03 Cosmology

Computational Cosmology
Alexander Knebe, Universidad Autonoma de Madrid
The
Universe in a
Computer
Computational
Cosmology
Cosmology
Cosmology is the study
of the origin, evolution, and future
of our Universe
Computational Cosmology
Cosmology
Computational Cosmology
The Computational Aspect
Cosmology
The Computational Aspect
1
2
3
Computational Cosmology
Cosmology
The Vastness of the Universe
  orders of ten
http://hometown.aol.com/nlpjp/cosmo.htm!
Computational Cosmology
Cosmology
The Vastness of the Universe
  orders of ten
http://hometown.aol.com/nlpjp/cosmo.htm!
Computational Cosmology
Cosmology
The Vastness of the Universe
  orders of ten
http://hometown.aol.com/nlpjp/cosmo.htm!
Computational Cosmology
Cosmology
The Vastness of the Universe
  orders of ten
http://hometown.aol.com/nlpjp/cosmo.htm!
Computational Cosmology
Cosmology
The Vastness of the Universe
  orders of ten
how did these structure come about?
http://hometown.aol.com/nlpjp/cosmo.htm!
Computational Cosmology
Cosmology
The Vastness of the Universe
  galaxy catalogues (2D)
•  Shapley & Ames (1932) •  Palomar Sky Survey (1950)
•  Lick Survey (1967)
•  APM catalogue (1990) Lick map
Computational Cosmology
1,250 galaxies
~5,000 galaxies
~1,000,000 galaxies
~2,000,000 galaxies
APM catalogue
Cosmology
The Vastness of the Universe
  galaxy catalogues (3D)
•  CfA (1986)
Computational Cosmology
~1,000 galaxies Cosmology
The Vastness of the Universe
  galaxy catalogues (3D)
•  CfA (1986)
„Great Wall“
Computational Cosmology
~1,000 galaxies „CfA Stickman“
Cosmology
The Vastness of the Universe
  galaxy catalogues (3D)
•  Las Campanas Redshift Survey (1998)
Computational Cosmology
~20,000 galaxies Cosmology
The Vastness of the Universe
  galaxy catalogues (3D)
•  2dF Survey (2003)
Computational Cosmology
~200,000 galaxies
Cosmology
The Vastness of the Universe
  galaxy catalogues (3D)
•  Sloan Digital Sky Survey (2003) Computational Cosmology
~1,000,000 galaxies
Cosmology
The Vastness of the Universe
  galaxy catalogues (3D)
•  Sloan Digital Sky Survey (2003) CfA (1986)
Computational Cosmology
~1,000,000 galaxies
SDSS (2003)
Cosmology
GRT
Albert Einstein
Computational Cosmology
The Equations
isotropy
homogeneity
Friedmann Equations
Alexander Friedmann
Cosmology
The Equations
GRT
isotropy
homogeneity
Friedmann Equations
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
GRT
isotropy
homogeneity
Friedmann Equations
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
  comoving coordinates


r = a(t) x
a(t 0 ) = a0 = 1
€
€
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
  comoving coordinates
€


r = a(t) x
˙
˙

r = ax + a˙ x
˙

= ax + Hr
˙ 

r = v pec + Hr
2
⎛
⎞
˙
a
−3
k −2
Λ
H€2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
  comoving coordinates
€


r = a(t) x
˙
˙

r = ax + a˙ x
˙

= ax + Hr
˙ 

r = v pec + Hr
Hubble law
2
⎛
⎞
˙
a
−3
k −2
Λ
H€2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
  redshift: definition
z=
λ0 − λ
λ0
€
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
  redshift: relation to expansion
a
1
=
a0 1+ z
€
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
  redshift: interpretion as Doppler effect
z=
λ0 − λ v Hr
≈ =
λ0
c
c
€
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
a(t)
a˙
H(t) =
a
a˙˙a
q(t) = − 2
a˙
expansion factor of the Universe
Hubble parameter
deceleration parameter
€
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
2
⎛
⎞
˙
a
−3
k −2
Λ
H 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
Ωm =
8πG
ρm
3H 2
matter energy density
Ωr =
8πG
ρr
3H 2
radiation energy density
Λc 2
ΩΛ =
3H 2
cosmological constant
kc 2
Ωk = − 2
H
curvature of the Universe
2
⎛
⎞
˙
a
−3
k −2
Λ
H€ 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
The Equations
Ωm =
Ωr =
8πG
ρm
3H 2
8πG
ρr
3H 2
matter energy density
3H2/8πG = critical density to “close” the Universe
(ca. 1 H-atom per m3)
radiation energy density
Λc 2
ΩΛ =
3H 2
cosmological constant
kc 2
Ωk = − 2
H
curvature of the Universe
2
⎛
⎞
˙
a
−3
k −2
Λ
H€ 2 = ⎜ ⎟ =.H 02 (Ω r0 a −4 +Ω m
a
+Ω
a
+Ω
0
0
0 )
⎝ a ⎠
1
q=. Ω m −Ω Λ −Ω r
2
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Ω0m ≈ 0.3
Ω0Λ ≈ 0.7
Ω0r ≈ 2.3 ×10−5 h −2
Ω0k ≈ 0
€
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Ω0m ≈ 0.3
Ω0Λ ≈ 0.7
•  the Universe is spatially flat
€
•  ca. 30% of the total energy density comes from matter
•  ca. 70% of the total energy density is vacuum energy
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Ω0m ≈ 0.3 = 0.26 + 0.04
Ω0Λ ≈ 0.7
„dark matter“
luminous matter
•  the Universe is spatially flat
€
•  ca. 30% of the total energy density comes from matter
•  about 85% of that matter is “dark”
•  only 15% of all matter in the Universe is luminous
•  ca. 70% of the total energy density is vacuum energy
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Ω0m ≈ 0.3 = 0.26 + 0.04
Ω0Λ ≈ 0.7
€
Computational Cosmology
„dark matter“
luminous matter
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Ω0m ≈ 0.3 = 0.26 + 0.04
0
Λ
Ω ≈ 0.7
€
Computational Cosmology
?
„dark matter“
luminous matter
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
(non-baryonic) Dark Matter Candidates
axion:
10-5 eV
neutrino:
10eV
WIMP:
1-103 GeV
monopoles: 1016 GeV
Planck relics:
α β γ
1019 GeV (h c G )
primordial BHs:
>1015g
€
Computational Cosmology
???
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
(non-baryonic) Dark Matter Candidates
hot dark matter
warm dark matter
cold dark matter
axion:
10-5 eV
neutrino:
10eV
WIMP:
1-103 GeV
monopoles: 1016 GeV
Planck relics:
α β γ
1019 GeV (h c G )
primordial BHs:
>1015g
€
Computational Cosmology
???
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Bahcall et al. (1999)
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
T=2.726K
ΔT≈mK
ΔT≈µK
Bahcall et al. (1999)
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
T=2.726K
ΔT≈mK
ΔT≈µK
decomposition into spherical harmonics
Bahcall et al. (1999)
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
T=2.726K
COBE (1992)
WMAP (2003)
ΔT≈mK
ΔT≈µK
decomposition into spherical harmonics
Bahcall et al. (1999)
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Bahcall et al. (1999)
Computational Cosmology
Cosmology
ΛCDM - The Standard Model
  ΛCDM - Λ Cold Dark Matter
Bahcall et al. (1999)
Computational Cosmology
Cosmology
Summary
  background cosmology
H 2 = H 02 (Ω 0m a −3 +Ω 0Λ )
1
q= Ω m −Ω Λ
2
•  the Universe is spatially flat
Ω0m ≈ 0.3 = 0.26 + 0.04
Ω0Λ ≈ 0.7
€
•  ca. 30% of the total energy density comes from matter
•  about 85% of that matter is “dark”
•  only 15% of all matter in the Universe is luminous
•  ca. 70% of the total energy density is vacuum energy
€
Computational Cosmology
Computational Cosmology
?
generating the initial conditions
Computational Cosmology
coming soon…
?
running the simulation
?
analysing the data