Dark Energy. Discovery accelera-ng universe in Leads to component with large nega-ve pressure: dark energy. Alterna-ve: modify GR

Transcription

1

2 Dark Energy Discovery accelera-ng universe in 1998 Leads to component with large nega-ve pressure: dark energy Alterna-ve: modify GR 2011: strong observa-onal evidence for dark energy

3 Nature of DE is one of biggest open ques6ons in physics: 3/4 of our universe understanding it could teach us about fundamental physics fate of the universe

4 Outline Discovery Theory Future Constraints

5 a Friedmann Equa6on: H 2 a The Equa6on of State basics/nota5on 2 = 8πG 3 ρ T k a 2 Con6nuity Equa6on: Equa6on of State: Constant EoS: Accelera6on equa6on: dρ i d lna + 3(ρ + p ) = 0 i i w i = p i /ρ i ρ i a 3(1+w i ) a a = 4πG 3 ( ρ T + 3p ) T = 4πG 3 ρ T (1+ 3w T ) total equa6on of state w T < - 1/3 accelera6on

6 DISCOVERY

7 Early Evidence 1980 s low ma1er density Dynamical mass es-mates: Ω m 0.2 Infla-on predicts: Ω tot 1 e.g. Peebles 1984, Turner, Steigman & Krauss 1984 Solu-on: add cosmological constant: Ω Λ 0.8

8 Early Evidence 1990 s the age problem Oldest globular clusters: age Gyr Given H 0, age of maier- only Universe: t Gyr Solu-on: adding cosmological constant makes universe older, t Gyr Color vs Magnitude Chaboyer 1998

9 Discovery: Type IA Supernovae cosmic distances Luminosity distance vs redshiq probes expansion history: Luminosity distance Need know intrinsic intensity! (spa-ally flat universe) Type IA supernovae all have same intrinsic intensity * ( standard candles )

10 Type IA Supernovae White dwarf accre5ng mass from companion turns supernova when reaches Chandrasekhar limit Brightness depends on amount of 56 Ni produced about the same for all type IA s We measure lightcurve (and redshiq): lightcurve Amanullah et al, 2010

11 Astronomers use magnitude * : * Thanks a lot, Ptolemy! The Hubble Diagram magnitudes with (spa-ally flat universe) ScaIer dm 0.3 AQer calibra-on lightcurve- width vs luminosity, dm 0.15 (!) Separate from z- dependent part cosmology

12 The Hubble Diagram remember: (spa-ally flat universe) Perlmufer et al, 1999 Riess et al, 1998

13 Original SN data Perlmufer et al, 1999 in general: Ω Λ > 0 at 99% CL assuming flatness: Ω Λ = /- 0.14

14 Current Constraints: Added informa6on from: - CMB: spa5al flatness verified (Boomerang, Maxima, DASI, around 2000), etc - Baryon Acous5c Oscilla5ons - Large Scale Structure Power Spectrum - Weak Lensing - Addi5onal SN data Ω Λ = / Amanullah et al, 2010

15 (assuming flatness) Beyond Λ Amanullah et al, 2010 Constant equa-on of state w=p/ρ: w = / Varying EoS w(a) = w 0 + w a (1 - a): σ(w 0 ) 0.2, σ(w a ) 0.6

16 THEORY

17 Einstein s Cosmological Constant GR has room for extra constant, Λ R µν 1 2 Rgµν Λg µν = 8πGT µν Einstein s biggest blunder A. Einstein 1917

18 Vacuum Energy Even if set bare Λ=0, quantum correc-ons give non- zero Λ Vacuum energy has general covariance R µν 1 2 Rgµν Λg µν Hence i p = T i = T 0 0 = ρ ( w = 1 ) T µν vac = ρ vac g µν = 8πGT µν µν 8πGT vac or because of Λ eff = Λ + 8πGρ vac ρ Λ = ρ vac + Λ e.g. Zel dovich πG

19 The Cosmological Constant Problem Why is the cosmological constant so small? Observed value: ρ Λ ρ c, ev M pl 1. Vacuum energy contribu-on for each boson/fermion diverges: M c ρ vac,i = ± 0 d 3 k 1 (2π) 3 2 k m i So, with SM par-cle content 4 ρ vac ρ Λ M cutoff - Planck scale cutoff: M cutoff = M pl ρ Λ ρ vac SUSY: M cutoff = M SUSY ρ Λ ρ vac 10 58

20 The CC Problem Phase TransiFons 2. Phase transi-ons Δρ vac >> ρ Λ e.g. electroweak transi-on: Δρ vac (200GeV ) 4 ρ Λ = ρ vac + Λ 8πG explaining observed CC requires enormous fine- tuning

21 Not a new problem *, but renewed interest since discovery of dark energy ATempts: - Global SUSY: ρ vac = 0 - SUGRA: scale- free models - String Theory afempts Any Solu6ons?, but broken + need gravity - No solu5ons that actually solve the CC problem * see e.g. Zel dovich 1968, Weinberg 1989

22 The Coincidence Problem ρ m ρ r ρ Λ Why does ρ Λ come to dominate now?

23 Bousso, Weinberg, Vilenkin,.. The Anthropic Approach String theory: mul-verse of >> different vacua with different values of ρ Λ Sketch of possible mechanism (see Bousso arxiv: for a review): can have 100 s of quan-zed four- form fields contribu-ng to vacuum energy N i=1 Λ = λ n i 2 q i 2 want at least one configura-on with N 2 λ < n 2 i q 2 i < 2( λ +Λ obs ) i=1 Works if: - λ < 0 of order Planck scale - N = 100 fields - charges of order 0.01

24 The Anthropic Approach eternal infla-on: pocket universes come into existence through bubble nuclea-on, popula-ng large number of different vacua Weinberg s original argument: only galaxies/observers if < ρ Λ < Schema-cally:" P(Λ) P prior (Λ) # observers(λ) Predic-on can be made to agree with observa-on: Bousso et al 2007

25 Dynamical Dark Energy Assumes ρ Λ =0 and dark energy dynamical Mo6va6on: Infla5on Toy models (something to look for observa5onally) Examples: quintessence k- essence modified gravity

26 Quintessence Single scalar field with canonical kine5c term Analogous to infla5on Ac6on: Equa6on of Mo6on: S = d 4 x g( 1 M 2 2 plr 1 2 µ φ µ φ V (φ)) + S b φ + 3H φ +V '(φ) = 0 Hubble fric5on driving force Energy Density: Friedman Equa6on: H 2 = 1 ρ φ = 1 2 φ 2 + V (φ) kine-c poten-al 3M pl ( ) 2 ρ rest + ρ φ maier/ radia-on Pressure: p φ = 1 2 φ 2 V(φ)

27 Example 1: Quadra6c Poten6al (representa6ve of thawing models ) V (φ) = 1 2 M 2 φ 2 Early Times: H >> M field frozen, ρ φ const. When H M : field starts rolling Late Times: field oscillates around minimum energy dilutes as cold maier Need: (1) M H ev to get w -1 today (2) to get φ 0 M pl V (φ 0 ) ρ 0

28 V (φ) = 1 2 M 2 φ 2 Ω φ : EquaFon of State History: 1 2 w = φ 2 V(φ) 1 φ 2 +V(φ) 2 φ in =1.5M pl φ in = 2M pl φ in =10M pl

29 Thawing Models V (φ) = 1 part of class of thawing models 2 M 2 φ 2 Field starts frozen (w=- 1), then moves toward larger w Analogy with large field models infla-on Examples: - Pseudo- Nambu Goldstone boson: Caldwell & Linder 2005 V (φ) = m 4 ( 1+ cos(φ / f +θ) ) - Other (posi5ve) power law poten5als: V (φ) = M 4 n φ n

30 Example 2: Inverse Power Laws Early behavior: V (φ) = M 4 +α φ α ρ φ << ρ other 1+ w = α attractor for wide range of initial conditions ρ ϕ decays more slowly than background ρ at equality: φ = ρ m = α 4 + α ( 1 3 α(2 + α)) α / 2 M M pl Ratra & Peebles, α (1+ w other) <1+ w other 4 +α 4 M pl 123 /(4 +α ) need M / M pl 10 maier! ρ(a) α=1 α=4 α=0.5 a

31 V (φ) = M 4 +α φ α Late behavior (asymptofc future): field freezes : w 1 when ρ ϕ dominates: 2 m eff α 2 φ H 2 V (φ) φ α m eff H φ α 0 EquaFon of State History: Mafer domina5on: w = α Quintessence domina5on: Today: Ω φ 0.72 Need α 0.5 and w 1 w 0.8 (from observa-on) α=4 α=1 α=0.5 a Ω ϕ (a) w(a)

32 Tracking Models AIractor reached from wide range of ini-al condi-ons AIractor solu-on determined by dominant component (maier/radia-on): w = w(w b ) Special class: tracing models : w = w b Examples: - SUGRA model: - Exponen-al poten-als: - Albrecht- Skordis: V (φ) = M 4 +α φ α e φ 2 / 2 V (φ) = M 4 e λφ V (φ) = M 4 ( χ(φ β) 2 +δ)e λφ

33 General Lessons Mass m H ev Field Δφ M pl Naturalness problem Can get interes5ng dynamics: equa5on of state approaching/ moving away from w=- 1 Models can be divided into classes: w a tracking modified gravity thawing w 0 de Pufer & Linder 2008

34 Other Models Within GR: K- Essence Mul5- field (spintessence) Coupled models Modified Gravity: F(R) DGP (extra dimensions) ( ) S = d 4 x g 1 2 M 2 pl R + L( 1 2 µ φ µ φ,φ) + S b

35 FUTURE CONSTRAINTS

36 Perturba6ons Small perturba-ons (10-5 ) seeded by infla-on lead to large scale structure Density perturba-on: Linear growth equa-on maier: Hubble fric-on term (self) source term

37 Dark Energy Probes Type IA Supernovae Baryon Acous6c Oscilla6ons Clusters Weak Gravita6onal Lensing 37

38 Some (Op6mis6c) Forecasts Dark Energy Equa6on of State: - σ(w 0 ) = 0.041, σ(w a ) = σ(w 0 ) = 0.02, σ(w a ) = 0.1 BOSS, e.g. arxiv: EUCLID, e.g. arxiv:

39 THE END