Welcome back - MIT OpenCourseWare · Welcome back Alexander Friedmann to 8.033! 1888-1925 (1922...
Transcript of Welcome back - MIT OpenCourseWare · Welcome back Alexander Friedmann to 8.033! 1888-1925 (1922...
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Welcome back
to 8.033!Alexander Friedmann
1888-1925 (1922 paper)
“As Copernicus made the Earth go round the Sun, so Friedmann made the Universe expand.”
(1993 biography)Image courtesy of Wikipedia.
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• Unification: gravitatation equivalent to acceleration
(accelerating frame indistinguishable from gravitational field)
• Law of motion: you move along geodesic
• Key to problem solving: working with metrics, variational calculus
Summary of GR so far:
Figure by MIT OCW.
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Implies both gravitational redshift and Newtonian gravity
Implies special relativity
(Why?)
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Implies special relativity
Implies both gravitational redshift and Newtonian gravity
φ = −ΜG/r, so how much time elapses on a clock
- at rest far away?
- moving far away?
- at rest on the ground?
- in GPS satellite?
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MIT Course 8.033, Fall 2006, Lecture 17Max Tegmark
Today’s topic: Cosmology 1/4• The FRW metric
• Expansion of the Universe
• Age of the Universe
• Brief history of the Universe
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KEY FACT 1: The (observable) Universe is homogeneous &
isotropic (on large scales)
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Image courtesy of NASA.
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Image of Kitt Peak observatory, courtesy of Wikipedia
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Cmbgg OmOl
Image courtesy of NASA
Image courtesy of Enoch Lau/Wikipedia.
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Alexander Friedmann1888-1925
(Russian; 1922 paper)
George Lemaître 1894-1936
(Belgian; indep. 1927 paper)
Arthur Geoffrey Walker 1909-?
(British; 1935 paper with H P Robertson showed that FLRW
metric is onlyhomogeneous & isotropic metric)MIT PhD!
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Let’s derive some implications!
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Figure by MIT OCW.
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q0 = 0
0 < q0 <12
0 < q0 <12q0 =
12
q0 =12
q0 >12
q0 >12
q0 = 0
1/H0
Distance
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Figure by MIT OCW.
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Figure 8 from "What is the Universe made of? How old is it?" by Charles Lineweaver.http://arxiv.org/pdf/astro-ph/9911294