Eric Linder

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Course on Dark Energy Cosmology at the Beach 2009
Eric Linder University of California,
Berkeley Lawrence Berkeley National Lab
JDEM constraints
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Outline
Lecture 1 Dark Energy in Space The panoply of
observations Lecture 2 Dark Energy in
Theory The garden of models Lecture 3 Dark
Energy in your Computer The array of tools
Dont try this at home!
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Nature of Acceleration
Is dark energy static? Einsteins cosmological
constant ?.
Is dark energy dynamic? A new, time- and
space-varying field.
How do we learn what it is, not just that it is?
How much dark energy is there? energy density
?? How springy/stretchy is it? equation of state
w, w?
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Whats the Matter with Energy?
Why not just bring back the cosmological constant
(?)? When physicists calculate how big ? should
be, they dont quite get it right.
They are off by a factor of
1,000,000,000,000, 000,000,000,000,
000,000,000,000, 000,000,000,000,
000,000,000,000, 000,000,000,000,
000,000,000,000, 000,000,000,000,
000,000,000,000, 000,000,000,000.
This is modestly called the fine tuning problem.
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Cosmic Coincidence
Why not just settle for a cosmological constant
?? ? For 90 years we have tried to understand
why ? is at least 10120 times smaller than we
would expect and failed. ? We know there was
an epoch of time varying vacuum once inflation.
We cannot calculate the vacuum energy to within
10120. But it gets worse Think of the energy in
? as the level of the quantum sea. At most
times in history, matter is either drowned or
dry.
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On Beyond ?!
We need to explore further frontiers in high
energy physics, gravitation, and cosmology. New
quantum physics? Does nothing weigh something?
Einsteins cosmological constant, Quintessence,
String theory New gravitational physics? Is
nowhere somewhere? Quantum gravity, supergravity,
extra dimensions? We need new, highly
precise data
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Scalar Field Theory
Scalar field Lagrangian - canonical, minimally
coupled L? (1/2)(???)2 - V(?) Noether
prescription ? Energy-momentum tensor T??(2/?-g)
?(?-g L )/?g?? Perfect fluid form (from RW
metric)
.
Energy density ?? (1/2) ? 2 V(?)
(1/2)(??)2 Pressure p? (1/2) ? 2 - V(?) -
(1/6)(??)2
.
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Scalar Field Equation of State
Equation of state ratio w p/? Klein-Gordon
equation (Lagrange equation of motion)
Continuity equation follows KG equation (1/2)?
2 6H (1/2)? 2 -V ? - V 3H (?p)
-V d?/dln a -3(?p) -3? (1w)
.
.
.
.
.
.
.
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Equation of State
Limits of (canonical) Equations of State w
(K-V) / (KV) Potential energy dominates (slow
roll) V gtgt K ? w -1 Kinetic energy dominates
(fast roll) K gtgt V ? w 1 Oscillation about
potential minimum (or coherent field, e.g.
axion) ?V? ?K? ? w 0
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Equation of State
Reconstruction from EOS ?(a) ?? ?c exp 3
?dln a 1w(z) ?(a) ?dln a H-1 sqrt ?(a)
1w(z) V(a) (1/2) ?(a) 1-w(z) K(a)
(1/2) 2 (1/2) ?(a) 1w(z)
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Dynamics of Quintessence

• Equation of motion of scalar field
• driven by steepness of potential
• slowed by Hubble friction
• Broad categorization -- which term dominates
• field rolls but decelerates as dominates energy
• field starts frozen by Hubble drag and then
  rolls
• Freezers vs. Thawers

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Limits of Quintessence
Distinct, narrow regions of w-w?
Caldwell Linder 2005 PRL 95, 141301
Entire thawing region looks like ltwgt -1
0.05. Need w? experiments with ? (w?) 2(1w).
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Calibrating Dark Energy
Models have a diversity of behavior, within
thawing and freezing.
But we can calibrate w? by stretching it w??
w?(a?)/ a?. Calibrated parameters w0, wa.
The two parameters w0, wa achieve 10-3 level
accuracy on observables d(z), H(z).
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Latest Results for w
Systematics already dominate error budget
We do not know w(z) -1 or what dark energy was
doing at zgt1.
Kowalski et al. 2008, ApJ arXiv0804.4142
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Beyond Lambda
Compare current data (SNCMBBAO) vs. 10 dark
energy models.
Choose motivated models widely covering Beyond
? physics. Includes thawing, freezing, phase
transition, modGR, geometric.
Most models have limit approaching ? but two
dont.
Rubin et al. 2008, ApJ arXiv0807.1108
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Doomsday Model
(also see Weinberg 2008)
First dark energy model - Linde 1986
V(?) V0 V0?(?-?0) Linear potential
2 parameters - ?m and w0 or tdoom or V0?
Rolls down potential to negative density and
universe collapses in finite time.
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DGP Braneworld
2 parameters - ?m and ?k or ?bw or rc
H2(8?G/3)?mH/rc
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Beyond Lambda
While ? is consistent with data, many varieties
of physics are also. (2 models do better than
?.) Improvements in systematics will have large
impact - e.g. Braneworld disfavored at ??215 if
statistical errors only. Uniform data set /
analysis key, as is next generation ability to
see w?. Apart from testing exotic cosmologies,
such comparisons are useful because model variety
includes sensitivity to systematics that dont
look like ?. No indication of any such
systematics. Diversity highlights need for
physical priors before model selection useful.
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Beyond Scalar Fields
Observations that map out expansion history a(t),
or w(a), tell us about the fundamental physics of
dark energy. Alterations to Friedmann framework
? w(a)
Suppose we admit our ignorance H2 (8?/3) ?m
?H2(a) Effective equation of state w(a) -1 -
(1/3) dln (?H2) / dln a Modifications of the
expansion history are equivalent to time
variation w(a). Period.
gravitational extensions or high energy physics
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Gravity Beyond 4D
DGP Braneworld, and H? mods, obey freezer
dynamics in w-w?
Can reproduce expansion or growth with
quintessence, but not both.
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Physics of Growth
Perturb the acceleration equation by
which conserves mass
This determines growth of density inhomogeneities
???/?
Fitting function
Peebles 1980 (pre-DM!)
Generalization
Growth index ? 0.550.051w(z1) Accurate
to 10-3 level for dark energy and can describe
deviations from Einstein gravity growth (as long
as usual matter domination at high z).
Linder 2005, Linder Cahn 2007
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Physics of Growth
Growth g(a)(??/?)/a depends purely on the
expansion history H(z) -- and gravity theory.
0
Expansion effects via w(z), but separate effects
of gravity on growth.
g(a) exp ?0ad ln a ?m(a)? -1
Linder 2005
Growth index ? is valid parameter to describe
modified gravity. Accurate to 0.1 in numerics.
Similar to Peebles 1980 (?0.6) and Wang
Steinhardt 1998 (constant w).
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Growth Beyond ?
Gravitational growth index ? is nearly constant,
i.e. single parameter (not function) to describe
growth separately from expansion
effects. Derivable from 1st principles, even for
modified gravity, accurate to 0.1 in growth.
Minimal Modified Gravity (aka Beyond the Standard
Model 2) uses simultaneous fit to expansion and
growth ?m,w0,wa,?, as a benchmark model to
explore the accelerating universe (cf. mSUGRA for
dark matter).
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The Nature of Gravity
To test Einstein gravity, we need growth and
expansion. Tension between distance and LSS mass
growth reveals deviations from GR. Keep
expansion history as w(z), growth deviation from
expansion (modGR) by ?. Fit both simultaneously.
Bias
?? gives deviations in growth from GR
Huterer Linder 2006
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Violating Matter Domination
Gravitational growth index ? depended on early
matter domination. Need calibration parameter
for growth, just like for SN (low z) and BAO
(high z) distances.
g(a) g exp ?0ad ln a ?m(a)? -1
Linder 2009 0901.0918
g is nearly constant, single parameter, handles
early time deviations modGR, early DE, early
acceleration. Separate from ?,w accurate to
0.1.
Beyond the Standard Model 3 simultaneous fit to
?m,w0,wa,?,g. Next generation data can test
?(?e)0.005, ?Gearly/G1.4, ?ln a1.7.
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Paths to Testing Gravity
Alternate approaches Solve for metric potentials
?, ? e.g. Hu Sawicki 2007 or parametrize
?/?-1 (PPN) e.g. Caldwell, Cooray, Melchiorri
2007 Jain Zhang 2007 Zhang, Bean, Liguori,
Dodelson 2007 Amendola, Kunz, Sapone 2007.
Test by spectroscopic vs. imaging surveys.
Blue (dynamics) ? Red (lensing/ISW) ?-?
Jain Zhang 2007
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Dark Energy Surprises

• Dark energy is
• Dark
• Smooth on cluster scales
• Accelerating

Maybe not completely! Clumpy in horizon? Maybe
not forever!
Its not quite so simple!
There is still much theoretical research needed!
Research is what I'm doing when I don't know what
I'm doing. - Wernher von Braun
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Finding Our Way in the Dark
Dark energy is a completely unknown animal. Not
completely dark? coupling to (dark) matter, to
itself Not energy? modified gravity --
physics, not physical
Track record Inner solar system motions ?
General Relativity Outer solar system motions ?
Neptune Galaxy rotation curves ? Dark Matter
Moral Given the vast uncertainties, go for the
most unambiguous insight.
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Clean Physics
What could go wrong? Potentials ?,?
anisotropic stress ?s gravitational strength
G(k,t) sound speed cs coupling ?. SN
distances come from the FRW metric. Period.
Lensing distances depend on deflection law
(gravity) even if separate mass (gravity) --
(?-?), cs,?s,G(k,t) BAO depends on standard CDM
(matter perturbations being blind to DE). --
(??),cs, ?, ?s,G(k,t)
What could go right? Ditto.
Yesterdays sensation is Todays calibration and
Tomorrows background. --Feynman
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END Lecture 2
Lecture 1 Dark Energy in Space The panoply of
observations Lecture 2 Dark Energy in
Theory The garden of models Lecture 3 Dark
Energy in your Computer The array of tools
Dont try this at home!
For more dark energy theory resources,
see Dynamics of Dark Energy http//arxiv.org/abs/a
stro-ph/06043057 (Copeland, Sami, Tsujikawa
2006) Dynamics of Quintessence, Quintessence of
Dynamics http//arxiv.org/abs/0704.2064 (Linder
2007) and the references cited therein.