Big Bang vs. Steady State Perfect cosmological : is unchanging in and => Steady-State universe - Bondi, Hoyle, Gold. True? No! • Hubble’s Law => expansion means no steady state, unless continually created to preserve • preference of AGN/ for large distances (early ) • cosmic background - consistent with Big Bang (BB) • predominance of elements (e.g., H, He) consistent with early hot universe • Olbers’ paradox (why is night sky dark?) resolved with BB model Cosmology

Cosmological Principle: At any instant in time, universe is homogeneous (same at all locations) and isotropic (same in all directions), i.e., the universe looks the same to all observers. This despite superclustering on scales up to ~ 100 Mpc; distribution apparently smoother on larger scales.

It turns out that the is completely consistent with the Hubble expansion. Cosmology

If vBA=H0rBA and vCA=H0rCA ,

then vBC= vBA- vCA = H0(rBA- rCA)

= H0rBC.

\ Hubble’s Law applies to every if it applies to just one. Cosmological principle <=> Hubble’s Law

where H0 can be positive, negative, or zero. Expansion of the Universe Cosmological principle => no boundary. How to understand this? Answer: introduces the idea of space-time . Curvature allows us to envision a boundary-free universe that is not infinite. A 3-D universe curved into a 4th dimension. Make analogy to a 2-D universe on surface of a 3-D sphere. If the sphere expands in 3-D, the 2-D surface area expands. A 2-D observer on the surface infers Hubble’s Law.

Expansion and subsequent contraction of a hypothetical 2-D universe on the surface of a sphere. Expansion of the Universe In GR cosmology, 3-D space itself expands. All lengths, e.g., distance between , wavelength of light, etc. expand with the universe. However, this expansion can be opposed locally by various .

Therefore, expansion of space itself is the real explanation for cosmological z, not the . General Relativity understood in a new light. Compare with old view. Newton: Gravitational causes matter to accelerate. Matter exerts gravitational force. Einstein: Gravitational acceleration is due to curved space-time. Curvature of space-time due to mass- (recall E = mc2). Geometry of Space and Time Newton: Euclidean geometry where ds2 = dx2 + dy2 + dz 2 is invariant, i.e., absolute space (and time).

Einstein (SR): No absolute space or time, but

ds2 = c2dt2 - (dx2 + dy2 + dz2 ) is invariant. Einstein (GR): Curvature of space time due to mass-energy yields

4 4 2 m n dx1,2,34==dx,,dydz, and dxcdt. ds = å å gmn dx dx where m =1 n =1

gmn is a tensor containing about curvature. Specifically, where no curvature, get back to SR limit

gmn = 0 for m ¹ n and g11 = g22 = g33 = -1, g44 = 1. Some Effects of Space-Time Curvature

• deflection of light around massive object, e.g., “gravitational lensing” • Euclidean geometry not valid on large scale • Large-scale structure and of universe affected by curvature Expansion of Curved Universe of General Relativity yields an equation for radius of curvature R, 1 2GM 1 R& 2 - = - c2 2 3p R 2

Solutions of this equation, R(t), yield evolution of the universe.

Our measurements of H0 yield current value of R& / R. Expansion of the Universe Follow a simpler Newtonian model. Imagine expansion of a spherical region of radius R(t). GM (R) F = ma Þ R&& = - . R2 Multiply by R&. GM (R) d æ 1 ö d æ GM (R) ö R&R&& = - R& Þ ç R& 2 ÷ + ç- ÷ = 0 R2 dt è 2 ø dt è R ø 1 GM (R) Þ R& 2 - = E = constant, 2 R

i.e., conservation of energy. Expansion of the Universe Does the universe expand forever? Analogy to earlier calculation. Universe unbound (open) if KE > |PE|, i.e., E > 0. marginal (flat) if KE = |PE|, i.e., E = 0. bound (closed) if KE < |PE|, i.e., E < 0. Rewrite in terms of Hubble constant and density: v = R& = HR, M (R) = 4 3p R3r, and note that r = r(t), H = H(t). 2 Open universe => r < r crit º 3H 8p G.

2 Flat universe => r = rcrit º 3H 8p G. 2 Closed universe => r > rcrit º 3H 8p G.

At current epoch (t = t0), we measure r0 , H0. Expansion of the Universe Key question in cosmology: 8p G 8p G What is the value of W = r rcrit = r 2 = r0 2 ? 3H 3H0 Important parameters r (1) W = r crit R& (2)expansion parameter H(t) = , currently H R 0 R&&R 1 r (3) q(t) = - 2 = , currently q0 R& 2 rcrit Current status of W: Observed luminous matter W << 1. Observed matter and inferred dark matter W £ 0.2. Theory of early universe W = 1.

-1 Earlier, we argued t0 < H0 if universe decelerating.

-1 Solve expansion equations for W = 1 => find t0 = 2/3 H0 .

-1 -1 \ open universe W <1 Þ 2 3 H0 < t0 < H 0 -1 flat universe W =1 Þ t0 = 2 3H0 closed universe -1 W > 1 Þ 0 < t0 < 2 3H 0 Ultimate fate? If W £1, expansion continues; all eventually die, > 1012 yr; universe becomes dark.

If W > 1, recontraction of universe; followed by rebound? Olbers’ Paradox In an infinite , every line of sight eventually intercepts a => night sky is everywhere bright!

Resolution in Big Bang model:

Finite age => can’t see beyond a distance r = cDt. Also, light from within this distance is increasingly redshifted as we approach the edge, the “cosmic ”. Light Elements Can trace expansion back to an early hot dense state. At high , exist in an unbound state. As universe expands and cools, synthesis of elements, then . Given presence of (1H) and , light elements 2H, 3He, 4He, 6Li, 7Li produced in early universe - these elements are also not produced efficiently in stars.

Cosmic abundances: 75% H, 25% He, trace Li, Be are all explained by Big Bang model. High H, He content implies a high past, since such matter prefers less binding energy, more light elements. Cosmic Microwave Background Back in time, at z ~ 103 (when T ~ 3000 K), and protons combine to form H atoms => matter is no longer opaque to , since free electrons were good at absorbing .

Blackbody radiation from this epoch flies out unhindered by matter. Should see this relic radiation, but redshifted so that l T max,0 = =1+ z »103 First observed by Penzias & Wilson lmax T0 (1965). Newer data from COBE T satellite (1992). Þ T = » 3 K. 0 1+ z Note: we can see galaxies/quasars back to z < 5, but CMB comes from z ~ 103! Cannot “see” any further back. Cosmic Microwave Background COBE’s measurement of the CMB spectrum. T = 2.726± 0.005 K.

COBE all-sky map of CMB. See fluctuations DT ~10-5 T which could have lead to structure. Seeing Through the Distance Extrapolating to Earliest Phases Before z ~ 103, guided only by theory. However, cannot go back arbitrarily far. Limit of current knowledge: Gm Gravity => can’t detect events within DL ~ . c2 h h Mechanics => can’t observe within DL < = . Dp mc Equate two DL’s. 1/2 photons GM h æ hc ö mass, a combination of 3 ~ Þ m = mp = ç ÷ , c 2 mc è G ø fundamental constants. Gm 1/2 Also, h p æ Gh ö Lp = = 2 = ç 3 ÷ , . mpc c è c ø 1/ 2 Lp æ Gh ö Planck time. Plug in #’s => t = = ç ÷ , p c c5 -43 è ø t p =1.35´10 s. Can’t describe t £ t p . Big Bang Model Expansion from highly condensed initial state. Theory combines general relativity and .

Four fundamental forces: strong nuclear - weak nuclear - electromagnetic - gravity

electroweak at high energies

combines at even higher energies

? Nucleons composed of . Quarks composed of …? All particles have corresponding . Big Bang Model Brief history: time

-43 10 s Planck time tp. Don’t know what precedes this. Need a quantum theory of gravity. 10-35 s Strong nuclear force decouples from electroweak. begins - rapid . Most quarks and antiquarks annihilate. Small asymmetry => some quarks remain. (made of quarks) to ratio 10-9-10-10. 10-32 s Inflation ends. went from 10-23 cm to 10 cm. 10-12 s Weak and electromagnetic force separate.

10-6 s Nucleons form. Big Bang Model Brief history: time 102 -103 s Cosmic - light nuclei form, e.g., He, Li.

1013 s (z ~ 103) electrons and protons combine => atoms form. Photons now able to stream freely. 1016 s Galaxies, stars, begin to form. 1016 s The .

1040 s Protons decay (perhaps). Atomic matter ceases to exist. Universe heads toward darkness/heat death. Last Word Observed luminous matter W < 0.01. Dark matter W » 0.2. Inflation theory W = 1. Where is the rest of the mass-energy? (1) In matter? Nucleons (e.g., brown dwarfs, white dwarfs, planets, rocks) can only account for up to W = 0.2, according to cosmic nucleosynthesis arguments. So look for exotic particles: massive n’s, , supersymmetric particles. (2) In energy? may make up the required deficit. An

unknown energy so that Weff= W + L = 1, where L is the (dark energy term) that makes the Hubble expansion accelerate at the current epoch! Recent evidence supports this hypothesis.