Alan Guth, The Cosmological Constant, 8.286 Lecture 19, November 19, 2013, p. 1.
Summary of Lecture 18
8.286 Lecture 19
November 19, 2013
THE
COSMOLOGICAL CONSTANT
CMB Data in 1975
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Summary of Lecture 18
Summary of Lecture 18
A Preliminary Measurement of the Cosmic
Microwave Background Spectrum by the
Cosmic Background Explorer (COBE) Satellite
J. C. Mather, E. S. Cheng, et al.
Data from Berkeley-Nagoya Rocket Flight, 1987
Cover Page of Original Preprint of the COBE Measurement of the CMB Spectrum, 1990
Alan Guth
Massachusetts Institute of Technology
8.286 Lecture 19, November 19
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Alan Guth, The Cosmological Constant, 8.286 Lecture 19, November 19, 2013, p. 2.
Summary of Lecture 18
Summary of Lecture 18:
Gravitational Effect of Pressure
3p
d2a
4π
= − G ρ+ 2 a .
c
dt2
3
Vacuum Energy and the Cosmological Constant:
uvac = ρvac c2 =
Λc4
.
8πG
Original COBE Measurement of the CMB Spectrum, Jan 1990. Energy density is in units of
ρ̇vac = 0
electron volts per cubic meter per gigahertz.
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Alan Guth
Massachusetts Institute of Technology
8.286 Lecture 19, November 19
=⇒
pvac = −ρvac c2 = −
Λc4
.
8πG
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Summary of Lecture 18
Defining ρ = ρn + ρvac and p = pn + pvac ,
3pn
d2a
4π
= − G ρn + 2 − 2ρvac a .
dt2
3
c
 2
8π
kc2
ȧ

 
 =
G(ρn + ρvac ) − 2 .
3
a
a
Dominance of vacuum energy at late time implies
H → Hvac =
Hvac t
a(t) ∝ e
Alan Guth
Massachusetts Institute of Technology
8.286 Lecture 19, November 19
8π
Gρvac ,
3
The age of an open (Ω < 1), closed (Ω > 1), or flat (Ω = 1) universe containing only
nonrelativistic matter.
.
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Alan Guth
Massachusetts Institute of Technology
8.286 Lecture 19, November 19
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Alan Guth, The Cosmological Constant, 8.286 Lecture 19, November 19, 2013, p. 3.
The age of a flat universe containing nonrelativistic matter and vacuum energy.
Alan Guth
Massachusetts Institute of Technology
8.286 Lecture 19, November 19
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MIT OpenCourseWare
http://ocw.mit.edu
8.286 The Early Universe
Fall 2013
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