Dissecting Dark Energy

1. DissectingDark Energy Eric Linder Lawrence Berkeley National Laboratory

2. Our Tools Expansion rate of the universe a(t) ds2 = dt2+a2(t)[dr2/(1-kr2)+r2d2] Einstein equation (å/a)2 = H2 = (8/3) m + H2(z) = (8/3) m + C exp{dlna [1+w(z)]} Growth rate of density fluctuationsg(z)= (m/m)/a Poisson equation2(a)=4Ga2 m= 4Gm(0) g(a)

3. Tying HEP to Cosmology ˙ ¨ Klein-Gordon equation  + 3H = -dV()/d Linder Phys.Rev.Lett. 2003 following Corasaniti & Copeland 2003 w(a) = w0+wa(1-a) Accurate to 3% in EOS back to z=1.7 (vs. 27% for w1). Accurate to 0.2% in distance back to zlss=1100!

4. All w, All the time Time variation w´ is a critical clue to fundamental physics. Alterations to Friedmann framework  w(z) Suppose we admit our ignorance: H2 = (8/3) m + H2(z) Effective equation of state: w(z) = -1 + (1/3) d ln(H2) / d ln(1+z) Modifications of the expansion history are equivalent to time variation w(z).Period. gravitational extensions or high energy physics Linder 2003

5. The world is w(z) Don’t care if it’s braneworld, cardassian, vacuum metamorphosis, chaplygin, etc. Simple, robust parametrization w(a)=w0+wa(1-a) Braneworld[DDG]vs.(w0,wa)=(-0.78,0.32) Vacuum metamorphvs.(w0,wa)=(-1,-3) Also agree on m(z) to 0.01 mag out to z=2

6. Revealing Physics Some details of the underlying physics are not in w(z). Need an underlying theory - ? beyond Einstein gravity? Growth history and expansion history work together. w0=-0.78 wa=0.32 Linder 2004 cf. Lue, Scoccimarro, Starkman Phys. Rev. D69 (2004) 124015 for braneworld perturbations

7. Questions How does a(t) teach us something fundamental (beyond w(z))? Benchmarks: à la energy scale for inflation models; rule out theories tying DE to inflation; scalar tensor 2; slow roll parameters of V() like linear potential Predictive power: Albrecht-Skordis-Burgess w(z); naturalness constraints ; flatness and w(z) w<-1: Crossing w=-1 with hybrid quintessence Other tools: astronomy (strong gravity, solar system), accelerator, tabletop experiments

8. Lambda, Quintessence, or Not? Many models asymptote to w=-1, making distinction from  difficult. Can models cross w=-1? (Yes, if w<-1 exists.) All models match CMB power spectrum for CDM

9. Naturalness and w´ Consider the analogy with inflation. Tiltn=1 (Harrison-Zel’dovich) is roughly predicted; profound if n=1 exactly (deSitter, limited dynamics). Same:w=-1 exactly is profound, but w≈-1 maybe not too surprising. Small deviation w-1 important so precision sought. However, while n=0.97, constant without running, is possible, w=-0.97 constant is almost ridiculous. Thus, searching forw´is critical even if find w very near -1.

10. Predictions & Benchmarks a t Linear potential [Linde 1986] V()=V0+ leads to collapsing universe, can constrain tc curves of  Would like predictions of w(z) - or at least w´. In progress for Albrecht-Skordis-Burgess model V() = (1+ /b + /b2) exp(-)

11. Predictions & Benchmarks Extensions to gravitation E.g. scalar-tensor theories: f/2-();;-V Take linear coupling to Ricci scalar R: f/ = F R Allow nonminimal coupling F=1/(8G)+ 2 R-boost (note R0 in radiation dominated epoch) gives large basin of attraction: solves fine tuning yet w ≈ -1. [Matarrese,Baccigalupi,Perrotta 2004] But growth of mass fluctuations altered: S0 since G  1/F.

12. Questions How does a(t) teach us something fundamental (beyond w(z))? Benchmarks: à la energy scale for inflation models; rule out theories tying DE to inflation; scalar tensor 2; slow roll parameters of V() like linear potential Predictive power: Albrecht-Skordis-Burgess w(z); naturalness constraints ; flatness and w(z) w<-1: Crossing w=-1 with hybrid quintessence Other tools: astronomy (strong gravity, solar system), accelerator, tabletop experiments