1 1 Dissecting Dark Energy Eric Linder Lawrence Berkeley National Laboratory

2 2 Our Tools Expansion rate of the universe a(t) ds 2 =  dt 2 +a 2 (t)[dr 2 /(1-kr 2 )+r 2 d  2 ] Einstein equation (å/a) 2 = H 2 = (8  /3)  m +  H 2 (z) = (8  /3)  m + C exp{  dlna [1+w(z)]} Growth rate of density fluctuations g(z) = (  m /  m )/a Poisson equation  2  (a)=4  Ga 2  m = 4  G  m (0) g(a)

3 3 Tying HEP to Cosmology Accurate to 3% in EOS back to z=1.7 (vs. 27% for w 1 ). Accurate to 0.2% in distance back to z lss =1100! Klein-Gordon equation  + 3H  = -dV(  )/d  ¨ ˙ Linder Phys.Rev.Lett following Corasaniti & Copeland 2003 w(a) = w 0 +w a (1-a)

4 4 All w, All the time Suppose we admit our ignorance: H 2 = (8  /3)  m +  H 2 (z) Effective equation of state: w(z) = -1 + (1/3) d ln(  H 2 ) / d ln(1+z) Modifications of the expansion history are equivalent to time variation w(z). Period. Time variation w´ is a critical clue to fundamental physics. Alterations to Friedmann framework  w(z) gravitational extensions or high energy physics Linder 2003

5 5 The world is w(z) Don’t care if it’s braneworld, cardassian, vacuum metamorphosis, chaplygin, etc. Simple, robust parametrization w(a)=w 0 +w a (1-a) Braneworld [DDG] vs. (w 0,w a )=(-0.78,0.32) Vacuum metamorph vs. (w 0,w a )=(-1,-3) Also agree on m(z) to 0.01 mag out to z=2

6 6 Revealing Physics Some details of the underlying physics are not in w(z). N eed an underlying theory -  ? beyond Einstein gravity? Growth history and expansion history work together. w 0 =-0.78 w a =0.32 Linder 2004 cf. Lue, Scoccimarro, Starkman Phys. Rev. D69 (2004) for braneworld perturbations

7 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 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 9 Naturalness and w´ Consider the analogy with inflation. Tilt n=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 for w´ is critical even if find w very near -1.

10 Predictions & Benchmarks Linear potential [Linde 1986] V(  )=V 0 +  leads to collapsing universe, can constrain t c a t curves of  Would like predictions of w(z) - or at least w´. In progress for Albrecht-Skordis-Burgess model V(  ) = (1+  /b +  /b 2 ) 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