Dark Matter and Dark Energy

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2 Dark Matter and Dark Energy Sean Carroll, University of Chicago Our universe, as inventoried over the last ten years: 5% Ordinary Matter 25% D ark M atter 70% Dark Energy Dark Energy Dark Matter Ordinary Matter

3 Two things to emphasize: Large-scale astrophysical gravitational fields cannot be accounted for by ordinary matter and ordinary gravity. We have very good reason to believe that the solution is dark matter, not a modification of gravity. By "dark matter" we mean something completely new, not baryons or even black holes (unless they're primordial). [Genzel et al.]

4 What makes us think it's dark matter, not modified gravity? Consider CMB anisotropies, arising from acoustic oscillations of the baryon/photon fluid in a dark matter background: [WMAP]

5 With modified gravity, you would expect (probably) that gravity is always dependent on the matter. That's not what we see in the CMB power spectrum. Baryons & DM out of phase Baryons & DM in phase [WMAP] Dark matter boosts odd-numbered acoustic peaks.

6 More directly: Gravitational lensing does not seem to directly be caused by visible matter. Hubble Space Telescope image of a cluster of galaxies.

7 Mass reconstruction of the cluster. Note the large, smooth distribution of (apparently invisible) matter. [Tyson et al.]

8 The really profound puzzle: 70% of the universe is dark energy (smoothly distributed through space, slowly-varying with time). Dark energy presents us with a problem, a puzzle, and a scandal. The cosmological constant problem: why is the observed vacuum energy so much smaller than it has any right to be? The dark energy puzzle: what is the nature of the dark energy energy that is causing the universe to accelerate? The coincidence scandal: why are the dark energy density and the density of matter approximately equal today?

9 How do we know there is dark energy? Contributes to density (Ω Tot = Ω M + Ω DE ), and hence to curvature κ. Redshifts away slowly, so makes the universe. accelerate: a 2 a 2 ρ (from Friedmann eq.) Fortunately, these are things we can go look for.

10 Fluctuations in the Cosmic Microwave Background peak at a characteristic length scale of 300,000 light years; observing the corresponding angular scale measures the geometry of space. [WMAP] Take angular power spectrum of temperature fluctuations; then Ω Tot = [θ peak (deg)] -1/2. Observation: θ peak = 1 o. Thus, the universe is flat: Ω Tot = 1.

11 Type Ia supernovae are standardizable candles; observations of many at high redshift test the time evolution of the expansion rate. Result: the universe is accelerating. There must be some sort of energy density which doesn't redshift away. [Riess et al.; Perlmutter et al.]

12 Concordance: Ω Μ = 0.3, Ω Λ = 0.7. Supernovae CMB + H 0 Large-Scale Structure

13 This is a preposterous universe. Why is the vacuum energy density so much smaller than it should be? Naive expectation: ρ DE (theory) = ρ DE (obs) What is the nonzero dark energy? A tiny vacuum energy, a dynamical field, or something even more dramatic? Why now? Remember ρ DE /ρ M ~ a 3. So why are they approximately equal today?

14 The Gravitational Physics Data Book: Newton's constant: G = ( ) x 10-8 cm 3 g -1 sec -2 Cosmological constant: Λ = ( ) x cm -2 Equivalently, E Planck = GeV, ρ vac = (10-3 ev) 4. Quite a "hierarchy problem": energy GeV 10 3 GeV 10-3 ev E Planck E EW/susy E vac

15 Why is the vacuum energy so small? We know that virtual particles couple to photons (e.g. Lamb shift); why not to gravity? e - e - photon e + graviton e + Naively: ρ vac =, or at least ρ vac = M Pl 4 = ρ vac (obs).

16 On the other hand, maybe an infinite answer is just wrong. Supersymmetry does better. (In a manner of speaking.) Good news: In a perfectly supersymmetric state, bosonic and fermionic contributions to ρ vac exactly cancel. fermion boson < 0, > 0. Bad news: We don't live in a perfectly supersymmetric universe; SUSY is (at least) broken around M SUSY = ev. Good news: This makes the cosmological constant problem not so bad: ρ vac (theory) = M SUSY 4 = ρ vac (obs). Bad news: This is a much more reliable calculation!

17 There are wilder ideas, of course. Holography: studying quantum gravity has taught us that the degrees of freedom giving us these vacuum fluctuations aren't really there. The degrees of freedom you see depend on how you look. This sounds like it should have something to do with the cosmological constant problem. Extra dimensions: if there are large extra dimensions, we are measuring the induced geometry on a brane, not the intrinsic geometry of all spacetime. This changes the problem (although doesn't solve it in an obvious way). [Cohen, Kaplan & Nelson; Banks; Thomas]

18 Why are vacuum and matter comparable? You are here The "best-fit universe" with Ω Μ = 0.3, Ω Λ = 0.7 is an unstable point, caught in the process of evolving from purely matter to purely vacuum.

19 R M And it's moving quickly: M a 3

20 What might be going on? Possibilities include: We just got lucky. The vacuum energy is very different in other parts of the universe. A slowly-varying dynamical component is mimicking a vacuum energy. Einstein was wrong.

21 1) Could we just be lucky? Perhaps, when we can successfully calculate the vacuum energy, it will just happen to coincide with the present matter density. For example: In supersymmetry, we expect M vac M SUSY, which is off by But if instead we found M M SUSY vac M it would agree with experiment. M SUSY, (All Planck we need is a theory that predicts this relation.)

22 2) Could the anthropic principle be responsible? What if: The vacuum energy ρ Λ takes on different values, with uniform probability, in different "parts of the universe" (in space, time, or branches of the wavefunction). Everything else remains the same from place to place: constants of nature, initial conditions, galaxy formation, etc. Then the most likely thing for observers in such an ensemble to find is that ρ Λ < 10 ρ Μ (just as we do). [Garriga & Vilenkin; Martel, Shapiro & Weinberg]

23 3) I s the dark energy a slowly-varying dynamical component? e.g. a slowly-rolling scalar field: "quintessence" V(φ) V kinetic energy gradient energy potential energy φ [Wetterich; Peebles & Ratra; etc.] This is an observationally interesting possibility, and at least holds the possibility of a dynamical explanation of the coincidence scandal. But it is inevitably finely-tuned: requires a scalar-field mass of m φ < ev, and very small couplings to matter.

24 Could dark-energy dynamics solve the coincidence problem? Two possibilities: Today is not so far (on a log scale) from matter/radiation equality (z eq ~ 10 4 ). k-essence: Armendariz-Picon, Mukhanov & Steinhardt L f g 2 Perhaps acceleration is something that just happens from time to time. ρ M R k a oscillating dark energy: Dodelson, Kaplinghat, and Stewart V e 1 sin

25 Testing models of dark energy Characterize using an effective equation of state relating pressure to energy density: p w For matter, w = 0; for actual vacuum energy, w = -1. More than anything else, we need to know whether w = -1 or not. [Melchiorri, Mersini, Odman & Trodden]

26 The future: Supernovae, Clusters, CMB, etc. SNAP South Pole Telescope Planck

27 Should we consider w < -1? [Caldwell; Carroll, Hoffman & Trodden] In GR, the dominant energy condition ensures that energy doesn't propagate faster than light; it says p ρ, so -1 w 1. But we can make a model with w < -1: a negative-kinetic-energy scalar field, L = -φ 2. exp(-φ 2 ). V(φ) φ Problem: instability to decay (positive-energy gravitons, negative-energy φ bosons). Can be avoided if we put a cutoff on the theory: momenta less than 10-3 ev. Remember: nobody ever measures w, really. We only measure the behavior of the scale factor.

28 Don't forget the possibility of direct detection of dark energy. Dynamical dark energy has no right to be completely "dark"; even if it only directly couples to gravity, there will be indirect couplings to all standard-model fields. ϕ quantum gravity γ γ Loophole: pseudo-goldstone bosons. (Or an honest cosmological constant.)

29 Direct dark energy detection search strategies: 5 th forces. Time-dependent "constants of nature" (e.g., α). Cosmological birefringence. [Webb et al.]

30 Imagine a modified Friedmann equation (e.g., from extra dimensions): H 2 p [Arkani-Hamed et al; Kachru et al; Carroll & Mersini] 4) Was Einstein wrong? This would render the cosmological constant invisible, rather than small. But: BBN provides good evidence that the Friedmann equation responds to density, not to pressure. [Carroll & Kaplinghat] Notice: there is a coincidence problem!

31 Alternatively, GR could break down at a fixed scale that becomes important only at the present day. Examples: 1) modified energy-density dependence H 2 8 G 1 x 3 2) modified Hubble-parameter dependence [Freese & Lewis] H 2 1 H x H It's very hard to distinguish between this and dark energy. 8 G 3 [Dvali & Turner]

32 A toy model for deviations from GR at long distances: Replace the Einstein-Hilbert action S 1 16 G Rd 4 x with the modified form S 1 16 G R L 4 R d4 x This implies deviations from ordinary GR at low curvatures. But does it make sense? [Carroll, Duvuuri, Trodden & Turner]

33 Conclusions There are many interesting ideas about the cosmological constant problem; none rises to the level of "promising". An ordinary cosmological constant is a perfect fit to the dark-energy data, even if we can't explain it. Dynamical mechanisms are interesting and testable; to date, they raise at least as many problems as they solve. My suspicion: we just got lucky. Our task then is to figure out how to correctly calculate the vacuum energy. This will require a significant breakthrough.