11

Eric Linder University of California, BerkeleyLawrence Berkeley National Lab

Interpreting Interpreting Dark EnergyDark Energy

JDEM constraints

22

The Challenge of Dark EnergyThe Challenge of Dark Energy

Dark energy is a tougher problem than inflation!

Slow roll is rare.

Slow roll only occurs for early “thawing” fields, and a few late “freezing” fields.

33

Dynamics and PhysicsDynamics and Physics

“Null” line

Phase plane w-w

+ 3H = -dV()/d¨ ˙

44

Dynamics of QuintessenceDynamics 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

+ 3H = -dV()/d¨ ˙

55

Limits of QuintessenceLimits of Quintessence

Distinct, narrow regions of w-w

Entire “thawing” region looks like <w> = -1 ± 0.05.

Need w experiments with (w) ≈ 2(1+w).

Caldwell & Linder 2005 PRL 95, 141301

2/2 - V()

2/2 + V()

.

.w =

66

Ask the Right QuestionAsk the Right Question

Start with CMB foundation in high redshift universe: match dlss

Models that match WMAP3 will automatically have wp= -1! This is not evidence for - must do experiments sensitive to w

77

The Quintessence of DynamicsThe Quintessence of Dynamics

If one conflates physics, rather than taking “fundamental modes”, or one randomizes initial conditions, any track is possible.

88

Model IndependenceModel Independence

Could test theories one by one, or take model independent approach. Simplest parametrization, with physical dynamics,

w(a)=w0+wa(1-a)

Virtues:

• Model independent

• Excellent approximation to exact field equation solutions

• Robust against bias

• Well behaved at high z

Problems: Cannot handle rapid transitions or oscillations.

N.B.: constant w lacks important physics.

99

Robustness of wRobustness of w00-w-waa

Early dark energy w(z)=w0/[1+b ln(1+z)]2 Wetterich 2004

w0-wa matches to 2% in w(a), 0.004m to z=2, 0.4% in dlss

Unbiased to 3rd parameter extension w(z)=w0+wa(1-ab)

w0-wa matches to 4% in w(a), 0.005m to z=2, 0.1% in dlss for b=0-1.5

1010

Is dark energy purely a late time phenomenon?

For , DE(zlss)=10-9. But dark energy is so unknown that we should test this.

Limits from CMB and LSS give DE(zlss) < 0.04 but this is enough to change the universe.

Early Dark EnergyEarly Dark Energy

Doran, Robbers, Wetterich 2007

Bartelmann, Doran, Wetterich 2006

de Putter & Linder 2007

1111

Physics of GrowthPhysics of Growth

Growth g(a)=(/)/a depends purely on the expansion history H(z) -- and gravity theory.

€

g + [5 + 12

d ln H 2

d ln a ] ′ g a−1 + [3 + 12

d ln H 2

d ln a − 32 G Ωm (a)] ga−2 = S(a)

Expansion effects via w(z), but separate effects of gravity on growth.

g(a) = exp { 0ad ln a [m(a) -1] }

Growth index (GR= 0.55+0.05[1+w(z=1)]) is valid parameter to describe modified gravity. Accurate to 0.2% in numerics. Formal derivation given by Linder & Cahn 2007.

0

1212

Growth FunctionGrowth Function

NB: using old =0.6 for LCDM can bias m by 0.03!

f = d ln /d ln a

1313

Revealing the Nature of the PhysicsRevealing the Nature of the Physics

Keep expansion history as w(z), growth deviation from expansion by .

Clear signal: 20% vs. 0.2%

Paradigm: To reveal the origin of dark energy, measure w, w, and . e.g. use SN+WL.

To test Einstein gravity, we need growth and expansion measures, e.g. Supernovae and Weak Lensing.

Linder & Cahn 2007

Minimal Modified Gravity (MMG)

1414

Dark energy is a completely unknown animal. What could go wrong?

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)

Clean PhysicsClean Physics

“Yesterday’s sensation is Today’s calibration and Tomorrow’s background.” --Feynman

What could go right? Ditto.

Moral: Given the vast uncertainties, go for the most unambiguous insight. Must include SN!