1. 1 1 Eric Linder University of California, Berkeley Lawrence Berkeley National Lab Interpreting Dark Energy JDEM constraints

2. 2 2 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.

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

4. 4 4 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  + 3H  = -dV(  )/d  ¨˙

5. 5 5 Limits of Quintessence Distinct, narrow regions of w-w Entire “thawing” region looks like = -1 ± 0.05. Need w experiments with  (w) ≈ 2(1+w). Caldwell & Linder 2005 PRL 95, 141301  2 /2 - V(  )  2 /2 + V(  ).. w =

6. 6 6 Ask the Right Question Start with CMB foundation in high redshift universe: match d lss Models that match WMAP3 will automatically have w p = -1! This is not evidence for  - must do experiments sensitive to w

7. 7 7 The Quintessence of Dynamics If one conflates physics, rather than taking “fundamental modes”, or one randomizes initial conditions, any track is possible.

8. 8 8 Model Independence Could test theories one by one, or take model independent approach. Simplest parametrization, with physical dynamics, w(a)=w 0 +w a (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.

9. 9 9 Robustness of w 0 -w a Early dark energy w(z)=w 0 /[1+b ln(1+z)] 2 Wetterich 2004 w 0 -w a matches to 2% in w(a), 0.004 m to z=2, 0.4% in d lss Unbiased to 3rd parameter extension w(z)=w 0 +w a (1-a b ) w 0 -w a matches to 4% in w(a), 0.005 m to z=2, 0.1% in d lss for b=0-1.5

10. 10 Is dark energy purely a late time phenomenon? For ,  DE (z lss )=10 -9. But dark energy is so unknown that we should test this. Limits from CMB and LSS give  DE (z lss ) < 0.04 but this is enough to change the universe. Early Dark Energy Doran, Robbers, Wetterich 2007 Bartelmann, Doran, Wetterich 2006 de Putter & Linder 2007

11. 11 Physics of Growth Growth g(a)=(  /  )/a depends purely on the expansion history H(z) -- and gravity theory. Expansion effects via w(z), but separate effects of gravity on growth. g(a) = exp {  0 a d 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

12. 12 Growth Function NB: using old  =0.6 for LCDM can bias  m by 0.03! f = d ln  /d ln a

13. 13 Revealing 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)

14. 14 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) -- (  -  ), c s,  s,G(k,t) BAO depends on standard CDM (matter perturbations being blind to DE). -- (  +  ),c s, ,  s,G(k,t) Clean 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!