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REES-SCIAMA EFFECT IN ACCELERATING UNIVERSE
Zdeněk Stuchlík and Jan Schee
Institute of Physics, Faculty of Philosophy and Science,Silesian University in Opava
Outline
● Cosmic Microwave Background Radiation● Einstein – Strauss - de Sitter vakuola model● Refraction of light at the matching hypersurface● Meszáros – Molnár model of temperature
fluctuations● Results and Concluding remarks
Temperature Fluctuations of CMBR
● Last Scattering Surface (z=1600)● Sachs-Wolfe effect● Voids, Clusters (z=2)● Rees-Sciama effect
Einstein-Strauss-de Sitter vakuola model
● Dust filled homogeneous and isotropic universe.
● Extract a sphere of mass M● Replace by Schwarzchild-de Sitter black hole
spacetime of the same mass.● Synchronize the cosmic time with the proper
time of observers co-moving with matching hypersurface.
Einstein-Strauss-de Sitter vakuola model
Schwarzchild-de Sitter:
Friedmanian geometry:
Einstein-Strauss-de Sitter vakuola model
Synchronization of proper time of radial geodesics and cosmic time T.
Junction conditions:
Refraction of light at MH
Geodesics crossing the matching hypersurface (SdS, LFRW ):
Refraction of light at MH
Lorentz transformation of static and radially moving frames:
Refraction of light at MH
Orthonormal tetrades:
Static SdS: Comoving LFRW:
Refraction of light at MH
Refraction formulae:
Refraction of light at MH
Refraction of light at MH
Refraction of light at MH
Speed parameter
LFRW
SdS
A
Meszáros-Molnár model
O
b
0
LFRW
SdS
A
Meszáros-Molnár model
b
0
O
LFRW
SdS
A
Meszáros-Molnár model
b
0
O
LFRW
SdS
S
+
A
Modified Meszáros-Molnár model
b
0
F
+
O
LFRW
SdS
S
+
A
Modified Meszáros-Molnár model
b
0
F
+
O
LFRW
SdS
S
+
A
Modified Meszáros-Molnár model
b
0
F
+
O
LFRW
SdS
S
+
A
Modified Meszáros-Molnár model
b
0
F
+
O
Modified Meszáros-Molnár model
LFRW
SdS
S
+
A
Settings for calculations
b
0
F
+
OD
LFRW
SdS
S
+
A
Settings for calculations
b
0
F
+
OD
LFRW
SdS
S
+
A
Settings for calculations
b
0
F
+
OD
Results and Comments
rb0=100 Mpc M vakuola=1.7×1017 M sol
H 0=72 km s−1 Mpc−1 m0=0.27
zD=0.5
=10−56 cm−2
Results and Comments
rb0=100 Mpc M vakuola=1.7×1017 M sol
H 0=72 km s−1 Mpc−1 m0=0.27
zD=1.0
=10−56 cm−2
Results and Comments
rb0=100 Mpc M vakuola=1.7×1017 M sol
H 0=72 km s−1 Mpc−1 m0=0.27
zD=1.5
=10−56 cm−2
Results and Comments
rb0=100 Mpc M vakuola=1.7×1017 M sol
H 0=72 km s−1 Mpc−1 m0=0.27 =10−56 cm−2
Results and Comments
rb0=100 Mpc M vakuola=1.7×1017 M sol
H 0=72 km s−1 Mpc−1 m0=0.27 =10−56 cm−2
THANK YOU FOR YOUR ATTENTION.