What is the Origin of the Universe? What is the Fate of the Universe?

How Old is the Universe? 1644: Dr. John Lightfoot, Vice Chancellor of Cambridge University, uses biblical genealogies to place the date of creation at September 21, 3298 BC at 9 AM (GMT?) 1650: James Ussher, Archbishop of Armagh and Primate of All Ireland, correlates Holy Writ and Middle Eastern histories to “correct” the date to October 23, 4004 BC Current Jewish calendar would “suggest” a date of creation about Sep/Oct 3760 BCE

Cosmological Principle At any instant of time, the universe must look homogeneous and isotropic to any observer. Perfect Cosmological Principle …….and indistinguishable from the way it looked at any other instant of time.

How Old is the Universe? 1760: Buffon uses cooling of Earth from its molten state to estimate age as 7.5x10 4 years 1831: Charles Lyell uses fossils of marine mollusks to estimate age as 2.4x10 8 years 1905: Lord Rutherford uses radioactive decay of rocks to estimate age as > 10 9 years (later refined to 4.3x10 9 years)

Consider a test particle with mass m and charge q Electrostatic force on q due to r is F e = q (kQ/r 2 ) Gravitational force on m due to r is F g = m (GM/r 2 )  acceleration = F g /m = m/m (GM/r 2 ) = GM/r 2 if gravitational and inertial masses are equivalent Equivalence Principle  acceleration = F e /m = q/m (kQ/r 2 )

… but the equilibrium is unstable. In order to prevent the universe from either expanding or contracting, Einstein introduced a scalar field that was called The Cosmological Constant in order to keep the universe static.

Astronomical Redshifts λ = observed wavelength λ o = “laboratory” or “rest” wavelength Δλ = λ – λ o = (1 + z) λ z = redshift = √[(c+v)/(c-v)] - 1 → v<<c v/c

The Age of the Universe No gravity: v = H o r  t o = r/v = H o -1 Newtonian gravity for a flat universe: ½ mv 2 - GmM/r = 0  v = dr/dt = (2GM/r) ½ so we can integrate r ½ dr = (2GM) ½ dt to get t o = 2/3 (r 3 /2GM) ½ = 2/3 (r/v) = 2/3 H o -1

from An Essay on Criticism by Alexander Pope Drink deep, or taste not the Pierian Spring: There shallow Draughts intoxicate the Brain, And drinking largely sobers us again. A little Learning is a dang'rous Thing;

Cosmological Principle At any instant of time, the universe must look homogeneous and isotropic to any observer. Perfect Cosmological Principle …….and indistinguishable from the way it looked at any other instant of time.

Steady-State Theory The expansion of the universe is balanced by the spontaneous production of bubbles of matter-anti-matter, so that the Perfect Cosmological Principle is preserved. Nucleosynthesis in stars can account for the abundances of all the elements except the very lightest – is that a problem?

Gamow’s Test for a Big Bang versus a Steady State Universe If there was a Big Bang, there should be some cooling remnant radiation (now maybe 5K?) that pervades the universe If, instead, the universe is always the same, there should NOT be any cooling radiation

Evidence for the Hot Big Bang Abundances of the light elements BBN measures the universe at approximately t = 200 s Hubble flow H o measures the universe at approximately t = yrs Cosmic microwave background radiation CMB measure the universe at approximately t = 4 x10 5 yrs

The Matter/Anti-matter Problem Why doesn’t there appear to be as much antimatter as ordinary matter in the universe? There is! In the early universe, the imbalance was less than one part in 10 10, so that when all the stuff in the dense early universe annihilated it left a small residual of matter and all those photons! (or at least there was!)

So What’s the Problem(s)? The horizon problem How did the universe become so homogeneous on large scales? The flatness problem Why is density of the universe so close to the critical density? The structure problem Is there a physical origin for the density perturbations?

Total energy associated with a galaxy of mass m: ½ mv 2 - GmM/r  0 if barely bound M = 4/3 πr 3 ρ now = 4/3 πr 3 ρ o r (t) = a(t) = H -1 (t)v(t)  r = H o -1 v ρ o = ¾ M/(πr 3 ) = 3/8 v 2 /(πGr 2 ) = 3H o 2 /(8πG) Critical Energy Density of the Universe Ω = ρ/ρ o  1 if the universe is flat

The current value of Ω…. …and it’s value at any time in the past …must be exactly …..

Hot Big Bang from Cosmic Background Radiation (CMB) But Ω B <.05 from light element nucleosynthesis Horizon and flatness suggest inflation Inflation demands that Ω = 1 very precisely Where is the other > 95% of the mass? Standard Model circa 1990 DARK MATTER

Galactic Rotation Curves For a star of mass m a distance r from the center of a galaxy, where the total mass interior to r is M(r): mv 2 /r = GM(r)m/r 2 so that we would expect v= [GM(r)/r] ½ so that v should go like r -½

Dark Energy

Oscillations on many scales Source: Wayne Hu: background.chicago.edu

Early Universe Acoustics Sound speed c s ≈ √w = √(p/ρ) ≈ c/√3 Density fluctuations are they random (Gaussian, scale-independent…?) Measure cross-correlation in spherical harmonics

CMB Anisotropy Power Spectra Dependence on Cosmological Parameters  tot = 1.0   = 0.0 h = 0.65 n= 1.0  b = 0.12  b = 0.08  b = 0.05  b = 0.03  b = 0.05 h = 0.65 n= 1.0  m = 0.3  m = 0.7  m = 1.0  m = 0.3   = 0.7   = 0.3   = 0.0 Multipole moment Anisotropy Power (µK 2 ) Angular Scale 90°0.5°0.2°2°

Power Spectrum cosmic variance limited for l<354 S/N>1 for l<658

The Top Ten Ω tot = 1.02 ±.02 Ω Λ =.73 ±.04  Ω m =.27 ±.04 H o = 71 ± 4 km/s-Mpc Ω b =.044 ±.004 T cmb = ±.002 K m ν <.023 eV t o = 13.7 ±.2 Gyr t dec = 379 ± 8 kyr z dec = 1089 ± 1 t r = 180 ± ~100 Myr z r = 20 ± 10 n s = 0.93 ±.03

Fire and Ice by Robert Frost Some say the world will end in fire; Some say in ice. From what I've tasted of desire I hold with those who favor fire. But if it had to perish twice, I think I know enough of hate To know that for destruction ice Is also great And would suffice.