1. Dark Energy Cosmology INPE Winter School September 12-16, 2005 Robert Caldwell Dartmouth College

2. Dark Energy The scalar field is a pioneer, sent out to explore new worlds of physics! Gravity and the Tenacious Scalar Field Carl Brans, gr-qc/9705069 Nordstrom’s Scalar Gravity Kaluza-Klein Unification Dirac and Jordan’s Cosmology Scalar-Tensor Gravity Inflaton Quintessence … Waves, Optics Electrodynamics Quantum Mechanics Scalar QED Field Theory Symmetry Breaking Dilatons, Moduli … 

3. Casimir Effect Vacuum Energy is not Immutable Energy density carried in vacuum fields has a quadrupolar distortion in response to a weak gravitational field Caldwell, astro-ph/0209312 Casimir Effect in a Weak Gravitational Field Model the EM degrees of freedom using scalar fields with the appropriate boundary conditions

4. Dark Energy Why do we need anything other than a cosmological constant? Maybe the dark energy is not static! Is there a theoretical reason to favor a dynamical dark energy? What will it mean for theory if the dark energy is found to closely resemble a  ? What will it mean for theory if the dark energy is found to to be time-varying? If the dark energy is found to be dynamical, does that mean there is no  ?

5. Dark Energy Scalar Field basics Energy density and pressure of homogeneous configurations Range of the equation-of-state The time-evolution of the homogeneous scalar field can be equivalently described by a time-dependent equation-of-state. “Quintessence” to distinguish from a cosmological constant

6. Dark Energy The basic scalar field If it evolves in time, it must also vary in space. h = synchronous gauge metric perturbation Ma & Bertschinger ApJ 455 (1995) 7 Fluctuations distinguish this from a smooth “x-matter” Coble et al, PRD 55 (1997) 1851 Caldwell et al, PRL 80 (1998) 1582

7. Dark Energy The basic scalar field Dispersion relation: small-scale sound speed Perturbation evolution:

8. Dark Energy Sensitivity of quintessence/scalar field to initial conditions Dave et al, PRD 66 (2002) 02351 Initial fluctuations decay Observed spectra are insensitive to a wide range of plausible initial conditions Field responds to gravity: inhomogeneities in b, dm Sensitivity to sound speed Relevant when field dominates

9. Dark Energy Influence on the CMB

10. Dark Energy The basic scalar field A scalar degree of freedom representing a system relaxing towards its global minimum. Such extreme values of the field strength and mass are difficult to accept…

11. Dark Energy It is difficult to understand how quintessence remains light, yet dark expect quintessence to couple to other particles Carroll, PRL 81 (1998) 3067 Kolda & Lyth, PLB 458 (1999) 197 Peccei, hep-ph/0009030 Doran & Jaeckel, PRD 66 (2002) 043519 Chung et al, PLB 556 (2003) 61 loop corrections alter the scalar potential composition-dependent, long-range forces time-variability of fundamental couplings ?

12. Dark Energy The basic scalar field Couplings to visible particles must be small Couplings cause long-range forces Carroll, PRL 81 (1998) 3067 Attractive force between lumps of  Frieman & Gradwohl, PRL 67 (1991) 2926; ApJ 398 (1992) 407 example: scalar field coupled to massive neutrino Why not?

13. Dark Energy The basic scalar field Even if the quintessence field is in a dark sector, isolated from the SM there can still be gravitationally-moderated interactions with visible matter. Not only is there is still no solution to the vacuum energy or cosmological constant problem, but the new scalar field further adds to the problem.

14. Dark Energy Scalar Field: pseudo Nambu-Goldstone Boson shift symmetry protects against unwanted couplings … Hill & Ross, NPB 311 (1988) 253 Frieman et al, PRD 46 (1992) 1226 Frieman et al, PRL 75 (1995) 2077 similar to axion f: symmetry breaking scale M: energy scale associated with a species of light neutrinos? Coble et al, PRD 55 (1997) 1851 Hill & Leibovich, PRD 66 (2002) 075010 Kim & Nilles, PLB 553 (2003) 1

15. Dark Energy Scalar Field: dynamical symmetry-breaking condensate Affleck et al, NPB 256 (1985) 557 Ratra & Peebles, PRD 37 (1988) 3406 Zlatev et al, PRL 82 (1999) 896 Binetruy, PRD 60 (1999) 063502 Masiero et al, PRD 61 (2000) 023504 … N: families and colors, N c >N f +1 M: symmetry breaking scale  superquark condensate mode These are not our (s)quarks! Tracking behavior relieves some tuning issues… vacuumless!

16. Dark Energy A balance between Hubble damping and the curvature of the potential allows the field to evolve with an equation-of-state w<w B, eventually coming to dominate. The tracker is insensitive to initial conditions, with many orders of magnitude of play in  at the end of inflation - including equipartition - which yield the dominant energy density today. Zlatev et al, 1999

17. Caldwell & Doran, PRD 69 (2004) 103517 Dark Energy Joint CMB/SN/LSS constraints Results shown from sampling a multi- dimensional parameter space using a Monte-Carlo Markov chain algorithm CMBeasy, Doran, astro-ph/03020138 www.cmbeasy.org

18. Dark Energy Is there a useful way to parameterize the evolution of the dark energy equation of state? or some other function? How big is dw/da? How closely do I need to look for dw/da?

19. Distinguish thawing and freezing fields Field is critically damped until Hubble friction drops; w starts at -1 and grows larger Field decays until curvature of potential causes field to slow; w evolves towards -1 Any field near minimum, V=0 & V’=0 massive scalar, axion / pngb “tracker” / runaway or vacuumless field These are among the simplest quintessence models. thawing freezing Dark Energy

20. Currently, there are no strong constraints on this phase diagram! Dark Energy Q: Is there a natural metric for the scale of time variations in w? Use as a target for future experiments and observations Caldwell & Linder, astro-ph/0505494

21. Energy Scale / Slope 0.2% difference from LCDM in distance to z=1 slow roll variable ~ 1+w > 0.01 Dark Energy

22. There are numerous other proposed models of dark energy. Artistic view of a universe filled by a turbulent sea of dark energy