1. Dark Energy Sean Carroll, Caltech SSI 2009 1.Evidence for Dark Energy 2.Vacuum Energy and the Cosmological Constant 3.Dynamical Dark Energy and Quintessence 4.Was Einstein Right? 25% Dark Matter 5% Ordinary Matter 70% Dark Energy

2. Dec. 1997: Something was in the air! - age of the universe - absence of power on small scales - measurements of matter density Theorists had a favorite model: a flat universe, full of matter (ordinary + cold dark), with primordial scale-free perturbations. That model couldn’t be right! Something had to give -- “flat,” “cold,” “scale-free,” or perhaps even “matter.” 1. Evidence for Dark Energy

3. The Friedmann equation with matter and radiation: Multiply by a 2 to get: If a is increasing, each term on the right is decreasing; we therefore predict the universe should be decelerating (a decreasing).. a t > Big Bang <

4. ToTo Two groups went out to look for the ‘deceleration’ of the universe, using type Ia supernovae as standardizable candles. SN 1994d

5. Result: supernovae are dimmer than expected. The universe is not decelerating at all, it’s accelerating. Can’t be explained by matter and radiation. [Riess et al.; Perlmutter et al.; Knop et al.]

6. size time > Big Bang < decelerating accelerating What could make the universe accelerate? From the Friedmann equation, we need something that doesn’t dilute away as the universe expands. Call it dark energy.

7. If the dark energy density evolves as then a DE-dominated universe obeys which implies acceleration for But people usually use the “equation-of-state parameter” so that acceleration happens for

8. Fun non-Euclidean fact: “constant expansion rate” = “acceleration.” The expansion rate is described by the Hubble constant, H, relating the distance of a galaxy to its velocity. Einstein tells us that the Hubble constant (squared) is proportional to the energy density . If  is constant (vacuum energy), H will be constant. But the distance d to some particular galaxy will be increasing, so from v = Hd its apparent velocity will go up: it will accelerate away from us.

9. Density parameter,  : Then, if we know  we can instantly infer the geometry of space: Matter (ordinary + dark) only accounts for  ≈ 0.3, implying negative curvature. Triangles should add up to < 180 o. How can we check this idea?

10. CMB temperature anisotropies provide a standard ruler. They were produced about 400,000 years after the Big Bang,and should be most prominent at a physical size of 400,000 light years across.  Tot = [  peak (deg)] -1/2. Observation:  peak = 1 o. The universe is flat:  Tot = 1. flat positively curved negatively curved [Miller et al.; de Bernardis et al; WMAP]

11. Concordance:   = 0.3,   = 0.7.

12. smoothly distributed through space varies slowly (if at all) with time  ≈ constant ( w ≈ -1) Dark energy could be exactly constant through space and time: vacuum energy (i.e. the cosmological constant  ). Energy of empty space. (artist's impression of vacuum energy) 2. Vacuum Energy (the Cosmological Constant) What we know about dark energy:

13. People sometimes pretend there is a difference between a cosmological constant, and a vacuum energy, There’s not; just set.

14. Problem One: Why is the vacuum energy so small? We know that virtual particles couple to photons (e.g. Lamb shift); why not to gravity? Naively:  vac = ∞, or at least  vac = E Pl /L Pl 3 = 10 120  vac (obs). e-e- e+e+ e-e- e+e+ photongraviton

15. You are here Problem Two: Why is the vacuum energy important now? We seem to be living in a special time. Copernicus would not be pleased.

16. The Gravitational Physics Data Book: Newton's constant: G = (6.67 ± 0.01) x 10 -8 cm 3 g -1 sec -2 Cosmological constant:  = (1.2 ± 0.2) x 10 -55 cm -2 If we set h = c = 1, we can write G = E Planck -2 and  vac = E vac 4, and E Planck = 10 27 eV,  vac = 10 -3 eV. Different by 10 30. Could we just be lucky?

17. Supersymmetry can squelch the vacuum energy; unfortunately, in the real world it must be broken at E SUSY ~ 10 12 eV. Typically we would then expect which is off by 10 15. But if instead we were able to predict it would agree with experiment. (All we need is a theory that predicts this relation!) energy E Planck E susy E vac 10 27 eV 10 12 eV 10 -3 eV

18. String theory has extra dimensions, with a vast “landscape” of ways to hide them. Perhaps 10 500 or more. The “constants of nature” we observe depend on the shape and size of the compact manifold. Everything changes from one compactification to the next, including the value of the vacuum energy. Is environmental selection at work? [Bousso & Polchinski; Kachru et al.]

19. Maybe each compactification actually exists somewhere. Regions outside our observable universe, where the laws of physics and constants of nature appear to be different. In that case, vacuum energy would be like the weather; not a fundamental parameter, but something that depends on where you are in the universe. Therefore (so the reasoning goes), it's hardly surprising that we find such a tiny value of the vacuum energy – regions where it is large are simply inhospitable. [Weinberg]

20.  V(  ) kinetic energy gradient energy potential energy [Wetterich; Peebles & Ratra; Caldwell, Dave & Steinhardt; etc.] This is an observationally interesting possibility. Might be relevant to the cosmological constant problem or the coincidence scandal -- somehow. 3. Dynamical Dark Energy (Quintessence) Dark energy doesn’t vary quickly, but maybe slowly.

21. A problem: mass. An excitation of the quintessence field is a quintessence particle: 

22. In quantum field theory, we don’t see the “bare” particle; we see the collective effect of the sum over fluctuating (virtual) quantum fields. 

23. The effect of these virtual particles is to drive the mass up! Unless there is a symmetry or other physics that cuts it off. Every particle we have observed has a symmetry keeping its mass low. (The Higgs is a mystery.) 

24.  A field with a large mass rolls quickly down its potential. Quintessence requires. That’s very small. A new fine-tuning.  V(  )

25. A related problem: interactions. If A couples to B, and B to C, A should couple to C. It’s hard to keep a new field completely isolated; it should couple to Standard Model particles.   

26. Coupling to a low-mass (long-range) field implies a fifth force of nature, which can be searched for in laboratory experiments. Also: gradual evolution of physical constants as the field evolves. Limit: couplings must be suppressed by ~ 10 5 M P. torsion-balance experiment [Webb et al.] [Adelberger et al.]

27. Both fine-tunings -- mass and interactions -- can be addressed in one fell swoop, by imagining a slightly broken symmetry  V(  ) [Frieman et al; Carroll] Then the quintessence is a pseudo-Nambu- Goldstone boson, with a cosine potential and naturally small mass and interactions.

28. But one interaction is allowed -- a parity-violating term of the form, coupling quintessence to the electromagnetic fields. This interaction produces cosmological birefringence: polarization vectors rotate as they travel through the evolving scalar field. WMAP 5-year data:. Radio galaxies also provide interesting constraints.

29. So: 1.A cosmological constant fits the data, at the expense of a dramatic fine-tuning. 2.Dynamical models introduce new fine-tunings, in the form of the small mass and couplings of the new scalar field. 3.Dynamical models have not yet shed any light on the cosmological constant problem or the coincidence scandal.

30. Simplest possibility: replace with The vacuum in this theory is not flat space, but an accelerating universe! But: the modified action brings a new tachyonic scalar degree of freedom to life. A scalar-tensor theory of gravity. [Carroll, Duvvuri, Trodden & Turner 2003] 4. Modified Gravity

31. Introduce a scalar field  ( x ) that determines the strength of gravity. Einstein's equation is replaced by Scalar-Tensor Gravity IntInt The new field  ( x ) is an extra degree of freedom; an independently-propagating scalar particle. variable “Newton's constant” extra energy-momentum from 

32. The new scalar  doesn’t interact directly with matter, because we say so. But it does influence the metric. A natural value for the Brans-Dicke parameter  would be  ~ 1, where  = 1 is GR. Experiments imply  > 40,000. [Chiba 2003] Cassini

33. [Khoury & Weltman; Hu & Sawicki] Loophole: the Chameleon Effect. Curvature contributes to the effective potential for . With the right bare potential, the field can be pinned (with large mass) in dense regions, e.g. the galaxy. Deviations from GR can be hidden on sub-galactic scales.

34. Dvali, Gabadadze, & Porrati (DGP) gravity: an infinite extra dimension, with gravity stronger in the bulk; 5-d kicks in at large distances. [Dvali, Gabadadze & Porrati 2000] 5-d gravity suppressed by r c ~ H 0 -1 4-d gravity 5-d gravity term suppressed by r c ~ H 0 -1 r S = 2GM r c ~ H 0 -1 r * = (r S r c 2 ) 1/3 4-d GR crossover 5-d GR

35. This exhibits self-acceleration: for  = 0, there is a de Sitter solution with H = 1/r c = constant. However: The acceleration is somewhat mild; think w eff ~ -0.7. Inconsistent with present data at about 5 . Fluctuations of the brane have negative energies (ghosts). Hard to fix this problem. Self-acceleration in DGP cosmology The DGP version of the Friedmann equation is (naturally):

36. So: 1.We would expect GR to be modified on short scales, not on long scales, but it could happen. 2. f(R) gravity can fit the data, but only through various fine-tunings (over and above the cosmological constant and coincidence problems) and the chameleon mechanism. 3.DGP gravity doesn’t really fit the data, and has issues with negative-energy ghosts.

37. Gravity is probably described by GR on large scales. Bottom line: Dark energy is probably a cosmological constant.