Meaning of deceleration parameter flat model q 0 tells you if the Universe is accelerating in its...
21
Meaning of deceleration parameter • flat model 2 3 1 models all For 2 3 1 ) 1 2 / ) 1 3 (( 1 2 / ) 1 3 ( constant because 1 0 2 0 ) 1 ( 3 2 0 ) 1 ( 3 2 0 0 0 1 2 / ) 1 3 ( 0 2 / ) 1 3 ( 1 3 2 0 1 3 0 2 0 2 3 3 3 3 0 0 2 0 0 2 0 2 i i w w w w w w w i w w q w a a a q t t t H w a a t H w y dt H dy y y H a a H dt dy a a a a a H dt dy q 0 tells you if the Universe is accelerating in its global expansion rate, or decelerating. Flat, matter dominated q0=1/2 Empty Universe q0=0 Flat, radiation dominated q0=1 Flat, Cosmological Constant dominated
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Transcript of Meaning of deceleration parameter flat model q 0 tells you if the Universe is accelerating in its...
Meaning of deceleration parameter
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q0 tells you if the Universe is accelerating in its global expansion rate, or decelerating.
Flat, matter dominatedq0=1/2Empty Universeq0=0Flat, radiation dominatedq0=1Flat, Cosmological Constant dominatedq0=-1
Equation of State Revisited
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Distance as a function of redshiftq0 0.5
z dproper d_L d_A0 0 0 0
0.1 0.093182 0.1025 0.0847110.2 0.175 0.21 0.1458330.3 0.248077 0.3225 0.1908280.4 0.314286 0.44 0.224490.5 0.375 0.5625 0.250.6 0.43125 0.69 0.2695310.7 0.483824 0.8225 0.2846020.8 0.533333 0.96 0.2962960.9 0.580263 1.1025 0.3054021 0.625 1.25 0.3125
1.1 0.667857 1.4025 0.3180271.2 0.709091 1.56 0.3223141.3 0.748913 1.7225 0.3256141.4 0.7875 1.89 0.3281251.5 0.825 2.0625 0.331.6 0.861538 2.24 0.3313611.7 0.897222 2.4225 0.3323051.8 0.932143 2.61 0.3329081.9 0.966379 2.8025 0.3332342 1 3 0.333333
2.1 1.033065 3.2025 0.3332472.2 1.065625 3.41 0.3330082.3 1.097727 3.6225 0.3326452.4 1.129412 3.84 0.332182.5 1.160714 4.0625 0.3316332.6 1.191667 4.29 0.3310192.7 1.222297 4.5225 0.3303512.8 1.252632 4.76 0.329642.9 1.282692 5.0025 0.3288953 1.3125 5.25 0.328125
3.1 1.342073 5.5025 0.3273353.2 1.371429 5.76 0.3265313.3 1.400581 6.0225 0.3257173.4 1.429545 6.29 0.3248973.5 1.458333 6.5625 0.3240743.6 1.486957 6.84 0.3232513.7 1.515426 7.1225 0.3224313.8 1.54375 7.41 0.3216153.9 1.571939 7.7025 0.320804
d_A
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0.1
0.15
0.2
0.25
0.3
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0.4
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d_A
Exact Distance Solutions for open/closed & mixed models
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Integrating functions
• Use trapezoid rule
f(x)
x1 x2
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x
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Area x(f(x1+x)+ f(x1))/2
Trial numerical integration
Microsoft Excel Worksheet
Angular Size Distance How big does an object look as a function of redshift
Proper Motion DistanceApparent Angular velocity as a function of redshift
Luminosity DistanceHow bright does an object appear as a function of redshift
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dA
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Cosmic ChronologyHow old is an object as a function of redshift
Volume TestHow does the Volume per dz change as a function of z
Structure TestHow does structure evolve relative to a model
Density TestMeasure local density of Matter
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k = -1
Luminosity Distance – GR + Homogenous Isotropic Universefor a monochromatic source (defined as inverse-square law)
the flux an observer sees of an object at redshift z 24 D
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Brightness of object depends exclusively on what is in the UniverseHow much and its equation of state.
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The Deceleration ParameterThe Deceleration Parameter
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Valid for all models
Mattig (1958) provides exact solution for matter only Universes
Mpc
DMm mag log525)(
Distance Modulus
Fractional distance change ½(mag change)
e.g. 0.1mag difference is 5% distance difference
Angular Size Distance
Attempts to fit/understand models: 1920-1995
•Number counts of Galaxies – Hubble,Yoshii/Peterson
•Angular Size Distances - distant radio cores Kellerman
•Loitering Universes with z=2 Quasars
•Luminosity Distance with Brightest Cluster Galaxies
Volume Effects
At low z, N z3, for any non-diverging luminosity function, Hubble observed this to be true, demonstrating that Galaxies uniformly fill the local Universe. He and Humason were unable to reach conclusions on Geometry.
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0=k
1=k
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)(
x
x
x
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Angular Size Distance with Compact Radio Sources
Kellerman(1993)
Stepanas & Saha 1995Result not that constraining
Excess z~2 QSOs: Loitering Universe
Petrosian, V., Saltpeter, E.E. & Szekeres, P. 1967
Brightest Cluster Galaxies
Sandage, Humason &Mayhall 1956Baum 1957Peach 1970
Deceleration q0>1
But Tinsley 1976 showed Evolution dominates Cosmology
Methods for Measuring Extra-Galactic Distances
• Brightest Cluster Galaxies • Cepheids• Fundamental Plane (Dn-/Faber Jackson)• Lensing Delay • Planetary Nebulae • Tully-Fisher• Sunyaev-Zeldovich • Surface Brightness Fluctuations• Supernovae Ia• Supernovae II
