Gravity in the Quantum World and the Cosmos XXXIII SLAC Summer Institute, August 2005 Rocky Kolb, Fermilab & Chicago

Transcription

1 Gravity in the Quantum World and the Cosmos XXXIII SLAC Summer Institute, August 2005 Rocky Kolb, Fermilab & Chicago

2 Precision cosmology MAP WMAP

3 What is the nature of dark energy? In questions like this, truth is only to be had by laying together many variations of error. -- Virginia Woolf A Room of Ones Own

4 Robertson-Walker metric () at k = 0, ± 1 = cosmic scale factor dr ds dt a () t r d 1 kr Big-Bang Bang G = + Ω 2 = 8π GT µν µν Perfect-fluid stress tensor ρ = p = T µ ν energy density pressure = diag( ρ, ppp,, )

5 2 Field equations a k 8π G a + = expansion rate 2 = ρ H a a 3 a a 4π G a 1 = ( ρ + 3 p) q 2 = deceleration parameter a 3 ah µν 3(1 w) T ; = 0 a + w= p ν ρ ρ T µν : fluids with different w radiation: p = ρ 3 w= 1 3 ρ a R R R matter: p = 0 w= 0 ρ a M vacuum: p = ρ w= 1 ρ a Λ Λ Λ M 4 3 0

6 scale factor a decelerated a < 0 ρ + 3p > 0 time Newton Einstein scale factor a 4π G a = ρ + 3p 3 ( ) accelerated a > 0 ρ + 3p < 0 fluid with w = p/ρ < 1/3 time

7 2 Dynamics Evolution a k 8π G + ( ) ( ) ( ) 2 = ρ ρ = ρm a + ρr a + ρ Λ a + a a 3 a(t), H(t), depend on matter/energy content a(t) measurable via redshift 1 + z a(0)/a(t) Redshift z is a proxy for time or scale factor

8 a(t) Time (billions of years from today)

9 Evolution of H(z) is a key quantity Many observables based on the comoving distance r Luminosity distance 2 Flux = Luminosity 4π dl Angular diameter distance sin Angular diameter = Physical size d A Comoving volume element ( ) 1 N V z ( ) r z ( ) ( ) Age of the universe t( z) -1 sinh r z -1 r z L z dz = H 0 ( z ) ( ) ( )( 1+ ) d z R z z d A ( z) R( z) ( 1 ) + z dv z R z dz dω H z ( ) 2 ( ) z ( + z ) H( z ) 0 1 ( ) dz R( z)

10 Hubble s Discovery Paper s v = Hd 0 ( H0 = Hubble's constant) -1-1 H0 = 100 h km s Mpc h = 5

11 h h = 0.72 ± 0.03± 0.07 Freedman et al. (Hubble Key Project) = ± 0.03 (WMAP 2003) Riess et al astro-ph/ Hubble s data

12 Type Ia supernova apparent magnitude [log(distance)] *Saul Perlmutter, PI *

13 deceleration acceleration transition at z = 0.46 ± 0.13 Riess et al. Astrophys.J.607: ,2004

14 High-z SNeIa are fainter than expected in an Einstein-deSitter model Ω VACUUM cosmological constant, or some changing non-zero vacuum energy, or or some unknown systematic effect(s) The case for Λ: 1) Hubble diagram d L (z) 2) subtraction Einstein-de Sitter flat, matter-dominated model (maximum theoretical bliss) Ω MATTER

15 Subtraction Ω i ρ i /ρ C dynamics lensing ρ C 3H 0 2 /8πG x-ray gas cmb simulations power spectrum Ω TOTAL = 1 (CMB), Ω M = 0.3, = 0.7

16 High-z SNeIa are fainter than expected in an Einstein-deSitter model Ω VACUUM Einstein-de Sitter flat, matter-dominated model (maximum theoretical bliss) cosmological constant, or some changing non-zero vacuum energy, or or some unknown systematic effect(s) The case for Λ: 1) Hubble diagram d L (z) 2) subtraction Ω TOTAL = 1 Ω Μ = = 0.7 3) age of the universe Ω MATTER

17 t 0 : age of the universe size challenged star white dwarf star cooling nucleocosmochronology globular cluster evolution 11± 2 Gyr 12.6 ± 3 Gyr 13.5 ± 2 Gyr H 0 =70 Flat Open Open Flat Flat Ω M Ω Λ t (Gyr)

18 High-z SNeIa are fainter than expected in an Einstein-deSitter model Ω VACUUM Einstein-de Sitter flat, matter-dominated model (maximum theoretical bliss) Ω MATTER cosmological constant, or some changing non-zero vacuum energy, or or some unknown systematic effect(s) The case for Λ: 1) Hubble diagram d L (z) 2) subtraction Ω TOTAL = 1 Ω Μ = = 0.7 3) age of the universe 4) structure formation

19 Einstein s Biggest Blunder? 1917 Einstein proposes cosmological constant 1929 Hubble discovers Expansion of the universe 1934 Einstein calls it my biggest blunder 1998 Astronomers find evidence for it

20 Mass density of space: ρ Cosmological constant ( ) ( ) ( 29 ) 2 ( 33 ) 2 10 g cm 10 ev = 10 cm Λ Λ= = = 8πG ρ 10 cm 10 ev Λ The unbearable lightness of nothing! Cosmo-illogical constant? Numerology: ρ = M exp 2 α ρ = M M m ( ) V W V SUSY Pl ν = 10 ev R = 10 cm 3 4 5

21 Cosmic coincidence Ω +Ω M R GUT Cosmic Coincidence? EWK BBN REC ρ ρ ρ ρ ρ ρ Λ DM B B VISIBLE B DARK υ Every party represented! Ω Λ

22 Dark energy depression? 1. Alcohol* 2. Drugs* 3. Anthropic principle* 4. Creative theories 5. Hard experimental work 6. Observational direction * Therapy, medication, and twelve-step programs available.

23 Field equation: Take sides! R g R g GT 1 µν 2 µν Λ µν = 8π µν Perfect fluid stress tensor: T µ ν = diag ρ, p, p, p ( ) I found it very ugly indeed that the field law of gravitation should be composed of two logically independent terms connected by addition. About the justification of such feelings concerning logical simplicity it is difficult to argue. I cannot help to feel it strongly and I am unable to believe that such an ugly thing should be realized in nature. Einstein in a letter to Lemaitre, Sept. 26, 1947 Modern view: It belongs on the right-hand side, and has many contributions. T µ ν = diag ρ, ρ, ρ, ρ ρ =Λ 8 π G ( ) Λ Λ Λ Λ Λ ( ) R g R= G T + T 1 µν 2 µν 8π µν µν

24 Take sides! Something is established ΛCDM too good to ignore SNIa Subtraction H(z) not given by Age Einstein de Sitter Large-scale structure cosmological model Dark energy (right-hand side of Einstein equations)? Is it just a cosmological constant? If not cosmological constant, what is dynamics? interpretation of w = ρ/p? Gravity (left-hand side of Einstein equations)? Beyond Einstein (non-gr: branes,etc.) (Just) Einstein (Back reaction of inhomogeneities)

25 Quantum uncertainty Fourier modes of all fields are harmonic oscillators with a zero-point energy classical E = 0 quantum E = ω 1 2 ρ = ± + all particles dk k m 3 2 2

26 ρ Quantum uncertainty all particles ΛC = ± + ± Photons couple to virtual particles Lamb shift γ dk k m dkk e - all particles Gravitons couple to virtual particles Cosmological constant g e - e + e + Λ = = = C 4 : ρλ bad prediction Λ = M = M = ( ) 4 28 C Pl : ρλ Pl 10 ev Λ = M = M = ( ) 4 12 C SUSY : ρλ SUSY 10 ev Λ = = C 3 10 ev: ρλ Observed 4 4

27 Spontaneous symmetry breaking V(φ) hightemperature lowtemperature GUT: (10 GeV) SUSY: (10 GeV) EWK: (10 GeV) CHIRAL: (10 GeV) OBSERVED: (10 GeV) φ

28 WD-40 Many possible contributions. Why then is total so small? Perhaps unknown dynamics sets global vacuum energy equal to zero but we re not there yet! V(φ) V(φ) Universe hung up Universe rolling along 0 Λ φ 0 Λ φ Frieman, Freese, Hill, Olinto,..

29 WD-40 But why now? n Tracker potentials, e φ, φ, relate dark energy to other contributions. Field equation for tracker: Why now?.. close to matter domination Why now?.. it s just that time Wetterich; Ratra & Peebles; φ + 3H φ+ dv dφ = 0 2 8π G H = ( ρ ) φ ρm Can have ρ φ track (stalk) ρ M - effective mass of the field decreases as H: close but not final answer

30 WD-40 φ dark energy destiny V ( φ ) = e φ 1+ αsinφ ( ) Ω Λ Dodelson, Kaplinghat, Stewart

31 WD-40 Quintessence models have very light scalar fields Long-range interactions? Carroll 1998

32 Entertaining conjecture Now entertain conjecture of a time When creeping murmur and the poring dark Fills the wide vessel of the universe. Shakespeare, King Henry V th All evidence for dark energy (creeping murmur) is indirect! SNIa Age : LSS dz H ( z) Observed time evolution of H does not fit Einstein de Sitter. We infer the existence of dark energy! Could Friedmann equation be modified-and no dark energy?

33 Modifying the left-hand side Braneworld modifies Friedmann equation Binetruy, Deffayet, Langlois Friedmann equation modified today Gravitational force law modified at large distance Tired gravitons n ( ) 1 2 H = Aρ 1+ ρ ρcutoff Five-dimensional at cosmic distances Gravitons metastable - leak into bulk Gravity repulsive at distance R Gpc n=1 KK graviton mode very light, m (Gpc) -1 Freese & Lewis Deffayet, Dvali & Gabadadze Gregory, Rubakov & Sibiryakov; Dvali, Gabadadze & Porrati Csaki, Erlich, Hollowood & Terning Kogan, Mouslopoulos, Papazoglou, Ross & Santiago Einstein (Hilbert) got it wrong = 16π µ ( ) ( ) S G d x g R R Backreaction of inhomogeneities Carroll, Duvvuri, Turner, Trodden Räsänan; Kolb, Matarrese, Notari & Riotto, Notari; Kolb, Matarrese & Riotto

34 Braneless cosmology Old Friedmann law: G = M T 2 00 Pl 00 3H = M ρ 2 2 Pl Friedmann (1921) SNIa evidence for dark energy: dz H( z)

35 Brane cosmology Israel junction condition (Israel 1966) the brane A n i i i n A : unit vector normal to the brane h = g n n κ AB AB A B = h n C AB A C B = 3 BRANE κ µν M* T µν : the induced metric : the extrinsic curvature [...] = discontinuity across the brane a = a + a y [ ] δ ( ) discontinuity in second derivative of scale factor

36 Braneless cosmology Old Friedmann law: G = M T 2 00 Pl 00 3H = M ρ 2 2 Pl Friedmann (1921) SNIa evidence for dark energy: dz H( z) Braneful cosmology New Friedmann law: Israel jump conditions 3H Binetruy, Deffayet, Langlois (2000) Λ M 6 2 * 2 = + ρ a ( t, y 0) c =

37 Brane cosmology New Friedmann law Binetruy, Deffayet, Langlois (2000) 3H Λ M 6 2 * 2 = + ρ a ( t, y = 0) Possible solution Randall & Sundrum (2000) 3H Introduce a tension σ on the brane ρ ρ+ σ Λ M M M c * 2 * * 2 = + σ + σρ+ ρ a ( t, y = 0) c cosmological constant (cancels?) 6 M* 8π G σ = 18 3 Friedmann equation unconventional corrections

38 Inhomogeneities Most conservative approach (no new fields, gravity, extra dimensions) Universe is inhomogeneous & anisotropic smooth Matter smoothing is straightforward (particles fluid), space-time metric smoothing not straightforward! Suppose Al s equations apply on some small inhomo/aniso scale Smooth on some larger scale Smoothing and evolution (going to field eqns.) do not commute Einstein tensor computed from smoothed metric is not the same as Einstein tensor computed from smoothed stress-energy Difference is a new term that enters Friedmann equation New term need not obey energy conditions! Ellis, Barausse, Buchert, Ellis, Kolb, Matarrese, Notari, Räsänan, Riotto, Schwarz

39 Inhomogeneities The Universe is inhomogeneous One can define an average density ρ The expansion rate of an inhomogeneous universe of average density ρ is NOT! the same as the expansion rate of a homogeneous universe of average density ρ! We deduce dark energy because we are comparing to the wrong model universe Acceleration is a pure GR effect

40 Inhomogeneities H(z) in a perturbed FLRW model: Gµν x t Gµν t Gµν x t FLRW 2 G00 t G00 x t T00 x t 2 2 ( ) ( 2 3 aa = κ ρ κ δg ) 00. (a/a) 2 is not κ 2 ρ /3. FLRW (, ) = ( ) + δ (, ) ( ) + δ (, ) = κ (, ). a/a is not even the expansion rate. Kolb, Matarrese, Notari & Riotto

41 Inhomogeneities For a general fluid, four velocity u µ = (1,0). (Local observer comoving with energy flow) For irrotational dust, work in synchronous and comoving gauge 2 2 i j ds = dt + hij ( x, t) dx dx Velocity gradient tensor 1 Θ = = =Θ + i i ik i i j ; j 2 kj j j u h h δ σ Θ is the volume-expansion factor and σ i j is the shear (Θ =3H and σ i j = 0 in the homogeneous case)

42 Inhomogeneities Local deceleration parameter positive (no-go theorem): ( 2 3Θ+Θ ) ( 2 q = = 6 σ + 2πGρ) 0 2 Θ Hirata & Seljak; Flanagan; Giovannini; Alnes, Amarzguioui & Gron However must course-grain over some finite domain: F D D = D 3 hfd x 3 hdx Evolution and smoothing do not commute: F F = FΘ Θ F D D D D D 2 2 Θ = Θ + Θ Θ Θ D D D D D Buchert & Ellis Kolb, Matarrese & Riotto astro-ph/ Invalidates no-go theorem

43 Define an effective scale factor: ( ) 1/3 3 a V V V d x h = D D D0 D Course-grained Hubble rate: a D 1 H D = = 3 Θ D a a a D D D Effective evolution equations: 4π G = eff a D = a D ( ρ 3p ) 8π G ρ 3 Inhomogeneities eff eff ρ p eff eff D Q R D D = ρ D 16π G 16π G Q R D D = + 16π G 48π G Kolb, Matarrese & Riotto astro-ph/ Buchert & Ellis not described by a simple p = w ρ Kinematical back reaction: ( 2 ) 2 QD D = Θ Θ σ D D

44 Inhomogeneities Does this have anything to do with our universe? Have to go to non-perturbative limit Toy model proof of principle: Tolman-Bondi dust model (Nambu and Tanimoto (gr-qc/ )

45 How do we sort it out? Something is established-λcdm too good to ignore SNIa Subtraction Age Large-scale structure.. Left-hand side or right-hand side? Left-hand side: Growth of structure New gravity? solar-system effects short-range effects branes (accelerator effects) Inhomogreneities? Right-hand side: w = 1 just Λ? w 1 what is dynamics? Scalars long-range forces?

46 For now parameterize High-z supernova team

47 w < 1? null dominant energy condition: energy doesn t propagate outside the light cone p ρ ρ p ρ model with w < 1: negative kinetic energy scalar field 2 2 L = φ exp φ ( ) instability cured with higher derivative terms?

48 Caution in interpretation Always read the fine print: Astrophysical systematic errors What are the model assumptions? w = constant? w', w a assume Ω Λ? What are the priors? Ω M, Ω B, H 0,

49 Riess et al.

50 Evolution of H(z) d L (z) d A (z) V(z) SNIA X-ray cluster luminosity Baryon Clumps Strong Lensing CMB Cl Weak lensing Cluster counting Growth of perturbations CMB Cluster counting weak lensing P(k,z)) Theory and simulation Models of dark energy Phenomenology Growth of structure

51 Don t focus on any one particular error contour Focus on fact that error contours for different methods are not parallel

52 Aether of the 21 st century? It s an infrared issue! It s an ultraviolet issue!

53 Gravity in the Quantum World and the Cosmos XXXIII SLAC Summer Institute, August 2005 Rocky Kolb, Fermilab & Chicago