Eric Linder University of California, Berkeley Lawrence Berkeley National Lab

Interpreting Dark Energy Eric Linder University of California, Berkeley Lawrence Berkeley National Lab JDEM constraints

The 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.

Dynamics and Physics “Null” line ¨ ˙  + 3H = -dV()/d Phase plane w-w

Dynamics of Quintessence   ¨ ˙  + 3H = -dV()/d • 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

Limits of Quintessence . 2/2 - V() . w = 2/2 + V() Distinct, narrow regions of w-w Caldwell & Linder 2005 PRL 95, 141301 Entire “thawing” region looks like <w> = -1 ± 0.05. Need w experiments with (w) ≈2(1+w).

Ask 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

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

Model 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.

Robustness of w0-wa Early dark energyw(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

Early Dark Energy 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. Doran, Robbers, Wetterich 2007 Bartelmann, Doran, Wetterich 2006 de Putter & Linder 2007

Physics of Growth Growthg(a)=(/)/adepends purely on the expansion history H(z) -- andgravity theory. 0 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.

Growth Function NB: using old =0.6 for LCDM can bias m by 0.03! f = d ln /d ln a

Revealing the Nature of the Physics To test Einstein gravity, we need growth and expansion measures, e.g. Supernovae and Weak Lensing. Linder & Cahn 2007 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. Minimal Modified Gravity (MMG)

Clean Physics 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) What could go right? Ditto. “Yesterday’s sensation is Today’s calibration and Tomorrow’s background.”--Feynman Moral: Given the vast uncertainties, go for the most unambiguous insight. Must include SN!

Eric Linder University of California, Berkeley Lawrence Berkeley National Lab