Ch 18: Cosmology

1. Ch 18: Cosmology • Understanding the entire Universe : • its global shape : space-time • its contents : atoms to galaxies • its rules : physical law/forces • its structure : smooth  lumpy • the evolution of all these • the origin of all these

2. (1) Global Properties • Universality of physical law • Physics is the same everywhere and at all times • Verified by observing light from distant galaxies • Isotropy : same in all directions (statistically) • Homogeneity : same at all locations (statistically) 3-D projected us • Note : same at all times  Steady State Theory (1960s) • Now known to be wrong; the Universe is evolving

3. (2) Cosmic Expansion • Recall: The Hubble Law : • galaxy spectra are redshiftedreceding • more distant galaxies recede faster : • V = Ho× d Ho=70 km/s/Mpc • Cake metaphor : • Cake expands  all raisins separate • More distant raisins separate faster • Raisins obey a Hubble Law

4. View from galaxy A B A

5. View from galaxy B B A

6. v 2v us 2d d (2b) Consequences of the Hubble Law The fact that V ~ d has some fascinating consequences • Everyone sees the sameexpansion ! • = Cosmological Principle (deeply egalitarian) • There is no central location ! • or…. everywhere feels central to the expansion • (we will discuss the question of edges later) • Future Universe  emptier & lonely • Past Universe more crowded v. different • Everything together at particular time  Big Bang !

7. km s Mpc 1 Ho 1 Mpc 70 km  = s • Ho = 70 1 3.08 × 1013 × 106 km 70 1 km Age = = 4.40 × 1017 sec (3) Age of the Universe When did the Big Bang happen ? Easy: use V = Ho× d • Assume expansion “velocities” have been constant : •  time to reach d moving at V is tstart = d / V • Hubble law gives : d = V / Ho • tstart = V / Ho / V = 1/Ho •  Age of Universe ≈inverse of the Hubble constant ! • (how long does it take to travel 1Mpc moving at 70 km/s) = 1.39 × 1010 years = 13.9 Gyr(13.7 with change in V) (Universe is ~ 3× older than the Earth/Solar system)

8. time (4) The Redshift • Cake metaphor : • raisins don’t move through the cake • space expands, galaxies fixed in space •  cosmological (not Doppler) redshift • photons stretched as they cross space • redshift z = Δλ/λ = (λobs– λem)/ λem • e.g. “nearby” z ~ 0.001 ; far z ~ 0.1 • HST deep field z ~ 0.5 – 3 • most distant gal z ~ 7 • astronomers use z, rarely Gpc. • 1+z = λobs/λem = λnow/λthen = Sepnow/Septhen • = change in size of Universe • e.g. at z = 4, everything is 5×closer •  Universe 5×smaller; so density 125 ×higher Grid = space expands

9. (5) Cosmic Geometry Assume Newtonian Space & time Reality: Einstein’s space-time Bad questions • simple questions: • Where is the center/edge of U ? • What is outside U (expanding into) ? • Where did BB go off ? • What was before BB ? • Mass & Energy curve space-time : • Impossible to imagine : 3-d curved in 4-d • Try 2-d curved in 3-d  a curved surface • 3 cases : curvature • Flat = 180° A = π r2 zero • Ball >180° A > π r2 +ve • Saddle < 180° A < π r2 –ve • Measure curvature using • giant cosmic triangle (see later)

10. (5b) Geometry (cont.) • Note: on a ball : no edges, no center, finite area • add expansion : Hubble law • start of expansion = Big Bang • flat & saddle : infinite (no edge, no center either) • Geometry depends on the average mass/energy density • critical densityρcrit = 9.5 × 10-27 kg/m3 ≡ 5 H atoms/m3 • ρ < ρcrit  –ve curvature; “open”; infinite • ρ = ρcrit  flat; infinite • ρ > ρcrit  +ve curvature; “closed”; finite • Observations : measure cosmic triangles (see later) •  Universe is flat (±2%) •  “simplest” geometry; infinite volume (>> horizon size)

11. (6) Contents • What is the Universe made of ? • Express each constituent as fraction of closure density : • Ω = ρ / ρcrit • Since ρtot = ρcrit , sum of Ωs must be 1.0 Ωstars = 0.01 Ωbaryons = 0.04 (atoms) Ωdark matter = 0.23 (non-baryonic) Ωdark energy = 0.73 (vacuum?) 1.00  total isρcrit

12. Big Bang Near Far Now red-shift Then Far Near Big Bang Then red-shift Now (7) Cosmic Microwave Background • Look very far away  very long ago  see Big Bang !! • Direction ? Everywhere = the whole sky !! • Spectrum ? Microwaves = red-shifted flash !! What we see Universe at Big Bang Universe today

13. Bell Labs (1963) Observing the Microwave Background (highlights, there are many others) COBE satellite (1992) WMAP satellite (2003)

14. (7b) Creating the CMB expansion cooling Big Bang dense hot rarified cool Now ionized foggy 380,000 yr 3000 K hot glowing fog us redshift z=1000 atomic transparent we see a glowing wall of bright fog orange light microwaves

15. (7c) The CMB is very young ! Human lifespan Conc- eption child teenage Old age 12hr Marathon race Finish 26 miles Start 4 feet 380,000 yr 5 Time (Gyr) 10 0 14 Big Bang here now “nearby” galaxies CMB NGST HST

16. 3000 K Blackbody (Optical) 2.73 K Blackbody (microwaves) red-shift z ~ 1000 keeps spectrum shape red-shift (7d) CMB spectrum • Accurate black-body shape • T = 2.725 ± 0.002 K • Early Universe was hot

17. (7e) CMB Image • Exceedingly uniform, • with two contaminants : 1) “dipole” : MW moving @ 540 km/s towards Virgo 2) MW plane contamination • Remove these to reveal : • Highly uniform  no stars or galaxies : diffuse hot gas • Very slight patchiness: ~10-5 variations = sound waves; grow into galaxies Flyby Rotate

18. (8) The First Million Years : Light

19. (9) Structure Formation @ CMB: very smooth Today: very lumpy How does this happen ? • Gravity amplifies CMB patches contrast (Δρ/ρ) grows • 10-4 10-2 1 → stars → galaxies → clusters • smooth fine-lumpy coarse-lumpy • ~100 Myr rapid ~1Gyr ~5Gyr • First structures form quickly, <½ Gyr • needs high density (Ω ~ 0.3)  dark matter important ! • dark matter enables prompt star/galaxy formation • without it, Δρ/ρ would still only be 0.1  no stars yet !! • Computers follow formation of stars / clusters / tapestry 

20. collapsing gas cloud becomes a cluster of stars computer simulation of this transformation

21. Galaxies in a Cluster computer simulation galaxy/cluster formation Simulation 10 Mpc region ~103 galaxies 14 Gyr = 8s

22. Computer Simulation ~1 Gpc region ~107 galaxies form 13 Gyr = 2s 15°~ 1Gpcco ~ SDSS Previous cluster simulation SDSS : ⅓ million galaxies 3 G l-yr MW here Tapestry Formation

23. bright dim bright dim bright compression rarefaction dim compression rarefaction compression rarefaction (10) Sound waves in the CMB • brighter/dimmer patches = peaks/troughs of sound waves !! • Sound in space ?!? • recall: Universe smaller & denser; matter spread out  dilute gas • Hot glowing fog = gas of protons, electrons & photons • photons : protons = billion : 1 !!  “In the Beginning was Light” • While foggy: pressure due to light • sound (pressure) waves move at speed ~60% c !! • After fog : light de-couples  sound ceases, waves frozen in place • Primordial lumpiness : gravity of DM drives sound waves

24. CMB Sound Spectrum • Cosmic triangle : • 1° on sky = 230,000 lyr Loudness 1st peak at 1° 13.7 Glyr (/1000) Frequency Wavelength Long Waves ~60° Short Waves ~0.1° (10b) Sound as diagnostic • wine glass & tea cup sound different  different structures • “sound” of Universe reveals its structure/properties • Sound is characterized by its spectrum • The CMB has a fundamental and harmonics !! • The fundamental has λ = 1° (twice full moon) • Fundamental is longest λ • = 380,000 x 0.6 = 230,000 lyr • Sum Δ angles = 180° ! •  Geometry is flat (±2%)

25. (10c) Diagnostics: Geometry & Baryons Baryon Fraction Region size ~ outstretched hand 8% 4% 2% Real Data Simulated data for different geometries Geometry/Density –ve flat +ve “critical” flat geometry flat lens medium blobs medium pitch low density -ve curvature concave lens small blobs high pitch high density +ve curvature convex lens big blobs deep pitch long short

26. (10d) The First Million Years : Sound Observed Sound at 380,000 yrs Reconstructed Evolving sound Pure Normalized Harmonics Foggy Clear E8-log 5E5-log

27. (11) Expansion History & Future Matter Gravity • First guess: expansion rate slows down i) Deceleration depends on density of Universe: four possibilities ↓ Λ=0 ii) Deceleration implies tage < tH (=1/Ho) eg ρ = ρcrit tage= ⅔ tH Ω=0 Λ>0 Ω<1 Ω=1 • Mid 1990s: problems • Ho = 70 tH = 14 Gyr • ρ ~ ρcrit tage = 9 Gyr • But : • Globular Cluster ages • tGC ~ 12 Gyr !!! •  Age problem Ω>1 tH = tH = 1/Ho = Hubble Time

28. (11b) Measure Expansion History • Look far away  measure expansion rate in past De-celerating faster in past Redshift (velocity) const Ac-celerating Distant Supernova Type Ia slower in past here now Distance far past • 1998 two independent teams: • SN-Ia  distance  accelerating !! • 2000 : very distant SN shows • early deceleration Data show accelerating

29. (11c) Cosmological constant: Λ • Is this possible in Einstein’s General Relativity (GR)? • Yes ! : Λ term  integration constant ≡ energy of vacuum •  cosmic repulsion • 1916 : Einstein uses Λ to balance matter  static universe • 1926 : Hubble discovers expansion • Einstein sets Λ = 0, says “my biggest blunder” • 1998 : acceleration discovered  reintroduce Λ ≠ 0 • called “dark energy” (contrast “dark matter”) • currently uncertain what it is; vacuum energy ? (6×10-10 J/m3) • adds to curvature : currently ΩΛ = 0.73 (± 5%)  dominates ! • since ρvac const  unimportant long ago  early deceleration • after ~ 6 Gyr, ρvac > ρmatterexpansion accelerates (transition seen) • Future : no recollapse; infinite future; increasingly lonely….

30. 4% IGM/ICM/ISM Hot: 106-108 K ~ 80 % Cold: 10-100K ~ 0.1 % Fraction by Composition Fraction by Location Hydrogen 74% C,N,O…Fe… Cu…Pb…U 2% Helium 24% Planets < 10-2% ? Stars ~ 20% Composition History of Universe 1.0 Dark Energy (? vacuum energy) 73% 0.5 Dark Matter (? WIMPS) Fraction 85% “heavy” elements H + He 23% 15% Baryonic matter 0.0 4% now 0 2 4 6 8 10 12 S.S. Age (Gyr)

31. Temperature (K) 10 105 104 103 102 1 106 RADIATION ERA MATTER ERA DARK ENERGY ERA ργ > ρM ργ = ρM ρM = ρDE ρM> ργ ρDE > ρM re-ionized accelerating expansion, very empty stars p+,e−, He4, DM (trace) photons dominate present QSOs X UVBGYOR p+e−→ H atoms free → bound galaxies H exhausted stars die ionized opaque neutral transparent 1 102 104 106 108 1010 1012 kyr Gyr matter free to collapse Now Sound waves : begin → grow Time (yr) Density evolution: radiation & matter The First 1000 Gyr

32. expansion hotter denser cooler less denser a) t ~ 1 min z ~ 108 T ~ 109K ρ ~ 1 gm/cm3 t ~ 380,000 yrs z ~ 1000 T ~ 3000 K ρ ~ fewatoms/cm3 simple physics 10-3 % H2 10-4 % He3 10-7 % Li7 76 % H1 24 % He4 insensitive to details depend on ρbaryons • 24% He4 seen everywhere • (even old stars) •  strong evidence for hot big bang • Use to estimate ρbaryons •  Ω bary = 0.04 (small !!) (12) Early Times (t<10 min): Helium synthesis ~ star core!Expect nuclear reactions b) Calculations show: p + n  He4 (+ …)

33. (12b) Cosmic Nucleosynthesis: details Cosmic thermal history : 1010yr (3K):now, 3K 109 yr(30K):first galaxies 108 yr (300K):first stars 4×105yr (3000K):fog clears 5×104yr(104K):ρrad= ρmatter 1 – 3min(109K):fusion allowed range ~4%

34. 1013 ~ ρN Temperature (K) density 1010 100 kg/cm3 1s 1µs time (13) Very Early Times (t < 1sec) • May seem absurd, but smooth hot gas is “simple”: • well-known physics : back to ~1µs (1013 K ≡ 1 Gev) • ~known physics : back to ~10-12 sec (1015 K ≡ 100 Gev) • ~rough guesses : back to ~10-35 sec (1028 K ≡ 1016 Gev) • profound ignorance : before ~10-43 sec • Key issues : (a) Origin of matter; (b) Origin of forces

35. p+ + p– proton/ anti-proton γ + γ photons particle anti-pcle 1 Energy 2 pcle a-pcle photon particles & antiparticles creation creation annihilation annihilation energy photons (γ rays) thermal energy exchange (13a) Origin of matter from energy • matter is concentrated energy (E=mc2) •  inter-conversion possible: • always happens • only when Eγ> mpc2 e.g. • = threshold energy 1 2 • KE can also create matter •  thermal creation, e.g. T > 1010 K for e+e– and T > 1013 K for p+p– •  new matter arises in the midst of existing matter equilibrium

36. (13b) The First Day: Four Eras • There are three important threshold temperatures: • Electron creation at T > 1010 K ( lepton era) • Proton creation at T > 1012 K ( hadron era) • Protons unbound at T > 1013 K  quarks free ( quark era) • These occur at roughly: 1s 100µs 1µs • They mark the change from one era to the next • quark  hadron  lepton  radiation • ( Recall: radiation era ends at ~104 yrs when ρrad < ρmatter ) • ( recall: pcle collisions ~10-23s so if this ≡1s then 1µs ≡ 1Gyr ) • The following diagram contains (too) much detail: • Note two interesting points: • physics @ 1 sec sets n/p ratio  He/H ratio = 1/3 as observed • when p+p– and e+e– annihilate, 10-9 left over !! (to make stars & us!!) •  Nγ /Ne ~109 as found  pre-existing matter/antimatter asymmetry

37. The First Day ρN ρW ρA Temperature (K) 1014 1010 108 1012 QUARK HADRON LEPTON ERA RADIATION ERA q q 3q 2q e+,e−, γ γ dominates q q p,n,π…. free bound electron freezout proton freezout qq ↔ E pp ↔ E e+e−↔ E ¯ ¯ p, e− 1:1 p, He4 12:1 (3:1) p, γ 1:109 ν decouple 2p2n→ He4 H fusion Matter: 109 + 1 (p) Anti-matter: 109 (p) p, n : 1 e±, γ : 109 ¯ e+e−→ 2γ pp →2γ ¯ (e±,μ±,γ….) p:n → 1:1 7:1 10-8 10-6 10-4 10-2 1 102 104 Time (s) μs ms min hr day Expansion & Cooling

38. (13c) The first nano-second: origin of forces • Current Universe has 4 forces : • Gravity, Weak, Electromagnetism, Strong • Strength depends on temperature • Early Universe: similar/same •  force identities merge  fewer forces expansion cooling • At Big Bang, one force 4 separate forces • 1. t ~ 10-10 s T ~ 1015 K weak + EM  electro-weak • 2. t ~ 10-35 s T ~ 1027 K strong + electro-weak  GUT • 3. t ~ 10-43 s T ~ 1032 K gravity + GUT  superforce?? • Next figure shows (too) much detail…

39. Strong Strong Strong Electro- magnetic GUT Electro- Weak Electro- Weak Weak Gravity Gravity Gravity Gravity The First Nanosecond ~1028K ~1028 ~1027K ~1015K GUT ERA QUARK ERA R × 1060 q (109+1) ¯ X X q (109) ¯ ? ? Seed fluctuations INFLATION reheat ~10-36 ~10-34 ~10-32 10-12 10-10 Time (s) The First Day QUARK HADRON LEPTON ERA RADIATION ERA 10-8 10-6 10-4 10-2 1 102 104 Time (s) The First 1000 Gyr DARK ENERGY ERA RADIATION ERA MATTER ERA 1 102 104 106 108 1010 1012 Time (yr)

40. (14) 4 puzzles for simple Big Bang theory • Four deep problems: antimatter; structure; horizon; flatness • slight matter/antimatter asymmetry : ~ (109 + 1) / 109 •  10-9 left after annihilation = current baryons. Why ?? • slight (10-4) CMB fluctuations structure (stars/galaxies) • what caused this ?? [if start smooth, then stays smooth] • CMB is too uniform. • regions separated by more than 2° are outside each other’s horizon •  deeply unconnected; come from different “parts” of big bang • Why so similar ?? E.g. all at 2.7K. • ρU = ρcrit(within 2%.) Why ?? • if close now, exceedingly close in the past • e.g. ρU = ρcrit within 10-10 % at 3 minutes. • why so exact, coincidence ??

41. broken symmetry @ 10-35 s : GUT strong + electro-weak force particles : X boson gluons W,Z bosons (15) Inflation: (possible) solution • 1980s bizarre solution suggested – inflation • 1990s evidence begins to support this (still uncertain) i) X boson decay slightly favors matter over antimatter  Explains matter universe ii) Energy release strong Λ term  drives brief exponential expansion  10-35 – 10-33 sec R grows by ×1030  period of inflation then resumes normal (Hubble) expansion

42. (15b) Solutions from inflation a) pre-inflation: obs. U ~10-25 cm causally connected  smooth post-inflation: obs. U ~105cm causally disconnected  explains isotropy of CMB • inflation drives ρ → ρcrit •  explains flat geometry • Inflation amplifies quantum fluctuations •  become 10-4 CMB fluctuations •  become stars/galaxies/tapestry •  CMB is image of quantum world !!

43. (16) Current Perspective • Cosmology is in a golden era • Extraordinary progress in the past century/decade • However, deep questions remain: • What is nature of dark matter & dark energy (96%) ? • Why was there a Big Bang ? • Did inflation really happen, and if so how ? • Need quantum gravity to probe t < 10-43 sec • Subject is no longer just speculative, • but it is not yet mature – it is young and exciting.