.5 .10
41
1 .10
39
1 H β .H α Cosmological Age (s)
ω h
St T
H α
c
5
λ x
G .h
2 .µ π
4 .µ ( 4 .µ )
4.
. µ
ω h
.c
λ x .ω h
µ
2
π
Hα ≈ 0.37ωh
λ x
2 2 .µ
1 .10
43
1 .10
42
1 .10
Big-Bang: 0(K)
41
1 .10
t = (ΗβηΗα)-1
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
40
1 .10 H β .H α
39
1 .10
1
Cosmological Age (s)
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
38
1 .10
37
1 .10
36
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
EGM
3.5 .10
Av. Cosmological Temp. vs. Hubble Cons.
31 Hα
The Cosmological Evolution Process
2
1 t1
Derived From Particle-Physics
H = HβHα
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
31 3 .10
3.5 .10
TU2(H) → TU3(Hβ)
5
9
.
r2
9
St ω
r1
→
Hα
T U2( H ) K W . St T . ln
. 2
. H5 µ
H
Av. Cosmological Temp. vs. Hubble Cons.
31
Av. Cosmological Temperature vs. Age
1
1
t2
t3
1
3.5 .1031
t1
Hα
3 .1031
3 .10
31 2.5 .1031
31 2.5 .10 1
T U3 e
2 5 .µ 31 2 .10 2 10 .µ
T U3 e
2 2 5 .µ . 5 .µ
T U3 e
ω h
St T
H α
2 2 2 5 .µ . 5 .µ . 5 .µ
c
5
λ x
G .h
2 3
λ x .ω h . µ π ( 4 .µ ) .c
ω h
1.5 .10
2 2 .1031 2
2 2 5 .µ . 5 .µ
1 1
2 2 15 .µ . 5 .µ T U3 e
2 2 2 5 .µ . 5 .µ . 5 .µ
2
1.5 .1031
2 3
2
5 .µ
1 .1031
2 5 .1030
31 2 .10 10 .µ
2
1 1 .10
T U3 e
2 2 5 .µ . 5 .µ
2 2 15 .µ . 5 .µ T U3 e
43
1 .10
42
1
2 2 2 5 .µ . 5 .µ . 5 .µ
2
2 3
1 .10
41
1 .10
40
1 .10 1 H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
31 1.5 .10 2
1 .10
31
5 .10
30
31 1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 H β .H α Hubble Constant (Hz)
39
1 .10
38
1 .10
37
1 .10
36
2
1 .10
31
2
5 .10
30
µ
2 2 .µ
Hα ≈ 0.37ωh
λ x
5 .µ
10 .µ T U3 e
2 .µ
4.
π
4 .µ
T U3 e
1
2
1 T U3 e
1
1
2 2 15 .µ . 5 .µ
31 2.5 .10
T U3 H β Av. Cosmological Temperature (K)
Av. Cosmological Temperature (K)
T U3 H β
Av. Cosmological Temperature (K)
T U3 H β
1 .10
43
1 .10
42
1 .10
41
1 .10
Big-Bang: 0(K) Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
40
1 .10 . Hβ Hα Hubble Constant (Hz)
39
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
1 .10
38
1 .10
37
1 .10
36
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
The Cosmological evolution process derived from Particle-Physics utilising the EGM construct (1 of 2) e
5 .µ
Av. Cosmological Temperature vs. Age
Av. Cosmological Temperature
1
31 3.5 .10
1
e
31 3 .10
31 3 .10
31 2.5 .10
1 T U3 e
2 5 .µ 31 1.5 .10
1 .10
0.01
3
1 .10
4
1 .10
5
1 .10
1 .10
6
43
42
1 .10
1 .10
41
1 .10
40
Hβ Dimensionless Range Variable
1 .10 1 H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
5 .µ
2 31 2 .10 2 10 .µ
T U3 e
1
2 2 5 .µ . 5 .µ
1
2 2 15 .µ . 5 .µ T U3 e
2
2 2 2 5 .µ . 5 .µ . 5 .µ
31 1.5 .10
2 3
2
Av. Cosmological Temp. vs. Hubble Cons.
3.5 .10
31
1
1.5 .10
31
T U3 H β
2
10 .µ
2
1 1
2 2 15 .µ . 5 .µ T U3 e
2
2
2 2 2 5 .µ . 5 .µ . 5 .µ
3
2 2 15 .µ . 5 .µ T U3 e
2 2 2 5 .µ . 5 .µ . 5 .µ
2
30 5 .10
1 .10
36
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 1 H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
1 .10
36
Av. Cosmological Temperature vs. Size
1
c
2.5 .10
31
2 .10
31
3.5 .10
10 .µ T U3 e
2
1.5 .10
31
1
2 2 5 .µ . 5 .µ
1
2 2 15 .µ . 5 .µ T U3 e
2
2
2 2 2 5 .µ . 5 .µ . 5 .µ
41
1 .10
40
39
1 .10 1 H β .H α Cosmological Age (s)
1 .10
38
1 .10
37
1 .10
36
3
Av. Cosmological Temperature vs. Size
31
3.5 .10
2
2.5 .10
31
2 .10
31
1.5 .10
31
T U3 H β
1 T U3 e
2
5 .µ
10 .µ T U3 e
2
1
2 2 5 .µ . 5 .µ
1
2 2 15 .µ . 5 .µ T U3 e
2
2 2 2 5 .µ . 5 .µ . 5 .µ
2 3
31
31 3 .10
2
2.5 .10
31
2 .10
31
1.5 .10
31
1 2
5 .µ
T U3 e
10 .µ
2
1
2 2 5 .µ . 5 .µ
T U3 e
1
2 2 15 .µ . 5 .µ
2
2 2 2 5 .µ . 5 .µ . 5 .µ
T U3 e
2 3
2
31
1 .10
31
1 .10
31
1 .10
31
5 .10
30
5 .10
30
5 .10
30
43
1 .10
42
1 .10
41
1 .10
40
1 .10 H β .H α Hubble Constant (Hz)
39
1 .10
38
37 1 .10
36 1 .10
1 .10
1st Derivative of Av. Cosmological Temp. t1
43
1 .10
42
1 .10
41
1 .10
40
1 .10 H β .H α Hubble Constant (Hz)
39
1 .10
38
37 1 .10
36 1 .10
1 .10
t2
71 8 .10
34
1 .10
33
1 .10
32
1 .10
31
1 .10
30
29
1 .10
1 .10
28
1 .10
27
71 6 .10
71 4 .10
34
1 .10
1 .10
33
1 .10
32
1 .10
1. H β .H α c EGM Cosmological Size (m)
1st Derivative of Av. Cosmological Temp.
72 1 .10
t2
2nd Derivative of Av. Cosmological Temp.
113 5 .10
t3
t1
5 .10
113
1 .10
114
31
1 .10
30
1 .10
29
1 .10
28
1 .10
27
1. H β .H α c EGM Cosmological Size (m)
2nd Derivative of Av. Cosmological Temp.
113 5 .10
t2
t2
t3
0
5 .10
113
1 .10
114
1.5 .10
114
114
2 .10
114
114 2.5 .10
2.5 .10
114
3 .10
114
71 2 .10
1
dT dt
H β .H α
1
dT2 dt2
dT dt t 1
71 2 .10
0
(K/s^2)
(K/s)
0
dT dt t 2
dT dt t 2 71 2 .10
dT dt t 3
71 4 .10
71 4 .10
71 6 .10
71 6 .10
71 8 .10
71 8 .10
72 1 .10
1
H β .H α
dT2 dt2
dT2 dt2 t 1
(K/s^2)
71 2 .10
(K/s)
1 .10
t 2 .c t 3 .c
T U3 H β
2
5 .µ
71 4 .10
dT2 dt2 t 2 dT2 dt2 t 3
dT2 dt2 t 1 dT2 dt2 t 2 dT2 dt2 t 3
114 1.5 .10
2 .10
1
H β .H α
72 1 .10
72 1.2 .10 42 1 .10
1 .10
41
1 .10
40
1 .10
72 1.2 .10 42 1 .10
39
1 .10
41
1 .10
1 H β .H α Cosmological Age (s)
40
1 .10
3 .10
39
114 2 .10
42
3 .10
42
4 .10
42
5 .10
42
42
6 .10
7 .10
42
8 .10
42
1 H β .H α Cosmological Age (s)
3rd Derivative of Av. Cosmological Temp.
157
t1
1 .10
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
t2
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
41
2 .10
42
3 .10
42
4 .10
42
5 .10
42
6 .10
156
1 .10
42
7 .10
42
8 .10
42
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
1.1 .10
1st Derivative of the Hubble Constant
3rd Derivative of Av. Cosmological Temp.
157
t2
1.1 .10
1.6 .10
t3
t1
156
1.4 .10
84
1.2 .10
84
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
41
1st Derivative of the Hubble Constant 2 .10
84
84 1
t4
t4
t1
Hα 1 .10
1 .10
42
31 3 .10
1 T U3 e
71 6 .10
1 .10
1 .10
t 1 .c
Hα
0
dT dt t 3
43
30
71 8 .10
dT dt t 1
2
1 .10
72 1 .10
H β .H α
31 1.5 .10
2 3
5 .10
1 .10
dT dt
2
30 5 .10
t2 t3
1
2 2 5 .µ . 5 .µ
1
30 5 .10
Av. Cosmological Temperature (K)
31
2 .10
1
31 1 .10
31 3 .10
Av. Cosmological Temperature (K)
Av. Cosmological Temperature (K)
2.5 .10
31 2 .10 2
31 1 .10
Av. Cosmological Temp. vs. Hubble Cons.
31
1 t1
31 3 .10
T U3 H β
2
10 .µ T U3 e
2 2 5 .µ . 5 .µ
Big-Bang: 0(K)
31 Hα
5 .µ
31 1 .10
Average Cosmological Temperature Maximum Av. Cosmological Temperature
3.5 .10
1 T U3 e
Av. Cosmological Temperature (K)
0.1
T U3 H β
1 T U3 e
Av. Cosmological Temperature (K)
31 2 .10
30 5 .10
1
T U3 H β Av. Cosmological Temperature (K)
2
T U3 H β
31 1 .10
T U3 e
31 3.5 .10
t3
31 2.5 .10
31 1.5 .10
5 .µ
t2
31 3 .10
1
T U3 e
Av. Cosmological Temperature vs. Age
31 3.5 .10
t1
31 2.5 .10
31 2 .10
5 .µ
1 Hα
31 2.5 .10
T U3 H β
T U3 e
2 5 .µ . 1 Hα
31 3 .10
Av. Cosmological Temperature (K)
Av. Cosmological Temperature (K)
Hα
Av. Cosmological Temperature vs. Age
31 3.5 .10
1
2
Region of positive Hubble gradient
84
0 0
dH dt H β
η
dH dt H β
1 155 dT3 dt3
dT3 dt3 t 2 1 .10
H β .H α
1 .10 1
155
dH dt e
dT3 dt3 t 1 dT3 dt3 t 2
154
1 .10
153
1 .10
2
1 .10
1
dH dt e
2 2 5 .µ . 5 .µ
dH dt e
2 2 5 .µ . 5 .µ
154
8 .10
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
2 1
2
6 .10
83
5 .µ
dH dt e
2 .10
83
84
2 .10
84
3 .10
84
4 .10
84
5 .10
84
6 .10
84
7 .10
84
1
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH dt e
83
2
1
83
4 .10
1 .10 1
84
1
dH dt e
1 .10
5 .µ
(Hz^2)
1 .10 1
(Hz^2)
H β .H α
(K/s^3)
(K/s^3)
dT3 dt3
dT3 dt3 t 1
Region of negative Hubble gradient
η
4
2 2 2 5 .µ . 5 .µ . 5 .µ
2 1
2
Cosmological Inflation
0 0 1 .10
152 2 .10
42
3 .10
42
4 .10
42
5 .10
42
6 .10
42
7 .10
42
8 .10
42
9 .10
42
H β .H α
1 .10 1
41
1.1 .10
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
1 .10
41
Max. Cosmological Temp. Line: 3.2x1031(K)
152 2 .10
42
3 .10
42
4 .10
42
5 .10
42
6 .10
42
7 .10
42
8 .10
42
9 .10
42
H β .H α
Cosmological Age (s)
1 .10 1
41
1.1 .10
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
41
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 η H β .H α
Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
1 .10
43
1 .10
42
1 .10
41
1
Cosmological Age (s)
2
H = HβHα
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
Cosmological Expansion
153
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
5
9
.
r2 r1
9
St ω
→
T U2( H ) K W . St T . ln
Hα H
. 2
. H5 µ
TU2(H) → TU3(Hβ)
T U3 H β
(i) “Big-Bang” properties: “t = 1/Hα”, “H = Hα”, “TU2(Hα) = TU3(1) = 0(K)”; (ii) “Maximum Cosmological Temperature = 3.2 x1031(K)” @ “t = t1”
K W .St T .ln
1 Hβ
. H .H β α
5 .µ
2
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The Cosmological evolution process derived from Particle-Physics utilising the EGM construct (2 of 2) 1st Derivative of the Hubble Constant 2 .10 t2 1 .10
2nd Derivative of the Hubble Constant
1st Derivative of the Hubble Constant
84
t5
84
1 .10
t4
0
1 .10 1
2 5 .µ
1
2 2 5 .µ . 5 .µ
2 .10
84
3 .10
84
dH dt e
1
4
2 2 5 .µ . 5 .µ
4 .10
84
5 .10
6 .10
7 .10
2 .10
84
3 .10
84
1
2 2 5 .µ . 5 .µ 2
1
1 1
dH dt e
2
2 2 2 5 .µ . 5 .µ . 5 .µ
127
4 .10
127
3.5 .10
127
t1
t2
t3
4
dH2 dt2 H β
2 2 2 5 .µ . 5 .µ . 5 .µ
3 .10
127
127
2.5 .10
127
2 .10
127
dH2 dt2 H β
η
127 1.5 .10 2
1
127
η
2 4 .10
84
84
5 .10
84
84
6 .10
84
84
7 .10
84
dH dt e
3 .10
2.5 .10
84
(Hz^3)
1
2 2 5 .µ . 5 .µ dH dt e
η
2 5 .µ
1 dH dt e
3.5 .10
1 Hα
0
dH dt H β
84
(Hz^2)
(Hz^2)
dH dt e
127
0
η 1 .10
4 .10
84
0
dH dt H β
2nd Derivative of the Hubble Constant
84
t3
(Hz^3)
2 .10
2 .10
127
1.5 .10
127
1 .10
127
1 .10
127
5 .10
126
5 .10
126
0
43
1 .10
42
1 .10
41
1 .10
40
39
1 .10 1 η H β .H α Cosmological Age (s)
1 .10
38
1 .10
37
1 .10
36
1 .10
43
1 .10
42
1 .10
2nd Derivative of the Hubble Constant
4 .10
127
3.5 .10
127
3 .10
127
41
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
2nd Derivative of the Hubble Constant
t1
dH2 dt2 H β
125 5 .10
127
1.5 .10
127
5 .µ
2
2 2 5 .µ . 5 .µ
1
125 3 .10
2 2 5 .µ . 5 .µ dH2 dt2 e
1 .10
dH2 dt2 e
125 4 .10
1 dH2 dt2 e
t5
125 6 .10
η
dH2 dt2 H β
125 5 .10
4
2 2 2 5 .µ . 5 .µ . 5 .µ
5 .µ
2 2 5 .µ . 5 .µ
125 2 .10
2
dH2 dt2 e
1
125 3 .10 4
2 2 2 5 .µ . 5 .µ . 5 .µ
dH2 dt2 e
1
125 4 .10
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ
125 3 .10 4
2
2 2 2 5 .µ . 5 .µ . 5 .µ
dH2 dt2 e
125 2 .10
2
1
125 1 .10
125 1 .10 0
0
0
125 1 .10
0
2
1
125 2 .10
2
0
126
5 .µ
2 1
125 1 .10
127
dH2 dt2 e
125 4 .10
2 2 5 .µ . 5 .µ
2 1
1 1
dH2 dt2 e
125 5 .10 1
2
0
5 .10
η
1 1
40
125 7 .10
125 6 .10
η
1 .10
2nd Derivative of the Hubble Constant
t4
125 7 .10
(Hz^3)
2 .10
(Hz^3)
(Hz^3)
dH2 dt2 H β
dH2 dt2 e
41 1 .10 1 η H β .H α Cosmological Age (s)
t3
1
127
42 1 .10
125 8 .10
t2
125 6 .10
η
43 1 .10
125 8 .10
t4
dH2 dt2 H β
40 1 .10
2nd Derivative of the Hubble Constant
125 8 .10
t5
41 1 .10 1 η H β .H α Cosmological Age (s)
125 7 .10
2.5 .10
0
42 1 .10
(Hz^3)
1 .10
0
0
43 1 .10
0
125 1 .10
125 1 .10
0
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10
42
1 .10
Mag. of Hubble Cons. vs. Cosm. Age 1 42
40
42
1 .10
1 .10
Max. Cosmological Temp. Line: 3.2x1031(K)
2.5 .10
42
1 .10
40
1 .10
42
41 1 .10 1 η H β .H α Cosmological Age (s)
η H β .H α Cosmological Age (s)
Av. Cosmological Temp. vs. Hubble Cons.
31 3.5 .10
40
1
Hα
t1
31 3 .10
1 .10
Av. Cosmological Temp. vs. Hubble Cons.
31 3.5 .10
1
Hα
t4
Hα
41 1
Mag. of Hubble Cons. vs. Cosm. Age 1
t1
Hα
1 .10
η H β .H α Cosmological Age (s)
η H β .H α Cosmological Age (s)
2.5 .10
41 1
1
t1
31 3 .10
Primordial Inflation
5 .µ
2
1 1.5 .10
dH dt e
42
(Hz)
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH dt e
4
2 1
2
1 .10
31 2.5 .10
1
2 2 5 .µ . 5 .µ
42
1
2 2 5 .µ . 5 .µ
42 dH dt e
5 .10
2
1 dH dt e
2 2 2 5 .µ . 5 .µ . 5 .µ
5 .µ
1.5 .10
t4
1 dH dt e
42
η
1
(Hz)
dH dt e
2 .10 dH dt H β
Hubble Inflation Hubble Expansion
4
2 2 2 5 .µ . 5 .µ . 5 .µ
41
2 1
2
1 .10
42
5 .10
41
T U2
dH dt H β
31 2.5 .10 Av. Cosmological Temperature (K)
Thermal Inflation
42
η
1
Av. Cosmological Temperature (K)
2 .10 dH dt H β
η 31 2 .10
T U3 H β 1 T U3 e
5 .µ
2 31 1.5 .10
1 .10
42
1 .10
41
1 .10
40
1 .10
39
1 .10
Big-Bang: 0(K)
Time
38
37 36 1 .10 1 η H β .H α Cosmological Age (s)
1 .10
1 .10
35
1 .10
34
TU2 (K)
1 .10
33
1 .10
32
1 .10
31
1 .10
0 43 1 .10
30
dHdt (km/s/Mpc)2
1 .10
42
1 .10
41
1 .10
40
1 .10
39
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t4 ≈ 2.093267·10-41(s) 9
AU ≈ 14.575885·10 (yr) Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
≈ 2.059945·1031 ≈ 2.724752
0
1 .10
35
3
≈ 3.845994·1061
34
1 .10
33
1 .10
32
1 .10
31
1 .10
Hα
t1
ω h λ x
t2
1 .10
2 . 4.µ . λ x ω h St T µ π ( 4.µ ) . c
t
e
e
2 .µ
t3
e
2
42
41 1 .10
. 1 Hα
1 .10
40
1 .10
39
2
dT dt ( t )
38 1 .10
1 .10
37
36 1 .10
43 1 .10
1 .10
42
41 1 .10
1 .10
2 5 .ln H α .t .µ
K W .St T .
1
2 2 5 .µ . 5 .µ
dT2 dt2 ( t )
. 1 Hα
1
2
2 2 2 5 .µ . 5 .µ . 5 .µ
K W .St T .
5 .µ
2
2
. 1 Hα
dT3 dt3 ( t )
39
38 1 .10
1 .10
37
36 1 .10
1
2 2 5 .µ . ln H α .t . 5 .µ 5 .µ
2
.t
1
2
K W .St T .
1
2
2.
2
1 .10
.t
t
3
40
η dH dt H β Hubble Constant (Hz)
t
2 2 5 .µ ln H α .t . 5 .µ . 5 .µ
t
1
t4
e
t5
e
2 2 5 .µ . 5 .µ
2 2 5 .µ . 5 .µ
η
31 1.5 .10
3
2
2 2 15.µ . 5 .µ
2
2
2 5 .µ . 3
t
2
1 H γ .H α
Hγ Hβ
5 .µ
2 2 15 .µ . 5 .µ
Hα ≈ 0.37ωh
2
30 5 .10
10 .µ
µ
5 .µ
η dH dt H β , H β .H α Hubble Constant (Hz)
2.µ π
31 2 .10
1 T U3 e
31 1 .10
1
λ x 4.
η
31 1 .10
30
5
≈ 67.084304
Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
1 .10
c G. h
0
≈ 1.479167·10123 ≈ 4.500304·10
37 36 1 .10 1 η H β .H α Cosmological Age (s)
1 .10
ω h
-∞
≈ 3.195518·1031
38
|H| (km/s/Mpc)
0
t1 ≈ 2.206287·10-42(s)
1 .10
dH dt H β
30 5 .10
43 1 .10 0 43 1 .10
T U2
2.
. 1 Hα
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
dH dt H γ
Hγ
2 1
Hα Hγ
2
. 1 Hα
dH2 dt2 H γ
5 .µ
2
. 5 .ln 1 .µ 2 Hγ
1
3 2 H α .H γ . 5 .µ 2 . ln 1 . 5.µ2 2 Hγ . 5µ Hγ
1
2
1
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
www.deltagroupengineering.com dgE
The Deceleration Parameter “q0” & Cosmological Constant “Λ0” [excerpts from “Quinta Essentia – Part 2” dgE]
1st Derivative of the Hubble Constant 2 .10
84 1
1 .10
t4
t1
Hα
Region of positive Hubble gradient
5
84
c G. h
ω h 0
2.µ
λ x 4.
π
Hα
µ
ω h λ x
Hα ≈ 0.37ωh
0
dH dt H β
Region of negative Hubble gradient
η 1 .10
84
2 .10
84
3 .10
84
4 .10
84
5 .10
84
1
(Hz^2)
dH dt e
5 .µ
2
St T
1 dH dt e
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH dt e
4.µ
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
.
2 .µ
2 λ x. ω h
µ ( 4.µ ) . c
2
t
π
1 H γ .H α
Hγ Hβ
η
2 2
1
1
Cosmological Inflation
Cosmological Expansion
84 6 .10
7 .10
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
t2
e
1
t1
Hα
dH dt H β
5 .µ
η
2
(Hz)
2 2 5 .µ . 5 .µ
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
H = HβHα
5
9
.
r2 r1
dH dt e
9
St ω
→
TU2(H) → TU3(Hβ)
T U2 ( H ) K W . St T . ln
T U3 H β
K W .St T .ln
Hα
1 .10
42
5 .10
41
t4
2
4
2 2 2 5 .µ . 5 .µ . 5 .µ
. 2
.H5 µ
1
2
1
t4
5 .µ
0 43 1 .10
2
K W .St T .
2 5 .ln H α .t .µ
t
2
5 .µ
2
1
.t
e
1 .10
42
1 .10
41
Big-Bang: 0(K)
1 .10
40
1 .10
39
1 .10
38
37 36 1 .10 1 η H β .H α Cosmological Age (s)
1 .10
1 .10
35
1 .10
34
1 .10
33
1 .10
32
1 .10
31
1 .10
30
e
2 2 5 .µ . ln H α .t . 5 .µ
1
2 2 5 .µ . 5 .µ
dT2 dt2 ( t )
. 1 Hα
1
2
2 2 2 5 .µ . 5 .µ . 5 .µ
2 2 5 .µ . 5 .µ
2 2 5 .µ . 5 .µ
t5
. H .H β α
dT dt ( t )
K W .St T .
t 2
3
2
. 1 Hα
dT3 dt3 ( t )
K W .St T .
5 .µ
2
1
2
1
.t 2
2 2 2 5 .µ .ln H α .t . 5 .µ . 5 .µ
t
3 5 .µ
2
2 .t
2 2 15.µ . 5 .µ
2
2
3
2.
1
H
Hβ
e
1
2 2 5 .µ . 5 .µ
2
42
1 dH dt e
t3
Hubble Inflation Hubble Expansion
1 1.5 .10
. 1 Hα
2 2 15 .µ . 5 .µ
Thermal Inflation
42
1 dH dt e
2
Max. Cosmological Temp. Line: 3.2x1031(K)
Primordial Inflation 2 .10
5 .µ
10 .µ
36
Mag. of Hubble Cons. vs. Cosm. Age
42
e
Max. Cosmological Temp. Line: 3.2x1031(K)
84
2.5 .10
t1
dH dt H γ
. 1 Hα
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
2
1
2
. 1 Hα
dH2 dt2 H γ
Hα Hγ . 5 .ln 1 .µ 2 2 Hγ 5 .µ Hγ 3 2 H α .H γ
Hγ
5 .µ
2
1
. 5 .µ 2 . ln 1 . 5.µ2 Hγ
1
2
1
(i) “Big-Bang” properties: “t = 1/Hα”, “H = Hα”, “TU2(Hα) = TU3(1) = 0(K)”; (ii) “Maximum Cosmological Temperature = 3.2 x1031(K)” @ “t = t1”
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
Key Artefact & Equation Summary [excerpt from “Quinta Essentia – Part 2” dgE]
ω Ω r 1 , M1
M1
ω Ω r 2 , M2
M2
5
9
.
r2 r1
9
St ω
dgE
Mag. of Hubble Cons. vs. Cosm. Age
EGM 1
The Cosmological Evolution Process 2.5 .10
Derived From Particle-Physics
42
Max. Cosmological Temp. Line: 3.2x1031(K)
t1
Hα
2
H = HβHα
Primordial Inflation
Thermal Inflation 42 2 .10 dH dt H β
dH dt e
M1
ω Ω r 2, M 2
M2
2
Hα
Region of positive Hubble gradient
t4
t1
0
42
0
Region of negative Hubble gradient
η 84 1 .10
FOR MORE INFO...
1
dH dt e
4
2
1
2
1 .10
42
84 2 .10
1 dH dt e
2 2 5 .µ . 5 .µ
1 84 3 .10
2 2 5 .µ . 5 .µ
2 1
5 .µ
dH dt e
2
4
2 2 2 5 .µ . 5 .µ . 5 .µ
1
2
84 4 .10
St T
H α
λ x 4.
http://www.deltagroupen gineering.com/public ations.htm
π
Hα ≈ 0.37ωh
λ x
5 .10
µ
λ x .ω h 4 .µ . µ π ( 4 .µ ) .c
ω h
1 .10
2 .µ
2
41
2 2 .µ
0 43 1 .10
1 .10
42
1 .10
41
1 .10
Big-Bang: 0(K)
40
1 .10
39
1 .10
t = (ΗβηΗα)-1
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
38
1 .10
37
1 .10 1
36
Gr ap h 15 dgE
Cosmological Expansion
Cosmological Inflation
Max. Cosmological Temp. Line: 3.2x1031(K)
84 7 .10
G .h
1
84 1 .10
84 5 .10
5
H
1
2 2 2 5 .µ . 5 .µ . 5 .µ
c
. 2
. H5 µ
Hα Hγ . 5 .ln 1 .µ 2 2 Hγ 5 .µ Hγ
dH dt H γ
84 6 .10
ω h
Hα
1st Derivative of the Hubble Constant
(Hz^2)
(Hz)
T U2( H ) K W . St T . ln 2.
1
dH dt H β
2 2 5 .µ . 5 .µ dH dt e
→
84 2 .10
1 2 2 5 .µ . 5 .µ
St ω
Hγ = Ηβη
t4
1
9
r1
Hubble Expansion 1.5 .10
dH dt e
r2
.
Hubble Inflation
η
1 5 .µ
ω Ω r 1, M 1
5
9
43
1 .10
1 .10
35
42
1 .10
1 .10
η H β .H α Cosmological Age (s)
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
41
34
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
1 .10
33
39
1 .10
1 .10
32
38
1 .10
1 .10
37
31
1 .10
36
1 .10
30
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
1st Derivative of the Hubble Constant
EGM
2 .10
84 1
The Cosmological Evolution Process
Hα
Derived From Particle-Physics 1 .10
Region of positive Hubble gradient
t4
t1
84
0 0 2nd Derivative of the Hubble Constant 8 .10
t5
η
dH dt H β
84 1 .10
6 .10
2
1 2 .10
dH2 dt2 H β
84
dH dt e
2 2 5 .µ . 5 .µ
1
dH2 dt2 e
4
dH dt e
η 125 5 .10
5 .µ
2
1
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH2 dt2 e
2 2 2 5 .µ . 5 .µ . 5 .µ
4 .10
125
3 .10
125
2 .10
125
2
1 .10
125
2 2 2 5 .µ . 5 .µ . 5 .µ
1
2
84 4 .10
ω h
St T
H α
2
1
0 0
1 .10
Hγ = Ηβ
1
2
4
2 1
3 2 H α .H γ . 5 .µ 2 . ln 1 . 5 .µ 2 2 Hγ 5 .µ Hγ
dH2 dt2 H γ
1
84 3 .10 2 2 5 .µ . 5 .µ
125
1 dH2 dt2 e
1 (Hz^3)
(Hz^2)
5 .µ
125 7 .10
Region of negative Hubble gradient
1 dH dt e
125
125
η 5 .10
c
5
G .h
λ x
ω h
π 2
µ
Cosmological Inflation 6 .10
84
7 .10
84
42
1 .10 η H β .H α
Cosmological Expansion
41
1 .10
40
1
Cosmological Age (s)
2 2 .µ
Hα ≈ 0.37ωh
λ x
1 .10
2 .µ
4.
λ x .ω h 4 .µ . µ π ( 4 .µ ) .c
84
Max. Cosmological Temp. Line: 3.2x1031(K)
1 .10
43
1 .10
42
Big-Bang: 0(K)
1 .10
41
1 .10
t = (ΗβηΗα)-1
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
40
1 .10
39
1 .10
38
1 .10
37
1 .10
36
1
η H β .H α Cosmological Age (s)
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
Av. Cosmological Temperature vs. Age
EGM
2
1
The Cosmological Evolution Process
t1
Hα
Derived From Particle-Physics
H = HβHα
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
5
9
.
r2 r1
9
St ω
TU2(H) → TU3(Hβ) t1
71 8 .10
t2
K W .St T .
dT dt ( t )
2 5 .ln H α .t .µ 5 .µ
2
2.5 .10
31
2 .10
31
1.5 .10
31
1 .10
31
5 .10
30
1
.t
71 4 .10
2 5 .µ
71 2 .10 dT dt
2 10 .µ
1
2 2 5 .µ . 5 .µ
H β .H α
1
dT dt t 1 (K/s)
0 5 .10
t2
dT dt t 3
1
2nd Derivative of Av. Cosmological Temp.
113
dT dt t 2 2 .10
71
4 .10
71
t3
0
dT2 dt2( t )
t
t2
H β .H α
3
2
8 .10
5 .µ
2
1
2
1
.t2
t3
1 114 1 .10
1 .10156
dT2 dt2 t 1 dT2 dt2 t 2 dT2 dt2 t 3
1.5 .10114
dT3 dt3 (K/s^3)
2 2 2 5 .µ . 5 .µ . 5 .µ
71 6 .10
2
2
2 2 5 .µ . ln H α .t . 5 .µ
3rd Derivative of Av. Cosmological Temp.
1 .10157
dT2 dt2
2 2 15 .µ . 5 .µ
K W .St T .
5 .10113
(K/s^2)
Av. Cosmological Temperature (K)
31
71 6 .10
1
T U3 e
3 .10
. 2
. H5 µ
H
t
T U3 H β
T U3 e
Hα
T U2( H ) K W . St T . ln
31
1st Derivative of Av. Cosmological Temp.
72 1 .10
T U3 e
→
3.5 .10
H β .H α
1 .10155 1
dT3 dt3 t 1 dT3 dt3 t 2 1 .10154
71
114 2 .10
1 .10153
dT3 dt3( t )
114 2.5 .10
1 .10
72
1.2 .10
72
3 .10114 42 2 .10
Hγ = Ηβη
42 1 .10
K W .St T .
2 2 2 5 .µ .ln H α .t . 5 .µ . 5 .µ
t 1 .10152 42 2 .10
3 .10
42
4 .10
42
41 1 .10
5 .10
42
6 .10
42
3 .10
7 .10
42
42
42
5 .10
8 .10
42
4 .10
42
6 .10
42
7 .10
42
8 .10
42
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
1.1 .10
41
1.1 .10
1.2 .10
41
1.2 .10
41
41
3 5 .µ
2
2
1.3 .10
2 2 15.µ . 5 .µ
2
2
.t 3
1.3 .10
41
41
1.4 .10
41
1.4 .10
1.5 .10
41
40 1 .10
41
1.5 .10
41
1 .10
39
1 H β .H α Cosmological Age (s)
ω h
St T
H α
c
5
λ x
G .h
2 .µ π
4 .µ ( 4 .µ )
4.
. µ
ω h
.c
λ x .ω h
µ
2
π
Hα ≈ 0.37ωh
λ x
2 2 .µ
1 .10
43
1 .10
42
1 .10
Big-Bang: 0(K)
41
1 .10
t = (ΗβηΗα)-1
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
40
1 .10 H β .H α
39
1 .10
1
Cosmological Age (s)
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
38
1 .10
37
1 .10
36
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
EGM
3.5 .10
Av. Cosmological Temp. vs. Hubble Cons.
31 Hα
The Cosmological Evolution Process
2
1 t1
Derived From Particle-Physics
H = HβHα
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
31 3 .10
3.5 .10
TU2(H) → TU3(Hβ)
5
9
.
r2
9
St ω
r1
→
Hα
T U2( H ) K W . St T . ln
. 2
. H5 µ
H
Av. Cosmological Temp. vs. Hubble Cons.
31
Av. Cosmological Temperature vs. Age
1
1
t2
t3
1
3.5 .1031
t1
Hα
3 .1031
3 .10
31 2.5 .1031
31 2.5 .10 1
T U3 e
2 5 .µ 31 2 .10 2 10 .µ
T U3 e
2 2 5 .µ . 5 .µ
T U3 e
ω h
St T
H α
2 2 2 5 .µ . 5 .µ . 5 .µ
c
5
λ x
G .h
2 3
λ x .ω h . µ π ( 4 .µ ) .c
ω h
1.5 .10
2 2 .1031 2
2 2 5 .µ . 5 .µ
1 1
2 2 15 .µ . 5 .µ T U3 e
2 2 2 5 .µ . 5 .µ . 5 .µ
2
1.5 .1031
2 3
2
5 .µ
1 .1031
2 5 .1030
31 2 .10 10 .µ
2
1 1 .10
T U3 e
2 2 5 .µ . 5 .µ
2 2 15 .µ . 5 .µ T U3 e
43
1 .10
42
1
2 2 2 5 .µ . 5 .µ . 5 .µ
2
2 3
1 .10
41
1 .10
40
1 .10 1 H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
31 1.5 .10 2
1 .10
31
5 .10
30
31 1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 H β .H α Hubble Constant (Hz)
39
1 .10
38
1 .10
37
1 .10
36
2
1 .10
31
2
5 .10
30
µ
2 2 .µ
Hα ≈ 0.37ωh
λ x
5 .µ
10 .µ T U3 e
2 .µ
4.
π
4 .µ
T U3 e
1
2
1 T U3 e
1
1
2 2 15 .µ . 5 .µ
31 2.5 .10
T U3 H β Av. Cosmological Temperature (K)
Av. Cosmological Temperature (K)
T U3 H β
Av. Cosmological Temperature (K)
T U3 H β
1 .10
43
1 .10
42
1 .10
41
1 .10
Big-Bang: 0(K) Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
40
1 .10 . Hβ Hα Hubble Constant (Hz)
39
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
1 .10
38
1 .10
37
1 .10
36
www.deltagroupengineering.com dgE Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
The Cosmological evolution process derived from Particle-Physics utilising the EGM construct (1 of 2) e
5 .µ
Av. Cosmological Temperature vs. Age
Av. Cosmological Temperature
1
31 3.5 .10
1
e
31 3 .10
31 3 .10
31 2.5 .10
1 T U3 e
2 5 .µ 31 1.5 .10
1 .10
0.01
3
1 .10
4
1 .10
5
1 .10
1 .10
6
43
42
1 .10
1 .10
41
1 .10
40
Hβ Dimensionless Range Variable
1 .10 1 H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
5 .µ
2 31 2 .10 2 10 .µ
T U3 e
1
2 2 5 .µ . 5 .µ
1
2 2 15 .µ . 5 .µ T U3 e
2
2 2 2 5 .µ . 5 .µ . 5 .µ
31 1.5 .10
2 3
2
Av. Cosmological Temp. vs. Hubble Cons.
3.5 .10
31
1
1.5 .10
31
T U3 H β
2
10 .µ
2
1 1
2 2 15 .µ . 5 .µ T U3 e
2
2
2 2 2 5 .µ . 5 .µ . 5 .µ
3
2 2 15 .µ . 5 .µ T U3 e
2 2 2 5 .µ . 5 .µ . 5 .µ
2
30 5 .10
1 .10
36
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 1 H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
1 .10
36
Av. Cosmological Temperature vs. Size
1
c
2.5 .10
31
2 .10
31
3.5 .10
10 .µ T U3 e
2
1.5 .10
31
1
2 2 5 .µ . 5 .µ
1
2 2 15 .µ . 5 .µ T U3 e
2
2
2 2 2 5 .µ . 5 .µ . 5 .µ
41
1 .10
40
39
1 .10 1 H β .H α Cosmological Age (s)
1 .10
38
1 .10
37
1 .10
36
3
Av. Cosmological Temperature vs. Size
31
3.5 .10
2
2.5 .10
31
2 .10
31
1.5 .10
31
T U3 H β
1 T U3 e
2
5 .µ
10 .µ T U3 e
2
1
2 2 5 .µ . 5 .µ
1
2 2 15 .µ . 5 .µ T U3 e
2
2 2 2 5 .µ . 5 .µ . 5 .µ
2 3
31
31 3 .10
2
2.5 .10
31
2 .10
31
1.5 .10
31
1 2
5 .µ
T U3 e
10 .µ
2
1
2 2 5 .µ . 5 .µ
T U3 e
1
2 2 15 .µ . 5 .µ
2
2 2 2 5 .µ . 5 .µ . 5 .µ
T U3 e
2 3
2
31
1 .10
31
1 .10
31
1 .10
31
5 .10
30
5 .10
30
5 .10
30
43
1 .10
42
1 .10
41
1 .10
40
1 .10 H β .H α Hubble Constant (Hz)
39
1 .10
38
37 1 .10
36 1 .10
1 .10
1st Derivative of Av. Cosmological Temp. t1
43
1 .10
42
1 .10
41
1 .10
40
1 .10 H β .H α Hubble Constant (Hz)
39
1 .10
38
37 1 .10
36 1 .10
1 .10
t2
71 8 .10
34
1 .10
33
1 .10
32
1 .10
31
1 .10
30
29
1 .10
1 .10
28
1 .10
27
71 6 .10
71 4 .10
34
1 .10
1 .10
33
1 .10
32
1 .10
1. H β .H α c EGM Cosmological Size (m)
1st Derivative of Av. Cosmological Temp.
72 1 .10
t2
2nd Derivative of Av. Cosmological Temp.
113 5 .10
t3
t1
5 .10
113
1 .10
114
31
1 .10
30
1 .10
29
1 .10
28
1 .10
27
1. H β .H α c EGM Cosmological Size (m)
2nd Derivative of Av. Cosmological Temp.
113 5 .10
t2
t2
t3
0
5 .10
113
1 .10
114
1.5 .10
114
114
2 .10
114
114 2.5 .10
2.5 .10
114
3 .10
114
71 2 .10
1
dT dt
H β .H α
1
dT2 dt2
dT dt t 1
71 2 .10
0
(K/s^2)
(K/s)
0
dT dt t 2
dT dt t 2 71 2 .10
dT dt t 3
71 4 .10
71 4 .10
71 6 .10
71 6 .10
71 8 .10
71 8 .10
72 1 .10
1
H β .H α
dT2 dt2
dT2 dt2 t 1
(K/s^2)
71 2 .10
(K/s)
1 .10
t 2 .c t 3 .c
T U3 H β
2
5 .µ
71 4 .10
dT2 dt2 t 2 dT2 dt2 t 3
dT2 dt2 t 1 dT2 dt2 t 2 dT2 dt2 t 3
114 1.5 .10
2 .10
1
H β .H α
72 1 .10
72 1.2 .10 42 1 .10
1 .10
41
1 .10
40
1 .10
72 1.2 .10 42 1 .10
39
1 .10
41
1 .10
1 H β .H α Cosmological Age (s)
40
1 .10
3 .10
39
114 2 .10
42
3 .10
42
4 .10
42
5 .10
42
42
6 .10
7 .10
42
8 .10
42
1 H β .H α Cosmological Age (s)
3rd Derivative of Av. Cosmological Temp.
157
t1
1 .10
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
t2
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
41
2 .10
42
3 .10
42
4 .10
42
5 .10
42
6 .10
156
1 .10
42
7 .10
42
8 .10
42
42 41 9 .10 1 .10 1 H β .H α Cosmological Age (s)
1.1 .10
1st Derivative of the Hubble Constant
3rd Derivative of Av. Cosmological Temp.
157
t2
1.1 .10
1.6 .10
t3
t1
156
1.4 .10
84
1.2 .10
84
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
41
1st Derivative of the Hubble Constant 2 .10
84
84 1
t4
t4
t1
Hα 1 .10
1 .10
42
31 3 .10
1 T U3 e
71 6 .10
1 .10
1 .10
t 1 .c
Hα
0
dT dt t 3
43
30
71 8 .10
dT dt t 1
2
1 .10
72 1 .10
H β .H α
31 1.5 .10
2 3
5 .10
1 .10
dT dt
2
30 5 .10
t2 t3
1
2 2 5 .µ . 5 .µ
1
30 5 .10
Av. Cosmological Temperature (K)
31
2 .10
1
31 1 .10
31 3 .10
Av. Cosmological Temperature (K)
Av. Cosmological Temperature (K)
2.5 .10
31 2 .10 2
31 1 .10
Av. Cosmological Temp. vs. Hubble Cons.
31
1 t1
31 3 .10
T U3 H β
2
10 .µ T U3 e
2 2 5 .µ . 5 .µ
Big-Bang: 0(K)
31 Hα
5 .µ
31 1 .10
Average Cosmological Temperature Maximum Av. Cosmological Temperature
3.5 .10
1 T U3 e
Av. Cosmological Temperature (K)
0.1
T U3 H β
1 T U3 e
Av. Cosmological Temperature (K)
31 2 .10
30 5 .10
1
T U3 H β Av. Cosmological Temperature (K)
2
T U3 H β
31 1 .10
T U3 e
31 3.5 .10
t3
31 2.5 .10
31 1.5 .10
5 .µ
t2
31 3 .10
1
T U3 e
Av. Cosmological Temperature vs. Age
31 3.5 .10
t1
31 2.5 .10
31 2 .10
5 .µ
1 Hα
31 2.5 .10
T U3 H β
T U3 e
2 5 .µ . 1 Hα
31 3 .10
Av. Cosmological Temperature (K)
Av. Cosmological Temperature (K)
Hα
Av. Cosmological Temperature vs. Age
31 3.5 .10
1
2
Region of positive Hubble gradient
84
0 0
dH dt H β
η
dH dt H β
1 155 dT3 dt3
dT3 dt3 t 2 1 .10
H β .H α
1 .10 1
155
dH dt e
dT3 dt3 t 1 dT3 dt3 t 2
154
1 .10
153
1 .10
2
1 .10
1
dH dt e
2 2 5 .µ . 5 .µ
dH dt e
2 2 5 .µ . 5 .µ
154
8 .10
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
2 1
2
6 .10
83
5 .µ
dH dt e
2 .10
83
84
2 .10
84
3 .10
84
4 .10
84
5 .10
84
6 .10
84
7 .10
84
1
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH dt e
83
2
1
83
4 .10
1 .10 1
84
1
dH dt e
1 .10
5 .µ
(Hz^2)
1 .10 1
(Hz^2)
H β .H α
(K/s^3)
(K/s^3)
dT3 dt3
dT3 dt3 t 1
Region of negative Hubble gradient
η
4
2 2 2 5 .µ . 5 .µ . 5 .µ
2 1
2
Cosmological Inflation
0 0 1 .10
152 2 .10
42
3 .10
42
4 .10
42
5 .10
42
6 .10
42
7 .10
42
8 .10
42
9 .10
42
H β .H α
1 .10 1
41
1.1 .10
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
1 .10
41
Max. Cosmological Temp. Line: 3.2x1031(K)
152 2 .10
42
3 .10
42
4 .10
42
5 .10
42
6 .10
42
7 .10
42
8 .10
42
9 .10
42
H β .H α
Cosmological Age (s)
1 .10 1
41
1.1 .10
41
1.2 .10
41
1.3 .10
41
1.4 .10
41
1.5 .10
41
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 η H β .H α
Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
1 .10
43
1 .10
42
1 .10
41
1
Cosmological Age (s)
2
H = HβHα
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
Cosmological Expansion
153
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
5
9
.
r2 r1
9
St ω
→
T U2( H ) K W . St T . ln
Hα H
. 2
. H5 µ
TU2(H) → TU3(Hβ)
T U3 H β
(i) “Big-Bang” properties: “t = 1/Hα”, “H = Hα”, “TU2(Hα) = TU3(1) = 0(K)”; (ii) “Maximum Cosmological Temperature = 3.2 x1031(K)” @ “t = t1”
K W .St T .ln
1 Hβ
. H .H β α
5 .µ
2
www.deltagroupengineering.com dgE
The Cosmological evolution process derived from Particle-Physics utilising the EGM construct (2 of 2) 1st Derivative of the Hubble Constant 2 .10 t2 1 .10
2nd Derivative of the Hubble Constant
1st Derivative of the Hubble Constant
84
t5
84
1 .10
t4
0
1 .10 1
2 5 .µ
1
2 2 5 .µ . 5 .µ
2 .10
84
3 .10
84
dH dt e
1
4
2 2 5 .µ . 5 .µ
4 .10
84
5 .10
6 .10
7 .10
2 .10
84
3 .10
84
1
2 2 5 .µ . 5 .µ 2
1
1 1
dH dt e
2
2 2 2 5 .µ . 5 .µ . 5 .µ
127
4 .10
127
3.5 .10
127
t1
t2
t3
4
dH2 dt2 H β
2 2 2 5 .µ . 5 .µ . 5 .µ
3 .10
127
127
2.5 .10
127
2 .10
127
dH2 dt2 H β
η
127 1.5 .10 2
1
127
η
2 4 .10
84
84
5 .10
84
84
6 .10
84
84
7 .10
84
dH dt e
3 .10
2.5 .10
84
(Hz^3)
1
2 2 5 .µ . 5 .µ dH dt e
η
2 5 .µ
1 dH dt e
3.5 .10
1 Hα
0
dH dt H β
84
(Hz^2)
(Hz^2)
dH dt e
127
0
η 1 .10
4 .10
84
0
dH dt H β
2nd Derivative of the Hubble Constant
84
t3
(Hz^3)
2 .10
2 .10
127
1.5 .10
127
1 .10
127
1 .10
127
5 .10
126
5 .10
126
0
43
1 .10
42
1 .10
41
1 .10
40
39
1 .10 1 η H β .H α Cosmological Age (s)
1 .10
38
1 .10
37
1 .10
36
1 .10
43
1 .10
42
1 .10
2nd Derivative of the Hubble Constant
4 .10
127
3.5 .10
127
3 .10
127
41
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
36
2nd Derivative of the Hubble Constant
t1
dH2 dt2 H β
125 5 .10
127
1.5 .10
127
5 .µ
2
2 2 5 .µ . 5 .µ
1
125 3 .10
2 2 5 .µ . 5 .µ dH2 dt2 e
1 .10
dH2 dt2 e
125 4 .10
1 dH2 dt2 e
t5
125 6 .10
η
dH2 dt2 H β
125 5 .10
4
2 2 2 5 .µ . 5 .µ . 5 .µ
5 .µ
2 2 5 .µ . 5 .µ
125 2 .10
2
dH2 dt2 e
1
125 3 .10 4
2 2 2 5 .µ . 5 .µ . 5 .µ
dH2 dt2 e
1
125 4 .10
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ
125 3 .10 4
2
2 2 2 5 .µ . 5 .µ . 5 .µ
dH2 dt2 e
125 2 .10
2
1
125 1 .10
125 1 .10 0
0
0
125 1 .10
0
2
1
125 2 .10
2
0
126
5 .µ
2 1
125 1 .10
127
dH2 dt2 e
125 4 .10
2 2 5 .µ . 5 .µ
2 1
1 1
dH2 dt2 e
125 5 .10 1
2
0
5 .10
η
1 1
40
125 7 .10
125 6 .10
η
1 .10
2nd Derivative of the Hubble Constant
t4
125 7 .10
(Hz^3)
2 .10
(Hz^3)
(Hz^3)
dH2 dt2 H β
dH2 dt2 e
41 1 .10 1 η H β .H α Cosmological Age (s)
t3
1
127
42 1 .10
125 8 .10
t2
125 6 .10
η
43 1 .10
125 8 .10
t4
dH2 dt2 H β
40 1 .10
2nd Derivative of the Hubble Constant
125 8 .10
t5
41 1 .10 1 η H β .H α Cosmological Age (s)
125 7 .10
2.5 .10
0
42 1 .10
(Hz^3)
1 .10
0
0
43 1 .10
0
125 1 .10
125 1 .10
0
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10
42
1 .10
Mag. of Hubble Cons. vs. Cosm. Age 1 42
40
42
1 .10
1 .10
Max. Cosmological Temp. Line: 3.2x1031(K)
2.5 .10
42
1 .10
40
1 .10
42
41 1 .10 1 η H β .H α Cosmological Age (s)
η H β .H α Cosmological Age (s)
Av. Cosmological Temp. vs. Hubble Cons.
31 3.5 .10
40
1
Hα
t1
31 3 .10
1 .10
Av. Cosmological Temp. vs. Hubble Cons.
31 3.5 .10
1
Hα
t4
Hα
41 1
Mag. of Hubble Cons. vs. Cosm. Age 1
t1
Hα
1 .10
η H β .H α Cosmological Age (s)
η H β .H α Cosmological Age (s)
2.5 .10
41 1
1
t1
31 3 .10
Primordial Inflation
5 .µ
2
1 1.5 .10
dH dt e
42
(Hz)
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH dt e
4
2 1
2
1 .10
31 2.5 .10
1
2 2 5 .µ . 5 .µ
42
1
2 2 5 .µ . 5 .µ
42 dH dt e
5 .10
2
1 dH dt e
2 2 2 5 .µ . 5 .µ . 5 .µ
5 .µ
1.5 .10
t4
1 dH dt e
42
η
1
(Hz)
dH dt e
2 .10 dH dt H β
Hubble Inflation Hubble Expansion
4
2 2 2 5 .µ . 5 .µ . 5 .µ
41
2 1
2
1 .10
42
5 .10
41
T U2
dH dt H β
31 2.5 .10 Av. Cosmological Temperature (K)
Thermal Inflation
42
η
1
Av. Cosmological Temperature (K)
2 .10 dH dt H β
η 31 2 .10
T U3 H β 1 T U3 e
5 .µ
2 31 1.5 .10
1 .10
42
1 .10
41
1 .10
40
1 .10
39
1 .10
Big-Bang: 0(K)
Time
38
37 36 1 .10 1 η H β .H α Cosmological Age (s)
1 .10
1 .10
35
1 .10
34
TU2 (K)
1 .10
33
1 .10
32
1 .10
31
1 .10
0 43 1 .10
30
dHdt (km/s/Mpc)2
1 .10
42
1 .10
41
1 .10
40
1 .10
39
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t4 ≈ 2.093267·10-41(s) 9
AU ≈ 14.575885·10 (yr) Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
≈ 2.059945·1031 ≈ 2.724752
0
1 .10
35
3
≈ 3.845994·1061
34
1 .10
33
1 .10
32
1 .10
31
1 .10
Hα
t1
ω h λ x
t2
1 .10
2 . 4.µ . λ x ω h St T µ π ( 4.µ ) . c
t
e
e
2 .µ
t3
e
2
42
41 1 .10
. 1 Hα
1 .10
40
1 .10
39
2
dT dt ( t )
38 1 .10
1 .10
37
36 1 .10
43 1 .10
1 .10
42
41 1 .10
1 .10
2 5 .ln H α .t .µ
K W .St T .
1
2 2 5 .µ . 5 .µ
dT2 dt2 ( t )
. 1 Hα
1
2
2 2 2 5 .µ . 5 .µ . 5 .µ
K W .St T .
5 .µ
2
2
. 1 Hα
dT3 dt3 ( t )
39
38 1 .10
1 .10
37
36 1 .10
1
2 2 5 .µ . ln H α .t . 5 .µ 5 .µ
2
.t
1
2
K W .St T .
1
2
2.
2
1 .10
.t
t
3
40
η dH dt H β Hubble Constant (Hz)
t
2 2 5 .µ ln H α .t . 5 .µ . 5 .µ
t
1
t4
e
t5
e
2 2 5 .µ . 5 .µ
2 2 5 .µ . 5 .µ
η
31 1.5 .10
3
2
2 2 15.µ . 5 .µ
2
2
2 5 .µ . 3
t
2
1 H γ .H α
Hγ Hβ
5 .µ
2 2 15 .µ . 5 .µ
Hα ≈ 0.37ωh
2
30 5 .10
10 .µ
µ
5 .µ
η dH dt H β , H β .H α Hubble Constant (Hz)
2.µ π
31 2 .10
1 T U3 e
31 1 .10
1
λ x 4.
η
31 1 .10
30
5
≈ 67.084304
Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
1 .10
c G. h
0
≈ 1.479167·10123 ≈ 4.500304·10
37 36 1 .10 1 η H β .H α Cosmological Age (s)
1 .10
ω h
-∞
≈ 3.195518·1031
38
|H| (km/s/Mpc)
0
t1 ≈ 2.206287·10-42(s)
1 .10
dH dt H β
30 5 .10
43 1 .10 0 43 1 .10
T U2
2.
. 1 Hα
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
dH dt H γ
Hγ
2 1
Hα Hγ
2
. 1 Hα
dH2 dt2 H γ
5 .µ
2
. 5 .ln 1 .µ 2 Hγ
1
3 2 H α .H γ . 5 .µ 2 . ln 1 . 5.µ2 2 Hγ . 5µ Hγ
1
2
1
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
www.deltagroupengineering.com dgE
The Deceleration Parameter “q0” & Cosmological Constant “Λ0” [excerpts from “Quinta Essentia – Part 2” dgE]
1st Derivative of the Hubble Constant 2 .10
84 1
1 .10
t4
t1
Hα
Region of positive Hubble gradient
5
84
c G. h
ω h 0
2.µ
λ x 4.
π
Hα
µ
ω h λ x
Hα ≈ 0.37ωh
0
dH dt H β
Region of negative Hubble gradient
η 1 .10
84
2 .10
84
3 .10
84
4 .10
84
5 .10
84
1
(Hz^2)
dH dt e
5 .µ
2
St T
1 dH dt e
2 2 5 .µ . 5 .µ
1
2 2 5 .µ . 5 .µ dH dt e
4.µ
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
.
2 .µ
2 λ x. ω h
µ ( 4.µ ) . c
2
t
π
1 H γ .H α
Hγ Hβ
η
2 2
1
1
Cosmological Inflation
Cosmological Expansion
84 6 .10
7 .10
1 .10
43
1 .10
42
1 .10
41
1 .10
40
1 .10 1 η H β .H α Cosmological Age (s)
39
1 .10
38
1 .10
37
1 .10
t2
e
1
t1
Hα
dH dt H β
5 .µ
η
2
(Hz)
2 2 5 .µ . 5 .µ
ω Ω r 1, M 1
M1
ω Ω r 2, M 2
M2
H = HβHα
5
9
.
r2 r1
dH dt e
9
St ω
→
TU2(H) → TU3(Hβ)
T U2 ( H ) K W . St T . ln
T U3 H β
K W .St T .ln
Hα
1 .10
42
5 .10
41
t4
2
4
2 2 2 5 .µ . 5 .µ . 5 .µ
. 2
.H5 µ
1
2
1
t4
5 .µ
0 43 1 .10
2
K W .St T .
2 5 .ln H α .t .µ
t
2
5 .µ
2
1
.t
e
1 .10
42
1 .10
41
Big-Bang: 0(K)
1 .10
40
1 .10
39
1 .10
38
37 36 1 .10 1 η H β .H α Cosmological Age (s)
1 .10
1 .10
35
1 .10
34
1 .10
33
1 .10
32
1 .10
31
1 .10
30
e
2 2 5 .µ . ln H α .t . 5 .µ
1
2 2 5 .µ . 5 .µ
dT2 dt2 ( t )
. 1 Hα
1
2
2 2 2 5 .µ . 5 .µ . 5 .µ
2 2 5 .µ . 5 .µ
2 2 5 .µ . 5 .µ
t5
. H .H β α
dT dt ( t )
K W .St T .
t 2
3
2
. 1 Hα
dT3 dt3 ( t )
K W .St T .
5 .µ
2
1
2
1
.t 2
2 2 2 5 .µ .ln H α .t . 5 .µ . 5 .µ
t
3 5 .µ
2
2 .t
2 2 15.µ . 5 .µ
2
2
3
2.
1
H
Hβ
e
1
2 2 5 .µ . 5 .µ
2
42
1 dH dt e
t3
Hubble Inflation Hubble Expansion
1 1.5 .10
. 1 Hα
2 2 15 .µ . 5 .µ
Thermal Inflation
42
1 dH dt e
2
Max. Cosmological Temp. Line: 3.2x1031(K)
Primordial Inflation 2 .10
5 .µ
10 .µ
36
Mag. of Hubble Cons. vs. Cosm. Age
42
e
Max. Cosmological Temp. Line: 3.2x1031(K)
84
2.5 .10
t1
dH dt H γ
. 1 Hα
1
4
2 2 2 5 .µ . 5 .µ . 5 .µ
2
1
2
. 1 Hα
dH2 dt2 H γ
Hα Hγ . 5 .ln 1 .µ 2 2 Hγ 5 .µ Hγ 3 2 H α .H γ
Hγ
5 .µ
2
1
. 5 .µ 2 . ln 1 . 5.µ2 Hγ
1
2
1
(i) “Big-Bang” properties: “t = 1/Hα”, “H = Hα”, “TU2(Hα) = TU3(1) = 0(K)”; (ii) “Maximum Cosmological Temperature = 3.2 x1031(K)” @ “t = t1”
Time
TU2 (K)
dHdt (km/s/Mpc)2
|H| (km/s/Mpc)
0
-∞
-∞
+∞
Hα-1 ≈ 3.646967·10-43(s)
0
≈ -7.158752·10123
≈ 8.460941·1061
t1 ≈ 2.206287·10-42(s)
≈ 3.195518·1031
0
0
t4 ≈ 2.093267·10-41(s)
≈ 2.059945·1031
≈ 1.479167·10123
≈ 3.845994·1061
AU ≈ 14.575885·109(yr)
≈ 2.724752
≈ 4.500304·103
≈ 67.084304
See: “Quinta Essentia Part 2, 3, 4” for the complete mathematical derivations and computational algorithms.
Applied Physical Constants NIST “≥ 2002” CODATA • c = 2.99792458·108 (ms-1) • G ≈ 6.6742·10-11 (m3kg-1s-2) • h ≈ 6.6260693·10-34 (Js) • KW ≈ 2.8977685·10-3 (mK) Derived Mathematical Constants λx, StT, Hα, η ≈ 4.595349, µ = 1/3 Graphic Range Variables Hβ, Hγ, t
Derived Physical Properties • Photon mass: mγγ ≤ 3.195095·10-45(eV) • Graviton mass: mgg = 2mγγ • Minimum gravitational lifetime of starving matter: TL = h/mγγ = 2h/mgg ≈ 4.101731·1022(yr) ≈ 2.814053·1012AU • Cosmological Constant: Λ0 ≈ 6.750456·103 (km/s/Mpc)2 Λ0/c2 ≈ 7.888431·10-47 (km-2) [3c2/8πG]·Λ0 ≈ 1.139608·10-9 (Pa)
Key Artefact & Equation Summary [excerpt from “Quinta Essentia – Part 2” dgE]
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