1. 1 1 The Darkness of the Universe Eric Linder Lawrence Berkeley National Laboratory

2. 2 2 The Night Sky is Dark The dark night sky is a profound cosmological observation! The universe is filled with stars emitting photons. Number of stars at distance r goes as r 2 ; Intensity dies as 1/r 2, so total flux received F tot =  dr F(r) N(r) =  0  dr (L/4  r 2 ) (4  nr 2 ) = Ln  0  dr  Why aren’t we cooked?

3. 3 3 The Night Sky is Dark More rigorously: Energy density of light today E =  ti t0 dt L (1+z) -1 If constant comoving luminosity density L, then finite past gives finite limit E < L t 0.

4. 4 4 The Night Sky is Dark Liouville’s Theorem approach: Photon phase space density N = N/d 3 xd 3 p is conserved, so I = N /(A  t)d d  = N 3 Therefore, I -3 is conserved and the surface brightness I 0 = I e (1+z) -4. Looking far enough, every line of sight should end on a star, and so the sky should be as bright as the surface of a star. The answer again is that we can’t look far enough, due to a finite past.

5. 5 5 Optical Depth of the Universe What is the probability of a line of sight intersecting a star? Consider a marble rolling on a tabletop. Will the marble hit another marble before rolling off the table top?

6. 6 6 Optical Depth of the Universe Mean free path is L = 1/(  n) Cross section to intersect a star is  =  r  2 =  (10 11 cm) 2 = 10 22.5 cm 2 Number density of stars is n =   /m  = (10 -31 g cm -3 )/10 33 g = 10 -64 cm -3 Effective volume V = 1/n = 10 64 cm 3 = (10 21 cm) 3 = [(1/3)kpc] 3 MFP L = 1/(  n) = V/A = 10 41.5 cm = 10 17 Mpc = 10 13.5 H 0 -1 Finite horizon solves Olbers’ paradox by 13 OOM!

7. 7 7 Expanding Universe? What role does the expanding universe play in Olbers’ Paradox? Almost none! I 0 = I e (1+z) -4 dimming arises from any frequency shift, not just expansion. E =  ti t0 dt L (1+z) -1 has little dependence on redshift. Expansion has factor of ~2 effect. So Newton could not have “discovered” the expanding universe. The solution is not expansion in Big Bang cosmology, but the Big Bang itself!

8. 8 8 Expanding Universe? Caveat 1 (CMB): Photons can be absorbed, and reradiated, e.g. IR degradation. For a diffuse glow like the CMB the sky is dark ( E << M p 4 ) because of the expansion. Caveat 2 (Inflation): In an inflationary epoch, 1+z ~ e H(t0-t), we are saved by the redshift, giving a finite energy density E = L /H even for an infinite past.

9. 9 9 What if Our Eyes Saw Dark (Energy)? The night sky is dark in photons, implying a finite past (Big Bang). The sky is bright in  (dark energy density dominates), implying an infinite future. Will this turn out to be as significant a discovery as the Big Bang?

10. 10 Cornerstones of Cosmology Another simple observation is that the universe appears rather isotropic. This is most notable in the cosmic microwave background (CMB) radiation. Isotropic to a part in 10 3, or part in 10 5 in comoving frame. Also holds (with less precision) in counts of galaxies, quasars, etc. Cosmological Principle (Copernican principle, principle of cosmic modesty) argues we are not in special location, so isotropy implies homogeneity.

11. 11 Cornerstones of Cosmology The global spatial geometry is isotropic and homogeneous. The theory of gravity characterizes the spacetime geometry, and relates the dynamics to the matter and energy contents. General relativity accurately describes gravity as far as it has been tested. Robertson-Walker metric: ds 2 =  dt 2 +a 2 (t)[dr 2 /(1-kr 2 )+r 2 d  2 ] scale factor a(t) ; spatial curvature k

12. 12 Expansion of the Universe The universe is expanding: Photons received from distant galaxies exhibit a change to lower frequencies (redshift). This shift is at lowest order proportional to the distance: z = H 0 r Isotropic, radial: suggests vector relation v = H 0 r Linearity predicted by Weyl, before Hubble. Note v 12 = v 2 -v 1 = H 0 (r 2 -r 1 ) = H 0 r 12.    

13. 13 Expansion of the Universe Approximate timescale of the expansion is the Hubble time H 0 -1. Since distances r ~ a, i.e. r = r 0 (a/a 0 ), then r = r (a/a). So H = a/a Volumes behave as V ~ a 3. So number densities n ~ a -3. Photon frequencies (inverse wavelengths) ~ a -1, so radiation energy density  ~ a -4 (T ~ a -1 ). Early universe was hot and dense....

14. 14 Big Bang This is the hot Big Bang theory: Expansion of the universe from a hot, dense state over a finite time. Tested by 1)Expansion redshift 2)Cosmic microwave background radiation 3)Primordial nucleosynthesis 4)Cosmic ages 5)General relativity 6)Dark night sky

15. 15 Our Expanding Universe Bertschinger & Ma ; courtesy Ma

16. 16 Our Cosmic Address Earth 10 7 meters Solar system 10 13 m Milky Way galaxy 10 21 m Local Group of galaxies 3x10 22 m Local Supercluster of galaxies 10 24 m The Visible Universe 10 26 m Our Sun is one of 400 billion stars in the Milky Way galaxy, which is one of more than 100 billion galaxies in the visible universe.

17. 17 The Cosmic Calendar Inflation 10 16 GeV Quarks  Hadrons 1 GeV Nuclei form 1 MeV Atoms form 1 eV Stars and galaxies first form: 1/40 eV Today: 1/4000 eV [Room temperature 1/40 eV]

18. 18 Characteristic Scales Physics today: Cosmic size (Hubble scale) -- H 0 -1 = 10 28 cm Cosmic time (Hubble age) -- H 0 -1 = 10 10 yr Mass scale -- H 0 = 10 -33 eV Energy density scale -- H 0 2 M P 2 = (10 -3 eV) 4

19. 19 Mapping Our History The subtle slowing down and speeding up of the expansion, of distances with time: a(t), maps out cosmic history like tree rings map out the Earth’s climate history. STScI

20. 20 Discovery! Acceleration

21. 21 accelerating decelerating accelerating decelerating cf. Tonry et al. (2003) Cosmic Concordance Supernovae alone  Accelerating expansion   > 0 CMB (plus LSS)  Flat universe   > 0 Any two of SN, CMB, LSS  Dark energy ~75%

22. 22 95% of the universe is unknown! Frontiers of Cosmology STScI Us

23. 23 Dark Energy Is!!! Dark Energy Is... 70-75% of the energy density of the universe Accelerating the expansion, like inflation at 10 -35 s Determining the fate of the universe ! 70-75% of the energy density of the universe 95% of the universe unknown! ! Accelerating the expansion, like inflation at 10 -35 s Repulsive gravity! ! Determining the fate of the universe Fate of the universe! Is this mysterious dark energy the original cosmological constant , a quantum zeropoint sea?

24. 24  : Ugly Duckling Astrophysicist: Einstein equations –  g ab  p = -  Naturally,  =const=  PL   = 10 120 Today    M Field Theorist: Vacuum – Lorentz invariant T ab ~  ab = diag { -1, 1, 1, 1}  p = -  Naturally, E vac ~ 10 19 GeV E  ~ (meV) 4  =0? Fine Tuning Puzzle – why so small? Coincidence Puzzle – why now?

25. 25 What’s the Matter with Energy? They are off by a factor of 1,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000. This is modestly called the fine tuning problem. Why not just bring back the cosmological constant (  )? When physicists calculate how big  should be, they don’t quite get it right.

26. 26 Matter Dark energy Today Size=2 Size=4 Size=1/2Size=1/4 But it gets worse: Think of the energy in  as the level of the quantum “sea”. At most times in history, matter is either drowned or dry. Cosmic Coincidence

27. 27 On Beyond  ! We need to explore further frontiers in high energy physics, gravitation, and cosmology. New quantum physics? Energy of the vacuum (nothing weighs something)? New gravitational physics? Quantum gravity, supergravity, extra dimensions? We need new, highly precise data

28. 28 Cosmic Archaeology CMB: direct probe of quantum fluctuations Time: 0.003% of the present age of the universe. (When you were 0.003% of your present age, you were 2 cells big!) Supernovae: direct probe of cosmic expansion Time: 30-100% of present age of universe (When you were 12-40 years old) Cosmic matter structures: less direct probes of expansion Pattern of ripples, clumping in space, growing in time. 3D survey of galaxies and clusters - Lensing.

29. 29 The Universe: Early and Late Relic imprints of quantum particle creation in inflation - epoch of acceleration at 10 -35 s and energies near the Planck scale (a trillion times higher than in any particle acclerator). These ripples in energy density also occur in matter, as denser and less dense regions. Denser regions get a “head start” and form into galaxies and clusters of galaxies. How quickly they grow depends on the expansion rate of the universe (traced by SN). It’s all connected!

30. 30 Cosmic Archaeology Inflation sets seeds of structure, patterning both radiation (CMB) and matter (galaxies) CMB Large scale structure: Baryon acoustic oscillations Lensing (weak and strong) Galaxy clustering Sunyaev-Zel’dovich effect } NASA GSFC/COBE

31. 31 Fundamental Physics Astrophysics  Cosmology  Field Theory a(t)  Equation of state w(z)  V(  ) V (  ( a(t) ) ) SN CMB LSS Map the expansion history of the universe The subtle slowing and growth of scales with time – a(t) – map out the cosmic history like tree rings map out the Earth’s climate history. STScI

32. 32 What if Our Eyes Saw Dark (Energy)? The night sky is dark in photons, implying a finite past (Big Bang). The sky is bright in  (dark energy density dominates), implying an infinite future. Will this turn out to be as significant a discovery as the Big Bang? Next: The Darkness of the Universe 2: Acceleration and Deceleration