Theoretical Explanations for Cosmic Acceleration

Transcription

1 Theoretical Explanations for Cosmic Acceleration Eanna Flanagan, Cornell Physics Colloquium, University of Guelph, 17 October 2006

2 Outline Recent observations show that the expansion of the Universe is accelerating, which according to general relativity implies the existence of a form of matter with negative pressure (dark energy). Negative pressure in general relativity Acceleration: observational pillars Why the new physics required is puzzling Survey of (i) frameworks (ii) models (iii) theoretical problems (iv) potential new observational channels Can we avoid dark energy by modifying gravity?

3 Image credit: Wayne Hu and Martin White The Hot Big Bang

4 Constituents of the Universe today Dark matter: we don t know what this is, but there are several well-motivated ideas (particles). Dark energy: we don t know what this is (not particles), many ideas but few compelling ones.

5 The Large-scale Universe Observations show that on scales larger than about 10 million light years, the Universe is homogeneous and isotropic Image credit: Stephen Landy

6 The Large-scale Universe Observations show that on scales larger than about 10 million light years, the Universe is homogeneous and isotropic Fluctuations in the temperature of the 3K cosmic microwave background, 1 in 100,000

7 Characterizing sources of gravity

8 Characterizing sources of gravity (cont) Examples:

9 Dynamics of the Expanding Universe Uniform expansion with scale factor a(t) Concentric spherical shells labeled by r, size a(t)r First law of thermodynamics: de = pdv d(ρc 2 r 3 a 3 ) = pd(r 3 a 3 ) p = wc 2 1 ρ = ρ a 3(1+w)

10 Dynamics of the Expanding Universe Uniform expansion with scale factor a(t) Concentric spherical shells labeled by r, size a(t)r First law of thermodynamics: de = pdv d(ρc 2 r 3 a 3 ) = pd(r 3 a 3 ) p = wc 2 1 ρ = ρ a 3(1+w) Newton s second law: ä(t)r = G [ 4 3 πr3 a 3 ρ ] ä a [ra] 2 = 4πG 3 [ρ ]

11 Dynamics of the Expanding Universe Uniform expansion with scale factor a(t) Concentric spherical shells labeled by r, size a(t)r First law of thermodynamics: de = pdv d(ρc 2 r 3 a 3 ) = pd(r 3 a 3 ) p = wc 2 1 ρ = ρ a 3(1+w) Newton s second law: ä(t)r = G [ 4 3 πr3 a 3 ρ ] ä a = 4πG 3 [ra] 2 [ ρ + 3pc 2 ] Correction due to general relativity

12 Dynamics of the Expanding Universe Uniform expansion with scale factor a(t) Concentric spherical shells labeled by r, size a(t)r First law of thermodynamics: de = pdv d(ρc 2 r 3 a 3 ) = pd(r 3 a 3 ) p = wc 2 1 ρ = ρ a 3(1+w) Newton s second law: ä(t)r = G [ 4 3 πr3 a 3 ρ ] ä a = 4πG 3 Correction due to general relativity [ra] 2 Acceleration if p < 1 [ ρ + 3pc 2 ] 3 c2 ρ

13 Analog of dark energy

14 Evidence for acceleration By combining first law of thermodynamics and acceleration equation: ȧ 2 = 8πG 3 ρa2 k, k = 0, ±1 Rewrite as: 1 H 2 0 ȧ 2 a 2 = Ω M a 3 + Ω Λ a + Ω R 3(1+w) a 4 1 = Ω M + Ω Λ + Ω R + Ω k + Ω k a 2,

15 Evidence for acceleration By combining first law of thermodynamics and acceleration equation: ȧ 2 = 8πG 3 ρa2 k, k = 0, ±1 Rewrite as: 1 H 2 0 ȧ 2 a 2 = Ω M a 3 + Ω Λ a + Ω R 3(1+w) a 4 1 = Ω M + Ω Λ + Ω R + Ω k Cosmic microwave background (standard yardstick) Ω R 10 4, Ω k Ω k a 2,

16 Evidence for acceleration By combining first law of thermodynamics and acceleration equation: ȧ 2 = 8πG 3 ρa2 k, k = 0, ±1 Rewrite as: 1 H 2 0 ȧ 2 a 2 = Ω M a 3 + Ω Λ a + Ω R 3(1+w) a 4 1 = Ω M + Ω Λ + Ω R + Ω k + Ω k a 2, Cosmic microwave background (standard yardstick) Ω R 10 4, Ω k 0.05 Infer a(t) from brightness and redshifts of standard candles (Type Ia supernova)

17 Evidence for acceleration (cont.)

18 Evidence for acceleration (cont.)

19 Evidence for acceleration (cont.) 3 Supernova Cosmology Project No Big Bang Knop et al. (2003) Spergel et al. (2003) Allen et al. (2002) 2 Supernovae 1 Ω Λ 0 Clusters CMB expands forever recollapses eventually closed -1 open flat Ω M

20 Evidence for acceleration (cont.) SNe Supernova Cosmology Project Knop et al. (2003) w 1 w dFGRS CMB Combined Assuming constant w With limits from; 2dFGRS (Hawkins et al. 2002) and CMB (Bennet et al. 2003, Spergel et al. 2003) w Ω M w = (statistical) (systematic)

21 Simplest model: Cosmological constant The case w = 1, constant energy density ρ Λ (10 3 ev) 4 Puzzle: expect quantum loops to generate a much larger energy density, ρ Λ Ecutoff 4 Unknown higher energy physics can in principle cancel out this contribution, but it requires exquisite fine tuning. String theory predicts a multiverse with huge number of different vacua, each with its own ρ Λ. Anthropic principle could explain smallness of our ρ ΛρΛ Problem: life might still evolve if were 1000 times larger. Puzzle: The Universe has expanded by 35 orders of magnitude. Why are dark energy and matter comparable right now? Seems to require fine tuning of initial conditions.

22 Dark energy versus time

23 Dynamical models of dark energy Typically do not address cosmological constant problem Can address the cosmic coincidence problem Typically invoke new fundamental or effective fields Quintessence: S = d 4 x g [ ] 1 2 ( Φ)2 + V (Φ) ρ = 1 2 Φ 2 + V (Φ), p = 1 2 Φ 2 V (Φ) Φ 2 V (Φ) = p ρ Like inflation models, but at much lower energy scale Problem: expect loop corrections to spoil flatness of potential and small mass of scalar field One solution: scalar field is the size of compact extra dimensions (radion), protected by diffeomorphism invariance

24 Modified Gravity vs. Dark Energy Evidence for dark energy presumes validity of general relativity. Perhaps, instead, general relativity is modified on large scales.

25 Modified Gravity vs. Dark Energy Evidence for dark energy presumes validity of general relativity. Perhaps, instead, general relativity is modified on large scales. How do we decide if a given a modification of the laws of physics involves a modification of gravity? Perhaps ask which side of the Einstein equation is modified, or which term in action is modified: S = G µν = 8πGT µν d 4 x R g 16πG + S matter[g µν, Ψ matter ]

26 Modified Gravity vs. Dark Energy Evidence for dark energy presumes validity of general relativity. Perhaps, instead, general relativity is modified on large scales. How do we decide if a given a modification of the laws of physics involves a modification of gravity? Perhaps ask which side of the Einstein equation is modified, or which term in action is modified: S = G µν = 8πGT µν d 4 x R g 16πG + S matter[g µν, Ψ matter ] This criterion is in fact ambiguous. Instead, we should ask if there are universal, long-range, 5th forces between macroscopic bodies.

27 Modified Gravity vs. Dark Energy Example: S = d 4 x g ḡ µν e α(φ) g µν, Φ f(φ), R 16πG + S matter[e α(φ) g µν, Ψ matter ] d 4 x g [ ] 1 2 ( Φ)2 V (Φ) S = d 4 x ḡ [ A( Φ) R 16πG 1 ] 2 ( Φ) 2 V ( Φ) + S matter [ḡ µν, Ψ matter ]

28 Modified Gravity vs. Dark Energy Example: S = d 4 x g ḡ µν e α(φ) g µν, Φ f(φ), R 16πG + S matter[e α(φ) g µν, Ψ matter ] d 4 x g [ ] 1 2 ( Φ)2 V (Φ) S = d 4 x ḡ [ A( Φ) R 16πG 1 ] 2 ( Φ) 2 V ( Φ) + S matter [ḡ µν, Ψ matter ] In this theory, scalar field both acts like quintessence and mediates 5th forces. This mixed character is generic, since loop corrections generate matter couplings. Solar system tests of gravity (light bending, perihelion precession) require α (Φ) 10 2 if V (Φ) (A.U.) 2 These theories can arise as effective description of extra dimensions Other possible observational signatures: time evolution of effective Newton s constant (fine structure constant for generalized models)

29 Modifying gravitational action: a catalog Are there successful models that are not mostly quintessence? S[g µν, Ψ m ] = d 4 x g f(r) 16πG + S m[g µν, Ψ m ] Equivalent to last model with α(φ) = Φ/ 6, ruled out by Solar System S[g µν, Ψ m ] = d 4 x g f(r, R µνr µν, R µνλσ R µνλσ ) 16πG + S m [g µν, Ψ m ] Problems with ghosts/acausality

30 Modifying gravitational action: a catalog S[g µν, µ, Ψ m ] = d 4 x g f( ˆR) 16πG + S m[g µν, Ψ m ] Ruled out; predicts modifications of particle physics at energy scale H 0 M p 10 3 ev S[g µν, µ, Ψ m ] = d 4 x g f(r, ˆR) 16πG + S m [g µν, Ψ m ] Some successful models. Equivalent to tensor bi-scalar model similar to the mixed models discussed earlier. Some interesting models based on extra dimensions do not have a simple effective 4-dimensional description, eg DGP model

31 Observational probes of dark energy Probes of the expansion history of the Universe Probes of the growth of perturbations Precision tests of general relativity Specific observational windows (i) Supernovae (ii) Measurements of numbers of clusters using CMBR (iii) Weak gravitational lensing (iv) Baryon acoustic oscillations

32 Image credit: Max Tegmark

33 Conclusions The discovery of the acceleration of the Universe requires new fundamental physics The dark energy might be a cosmological constant. We may never be able to explain its tiny size. The dark energy may be dynamical. Potential observational windows include (i) Probing the expansion history of the Universe (ii) Probing the growth of structure in the Universe (iii) High precision tests of general relativity (iv) Measurements of time evolution in fundamental constants of nature.