Dark Energy and The Preposterous Universe

Transcription

1 Dark Energy and The Preposterous Universe Sean Carroll, University of Chicago With: Jennie Chen, Mark Hoffman, Manoj Kaplinghat, Laura Mersini, Mark Trodden Time Relative size at different times is measured by the scale factor a(t). Executive Summary: We finally have a good idea of what the universe is made of. But it makes no sense. The next step is to move from inventory to understanding. a The universe: uniform (homogeneous and isotropic) space expanding with time. > Big Bang < c t Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 1

2 Einstein s General Relativity relates the expansion rate H (the "Hubble constant") to the energy density ρ (ergs/cm 3 ) and the spatial curvature κ : H 2 = 8 π G 3 ρ κ a 2. H is related to the scale factor by H = a/a. You can figure out the history of the universe if you know how ρ scales as a function of a. So cosmologists want to know: what kind of stuff makes up the universe, and how does it evolve with a? What makes up the universe? Stars and gas are slowly moving (compared to c, the speed of light). Most of their energy is rest energy, from their mass (E = mc 2 ). Anything which is mostly rest energy, cosmologists call "matter". The energy density in matter is its rest energy times its number density n M : ρ M = n M m c 2 Hence: ρ M a 3, since the number density gets diluted as the volume expands. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 2

3 In contrast to matter, consider "radiation" (particles moving at speeds close to c). Radiation redshifts as the universe expands, as wavelengths get stretched; each particle loses energy as 1/a. Particles redshift and number density dilutes, so the energy density in radiation goes as ρ R a 4. Today, there is much more matter than radiation. First surprise: Most matter in the universe is not comprised of ordinary stuff (atoms etc.), but some completely different kind of particle. It s invisible and transparent, and is given the name Dark Matter. There is about five times as much dark matter as ordinary matter. How do we know? We can detect its gravitational pull, through dynamics of galaxies, gravitational lensing, etc. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 3

4 Even with dark matter, there is still not as much matter in the universe as we might expect. Define the density parameter, Ω : Then, from the Friedmann equation, Ω > 1 κ > 0 Ω = 1 κ = 0 Ω < 1 κ < 0 Ω = 8 π G 3 H 2 ρ positive curvature Observed matter content (ordinary plus dark): Ω M = 0.3. flat negative curvature Second surprise: Most of the universe isn t even matter! It s something called Dark Energy, which: is smoothly distributed through space varies slowly (if at all) with time. Paradigmatic candidate: vacuum energy (a/k/a the cosmological constant, Λ). An immutable energy inherent in every cubic centimeter of space. (artist s impression of vacuum energy) Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 4

5 If there were dark energy, how would we know? Contributes to density (Ω Tot = Ω M + Ω DE ), and hence to curvature κ. Redshifts away slowly, so makes the universe. accelerate: a a ρ (from Friedmann eq.) Fortunately, these are things we can go look for. 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. Result: the universe is flat! Ω Tot = 1. [TOCO; Boomerang; Maxima; DASI] Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 5

6 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.] Concordance: Ω Μ = 0.3, Ω Λ = 0.7. [Jaffe et al.] Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 6

7 The final accounting seems to be: 5% Ordinary Matter 25% Dark Matter 70% Dark Energy This is a preposterous universe. Dark Energy Dark Matter Ordinary Matter Why is the dark energy density small, but not quite zero? Naive expectation: ρ DE (theory) /ρ DE (obs) = Why now? Remember ρ DE /ρ M ~ a 3. So why are they approximately equal today? For that matter: Why are the amounts of "ordinary" and "dark" matter comparable? (And why isn t there as much antimatter as matter?) Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 7

8 Why is the vacuum energy so small? Vacuum energy is the most natural thing in the world. Consider a single scalar field: V(φ) ρ φ = 1 2 φ φ 2 V φ φ = const ρ φ = V φ = const. Crucial point: no known (unbroken) symmetry would prefer V(φ) = 0. Another contributor to vacuum energy: quantum fluctuations. Every Fourier mode of any quantum field acts like an harmonic oscillator, with a corresponding zero point energy. Classical: E 0 = 0 Quantum: E 0 = 1 2 ħ ω Integrating over these modes gives an infinite vacuum energy; imposing a Planck scale cutoff yields ρ vac (theory) = (M Pl = ev) 4 = ρ vac (obs) Obtaining agreement would require neglecting all modes smaller than (10 3 ev) 1 = 1 mm. φ Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 8

9 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. Bad news: We don t live in a perfectly supersymmetric universe; SUSY is (likely) broken around M SUSY ev. Good news: This makes the cosmological constant problem (theory) not so bad: ρ vac = (M SUSY = ev) 4 = ρ (obs) vac. Bad news: This is a much more reliable calculation! You are here Why are vacuum and matter comparable? The "best fit universe" with Ω M = 0.3, Ω Λ = 0. 7 is an unstable point, caught in the process of evolving from purely matter to purely vacuum. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 9

10 And it s moving quickly: Ω Λ Ω M a 3 Ω R Ω M Ω Λ What might be going on? Possibilities include: The true vacuum energy is small, but nonzero. We live in a false vacuum; the true vacuum has zero energy. A slowly varying dynamical component is mimicking a vacuum energy. Einstein was wrong. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 10

11 1) Might the true vacuum energy be nonzero? Some numerology: M S U S Y = M Pl anck M v a c 4 M vac = e 2 α 4 M Planck There are no very good reasons why any such formula ought to be true. But the idea is to derive the vacuum energy from other parameters, and attribute the coincidence problem to just being lucky. By the way: String theorists find it very hard to get ρ v a c > 0. Perfectly reasonable people are driven to invoke the anthropic principle. 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 = (1 10) ρ Μ (just as we do). [Garriga & Vilenkin; Martel, Shapiro & Weinberg] Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 11

12 V(φ) 2) Do we live in a false vacuum? Good: compatible with ρ v a c = 0 ultimately. Bad: why would the splitting be so tiny? φ Keep in mind: No observational signature. Stability not really an issue. 3) Is the dark energy a slowly varying dynamical component? e.g. a slowly rolling scalar field: "quintessence" V(φ) Good: Consistent with ρ vac = 0 ultimately. Observationally interesting. Consistent with string theory? Solve the coincidence problem? Bad: Unnatural particle physics. (m φ ~ ev) Should have been detected already. φ Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 12

13 Characterize using an effective equation of state relating pressure to energy density: p = w ρ For matter, w = 0; for actual vacuum energy, w = 1. Limits from supernovae and large scale structure are already pretty good: Should we consider w < 1? [Perlmutter, Turner & White] Against: Violates "null dominant energy condition" ( ρ <= p ; ρ +p >= 0). For: Nevertheless possible to find apparently stable models [e.g. L = -φ 2 exp(-φ 2 )].. [Caldwell] V(φ) φ Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 13

14 Could dark energy dynamics solve the coincidence problem? e φ "Tracker" potentials like and 1 φ lead to a dark energy density which remains proportional to the dominant source; of course, this doesn t make the universe accelerate! At issue: we need something special about today in order to make today special. Two possibilities: Today is not so far (on a log scale) from matter/radiation equality (z eq ~ 10 4 ). Perhaps acceleration is something that just happens from time to time. "k essence": energy density evolves differently during matter & radiation dominated eras "Tracks" during radiation era, then "sticks" during matter era. Mechanism: Novel kinetic energy: ρ M R k L= f φ g φ 2 a [Armendariz Picon, Mukhanov & Steinhardt] Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 14

15 Oscillating dark energy: just something that happens from time to time. Mechanism: Perturbed tracker: V φ =e φ 1 α sin φ Dark energy has no right to be completely "dark"; it should couple weakly to standard model fields. ϕ quantum gravity [Dodelson, Kaplinghat & Stewart] Slowly rolling, nearly massless fields lead to long range "5 th forces", in addition to gradual evolution of the "constants" of nature. γ γ L β M Pl φ F µ ν F µ ν (β is a dimensionless constant) To avoid detection in experiments to date, we need to introduce dimensionless couplings of order or less. on the other hand... Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 15

16 ... maybe α is changing slowly with time? [Webb et al.] But there s a competing limit: the Oklo Natural Reactor. 1.8 billion years ago, a natural water moderated fission reactor operated in Gabon, West Africa. Isotopic abundances constrain the 149 Sm neutron capture cross section, and thus α. Result: α/α < (95% CL) at redshift z [Damour and Dyson] Issues: initial abundances, variation of other constants. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 16

17 Can the Oklo and absorption α/α Oklo line results be reconciled? If a scalar field ϕ is responsible, we need the evolution of ϕ to have slowed down signficantly. This can happen in some models, but usually not by so much. Sensible particle physics models? Pseudo Goldstone bosons: approx symmetry φ φ const. Naturally small masses; naturally small couplings. V φ = µ 4 1 cos φ z V(φ) No tracking behavior; any effective w possible. Possible signature: cosmological birefringence. φ [Hill, Freiman, et al; Carroll] Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 17

18 Dynamical dark energy doesn t have to be a rolling scalar field. Some alternatives: A web of tangled topological defects (i.e. a "solid") Dark matter particles with gradually increasing masses Ultra short wavelength (transplanckian) modes Curved spacetime renormalization effects 4) Was Einstein wrong? Extra dimensions, scalar fields, holography... Test using Big Bang Nucleosynthesis. Usual story: T > 1 MeV: [Vilenkin, Bucher, Pen, Spergel] [Anderson & Carroll] [Bastero Gill, Mersini] [Parker & Raval] Weak interactions rapidly interconvert protons and neutrons. 1 MeV > T > 80 kev: Weak interactions frozen out; n/p decays from 1/6 to 1/7. T = 80 kev: Deuterium can survive; neutrons rapidly converted to 4 He, plus trace amounts of 2 D, 3 He, 7 Li. Generally: Increasing H increases 4 He, and vice versa. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 18

19 Result: a range of allowed histories, but all within the vicinity of the conventional model. Notice: there is a coincidence problem! [Carroll & Kaplinghat] BBN tests GR on length scales of the Hubble radius at z ~ 10 9 (solar system scales). Alternatively, GR could break down at a fixed length scale corresponding to the current Hubble radius. Even better: perhaps this breakdown explains away both dark matter and dark energy. Milgrom (infamously) points out: galactic dark matter is only required for accelerations a c < s 1 Meanwhile, the universe starts accelerating when the Hubble constant reaches H 0 Coincidence? Probably s 1 [see e.g. Kaplinghat & Turner] Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 19

20 Conclusions Something dark and mysterious is going on. An ordinary cosmological constant is a perfect fit, even if we can t explain it. Dynamical mechanisms are interesting and testable; they also raise additional problems. Answering these questions will tell us something extremely profound: either about particle physics or about gravity, and certainly about cosmology. Dr. Sean Carroll, Enrico Fermi Institute (ITP Colloquium ) Dark Energy and the Preposterous Universe Page 20