Dark Energy

Dark Energy

Friday, February 13, 2009

Theory Expansion Supernovae Acceleration


Einstein’s equation says mass/
energy causes space-time curvature

• Curvature = Energy Density


What about empty space?


What is so special about
empty space?


empty space?

Can have curvature even with no matter


empty space?

Can have curvature even with no matter
Can have energy in empty space


Pressure is related to change in
energy in expanding volume

Positive pressure does work as it expands --
loses energy and cools

Positive energy density has
negative pressure Λ
Λ
Λ
Λ

Λ
Λ
Λ

Volume increased
Internal energy increased
Pressure is negative

In General relativity,
pressure causes gravity
• Relativity: Space ~ Time
• Energy ~ Momentum
• Energy density ~ Pressure
• T is a mix of pressure and energy density
μν

• Positive vacuum energy causes anti-gravity


Einstein introduced the cosmological
constant to allow a static universe
“In order to arrive at this consistent view, we admittedly had to
introduce an extension of the ﬁeld equations of gravitation
which is not justiﬁed by our actual knowledge of gravitation. ...
That term is necessary only for the purpose of making possible a
quasi-static distribution of matter....”

The antigravity from the cosmological
constant balances the gravity from matter
Disproved by the discovery of the expansion of the universe
“My Greatest Blunder”

Recap
Einstein introduced cosmological constant negative
pressure antigravity to allow static universe


Measure distance in Astronomy by
comparing brightness of object to known
reference

Apparent Magnitude
20

15

Color


Measure distance in Astronomy by
comparing brightness of object to known
reference

Du
st

Apparent Magnitude
20

Distance Modulus

15

Color
Bigger apparent magnitude = fainter = farther away

Cepheid Variable are a
good reference


Henrietta Leavitt discovered
Cephied Period Luminosity relation


Original plates used to
discover Cepheids


Take negative of one
plate


Overlap eliminates all
but variable star


Distance

Time
Today

Distance

Time
Age of the Universe
12 Gya Today

HST Hubble Constant Key Project
Freedman et al. 2001


Distance

Time
12 Gya Today

Distance

Time
Age of the Universe
12 Gya 10 Gya Today

M55 Globular Cluster


Distance

Time
12 Gya 10 Gya Today

Formation of
Globular Clusters
Distance

13 Gya Time
Age of the Universe
12 Gya 10 Gya Today

Recap

Cepheid variables used to measure distance
(bright, identiﬁable, known brightness) also used to
show expansion of the universe


Looking for a brighter
standard
Cepheids are the brightest stars

Supernovae are much brighter than cepheids


A star is in balance between
gravity and pressure

Hydrostatic equilibrium

When stars are hot, pressure
comes from gas pressure

PV=NRT


When stars are cold, pressure
comes from quantum mechanics

Cannot put
more than two
electrons in
the same state
Electrons must
be moving
quickly even if
cold


Finite speed of light places a
limit on maximum size of core


Finite speed of light places a
limit on maximum size of core
• As core gets heavier, electrons have to move
faster to hold it up
• Eventually, the speed of light prevents them
from moving faster
• Core starts to shrink
• Gravity gets stronger
• Core shrinks faster
• Gravity gets stronger

Two types of
supernovas

• Binary white dwarf (Type Ia)
• Massive star (Type Ib,c Type II)


Type 1a supernovas
should be similar

• Progenitors have same mass
• Formed slowly, history not important
• Should have same brightness
• Make a good distance estimator


Follow up image


•Supernovae seen long ago are moving more slowly than they should.
•Expansion of universe was less in the past than today
•Universe is accelerating

Recap


Supernovae much brighter than cepheids, can show
expansion in distant galaxies.


Expansion History of the Universe

s
Perlmutter, Physics Today (2003) nd r
a
xp eve
er

0.0001

0.001
fo s

0.01
relative

0.1
1
se
lap
brightness
1.5 l
co
Relative to Today's Scale
Scale of the Universe

1.0 0

0.25

redshift
After inflation, 0.5

ed
the expansion either... 0.75
ted

rat
ra 1
0.5
ele
e le
cc
dec
1.5
a
en 2
th
,
ys

te d 2.5
a 3
r
lwa

e le
c
de 5
...or a

past today future
st 0.0
0.0
f ir

–20 –10 0 10
Billions Years from Today

Supernova Cosmology Project
3
Knop et al. (2003)
No Big Bang Spergel et al. (2003)
Allen et al. (2002)

2

Supernovae

1
ΩΛ
CMB

expands forever
ly
ollapses eventual
0
rec
Clusters clo
se
d
fla

-1
t
op
en

0 1 2 3
ΩM

The ﬁne tuning problem
“Natural” value for energy density:
or
46,000,000,000,000,000,000,000,000,000,000
,000,000,000,000,000,000,000,000,000,000,0
00,000,000,000,000,000,000,000,000,000,000
,000,000,000,000,000 J/m3

Therefore, the cosmological constant was
believed to be zero until 1998


No one knows what makes
the cosmological constant

Is it really constant?

Need more distant supernovae

SNAP
DESTINY

ADEPT


Supernova Cosmology Project
ΩΜ , ΩΛ
Knop et al. (2003)
0.25,0.75
0.25, 0
1, 0
24

Supernova
22
Cosmology
Project
effective mB

20

18
Calan/Tololo
& CfA

16

14
0.0 0.2 0.4 0.6 0.8 1.0

redshift z


0.0

Flat Universe network of cosmic strings
Constant w
–0.2 w = –1/3

–0.4
w = pu / quot;u

99%
range of
95%
Quintessence
–0.6 90%
models
68%

–0.8
cosmological constant
w = –1
–1.0
0.0 0.2 0.4 0.6 0.8 1.0
!M = 1 - !w
SNAP Satellite
Target Statistical Uncertainty

68%, 90%, 95%, and 99% confidence regions in the ΩM –w plane for an additional energy density component, Ωw ,
n equation-of-state w = p/ρ. (For Einstein’s cosmological constant, Λ, w = −1.) The fit is constrained to a flat
Ωw = 1). Also shown is the expected confidence region allowed by SNAP assuming w = −1 and ΩM = 0.28.

wavelength calibrated spectra extending to wavelength regions where “gray” dust is no longer gray will
hypothetical large-grain dust’s absorption properties. Armed with the extinction – color excess properties

Recap


Supernovae much brighter than cepheids, can show
expansion in distant galaxies.

Expansion of the universe is accelerating, deep
challenge to explain why.


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