History of Science (Part II) :Cosmology

Recall: Galileo

Telescopic observation

Moons of Jupiter

Phases of Venus

Sunspots

Promoted Copernicus

Censored

Defended Copernican system

Dialogue of the Two World Ssytems

Tried by the Inquisition (1633)

Discourse on Two New Sciences (1637): kinematics

No treatment of causes of motion

Recall:

Newton: Principia (1687)

Law 1 Every body continues in its state of rest, or uniform motion in a straight line, unless compelled to change by forces acting on it

Law 2: The change in motion is proportional to the force impressed, and in the direction of the force

Law 3: To every action there is always an equal and opposite reaction: the mutual actions of two bodies upon each other are always equal, and directed to contrary parts

Summ: N2

F = force acting

F = mam = mass

a = accel

Notes

  1. force causes accel (F = 0 ↔ a = 0)
  2. accel is proportional to force acting

3. accel is inversely proportional to mass of object

4. inertial mass is constant

Law 4: Universal Law of Gravitation

FG = GMm/r2

FG= force of gravity

M= mass of one object

m = mass of other object

r = separation of objects

G = constant (6.6x 10-11)

Unites terrestrial and celestial gravity

Force on apple = force on planets

Notes:

  1. FG v. weak force (G extremely small)

FG only seen when one mass is a planet

  1. FG always attractive
  2. FG acts instantaneously across huge distances
  3. M,m = inertial mass (see N2)

Newton’s Cosmos

1. Force of gravity –

Attractive, weak, infinite range

2. Univ. infinite in time (eternal)

no beginning, no end

3. Univ. finite in content

Gravity would crush universe

Olber’s paradox

4. Space – infinite?

Space and time a fixed stage

19th century cosmology

  1. Improved telescopes

Distances to stars

  1. Photography

Improved images

  1. Spectroscopy

Analysis of starlight

Spectral lines of known elements


The Great Debate 1900-1920

  1. Detection of the distant nebulae
  1. Stars within Milky Way ? (Shapley)

Measured diameter of Milky way – enormous

  1. Galaxies outside Milky Way ? ( Curtis )

Motion too great to be confined to Milky way

Emission lines doppler-shifted : Vesto Slipher

  1. Measurement of distance to nebulae (Hubble, 1925)

Cepheid variables

Much larger than diameter of Milky Way

Conclude: many distant galaxies !

Hubble’s Law

  1. Detected galaxies outside Milky Way

Cepheid variables

  1. Combined with velocity measures of nebulae (galaxies)

Vesto Slipher

  1. Relation between distance and velocity of a galaxy

Hubble’s Lawv = Hod(1929)

Linear relation

Ho = slope = measure of expansion rate

uncertain due to distance calc

  1. Hubble’s Law II (1931)

more accurate

measurements of distance to 40 galaxies – Hubble

measurement of 40 redshifts – Humason (assistant)

Albert Einstein (1867-1955)

Special Relativity (1905): breakdown of Newtonian mechanics

at high velocities

Speed of light universal const

Distance, time and mass velocity-dependent!

Space-time

Mass-energy (E = mc2)

General Relativity (1915) : breakdown of Newtonian mechanics

at high gravitational fields

Gμν = -kTμν(10 eqs)

Geometry of space-time (Gμν) is determined by distribution

of matter and energy (Tμν)

“Gravity = distortion of space-time by mass”

Relates

geometric properties of space-time

(curvature and expansion)

to

properties of matter

(density and state of motion)

GR and cosmology

Note: 10 equations of GR : solutions?

Note: Assume Cosmological Principle:

U is homogeneous

U is isotropic

Note : Solutions of GR equations are dynamic

(U expanding or contracting)

Solutions: Einstein, deSitter, Friedmann,Lemaitre
1. Einstein’s cosmology

Believed U static, unchanging

Introduced cosmological constant λ for static U

Gμν + λgμν = -kTμν

Note: Failed to predict expanding U

Greatest blunder

Rejected Friedmann solns

2. Alexander Friedmann

Solns of GR (1922) assuming Cosmological Principle

No cosmological constant: space-time dynamic

Expanding U: balloon model

Density of matter = clock

Friedmann Models

Closed U: gravity > expansion (+ve curvature)

Open U: gravity < expansion (-ve curvature)

Flat U : gravity = expansion (flat U)

  1. Def: critical density of matter dc

If density of U > dc → U eventually collapse

If density of U < dc → U expand forever

2. Define Ω = d/dc

Ω > 1→U eventually collapse

Ω 1→U expand

Ω = 1→Dividing line

3. Georges Lemaitre

Mathematician and physicist (Louvain)
Astronomy at Cambridge, Harvard and MIT
1.Solns of GR (1922) assuming Cosmological Principle

No cosmological constant: space-time dynamic

Expanding U: balloon model

Independent of Friedmann

Three Models

Closed U: gravity > expansion (+ve curvature)

Open U: gravity < expansion (-ve curvature)

Flat U : gravity = expansion (flat U)

  1. Compares to astronomical measurements

Dynamic U and Slipher redshifts

Obscure journal(1927)

  1. Shows to Einstein (1927)

Rejected

Referred to Friedmann’s work

  1. Republished in 1931 (Eddington)

Hubble’s law causes Eddington rethink

Redshift section missing?

Hubble’s Law and relativity

Linear relation between distance and velocity of a galaxy

Red-shifted galaxies: receding source

Coverted redshift to recession velocity v

Hubble’s Lawv = Hod(1929)

Ho = slope = measure of expansion rate, of K.E.

- difficult to measure due to distance calc

Hubble’s Law II (1931)

Measurements of distance to 40 galaxies – Hubble

Measurement of 40 redshifts – Humason (assistant)

Hubble’s Law and relativity

Einstein accepts dynamic universe (1931)

Eddington, Einstein consider new universe

Lemaitre paper republished (1931)

Lemaitre/Friedmann model accepted

Note: redshift due to stretching of space-time (expansion)

Note: gravity prevents expansion locally

Origin of Universe

Reverse expansion: age of U ~ 1/Ho(if const)

Lemaitre (1931): cataclysmic origin to U

super-hot genesis of U

singularity predicted by GR

Lemaitre (1931): primeaval atom

process of radioactive decay?

Problem: Hubble age ~ 2 billion yr (faulty Ho)

Conflict with age of oldest stars: ~ 12 billion yr

Suggests: open U

Resolution: Modern value for Ho reduced

Age of U ~ 13.7 billion yr

Big Bang Model

George Gamow: prelim BB theory (1946)

Eextended model of Friedmann, Lemaitre

All Friedmann expanding models can be reversed back

intergalatic distance = 0

density of matter = ∞

curvature of space-time = ∞

temperature = ∞

Primordial state: neutons, protons, electrons + radiation

Expansion + cooling

Nucleosynthesis

Formation of atomic matter: 75% H, 25% He

Alpher, Bethe and Gamow (1948):

radiation should remain as cosmic backgound field

Temp ~ 5 Kelvin

Steady State model of U

Gold, Hoyle, Bondi: U expanding but homogenous in time

Perfect Cosmological Principle

Expansion rate constant

De Sitter soln of GR equations

Necessitates continuous creation for balance

Evidence that U was different in the past would rule it out

Hoyle: coined term Big Bang in derision

Cosmic Background Radiation

Penzias and Wilson (1965): background radiation

Microwave radiation (red-shifted)

Independent of time, place

Extra-galactic source

Black-body spectrum

Temperature: 3 Kelvin

Explanation: Alpher, Bethe and Gamow (1948):

Dicke and Peebles (1965)

CBR Leftover from Big Bang

Correct spectrum, temp

Main evidence for Big Bang

Cosmic background radiation: theory

Radiation produced in early stages of primordial fireball

Electrons stripped off atoms – plasma

Up to 300,000 yr after BB:

U as hot as the sun

opaque to light

photon scattering

As universe cools:

atoms form

recombination

photon scattering reduced

U transparent

Cosmic Microwave Background:

relic of radiation at recombination

u.v radiation

red-shifted by U expansion

observed at microwave frequencies

Expansion problems

1. Ho= measure of expansion rate

= measure of K.E. of U

2. Ω = measure of density of U

= measure of P.E. of U

3. Expansion = competition Hovs Ω

4. Neither Ho, Ω specified by Friedmann eq

5. Originally Ω ≈ 1

6. Nowadays Ω ≈ 0.3 ? (observation)

Suggests most matter is dark

7. Cosmological flatness problem

(see inflation)

Evidence for Big Bang

1.Hubble’s Law

Expansion of U

2. Cosmic background radiation (1965)

Temperature, uniformity, extra-galatic

3. Stellar composition

Nucleosynthesis of the elements

Hydrogen and helium proportions

3. Baryongenesis (Sakharov)

Early U baryon-symmetric

Slight preference for baryons during cooling

Huge numbers of photons

4. Stellar age

Agrees with reversed Friedmann model

5. Space-time structure (1992)

Wrinkles in CMB

Big Bang problems

  1. Spacetime singularity at beginning (BH)

-extrapolation of GR to quantum times incorrect?

-need quantum gravity

  1. Flatness problem

Ω must ≈ 1 (GR: deviations accelerate)

Observation : Ω ≈ 0.3

  1. Horizon problem

Large-scale smoothness of U

Faster than light communication?

≈ 1

  1. Acceleration of U (Supernova evidence)
  1. reintroduce cosmological constant
  2. energy density of vacuum
  3. causes gravity to push
  4. reconciles inflation with low Ω

Solution: Inflation (Guth, 1981)

Original expansion much more rapid

Black Holes

Schwarzschild (1916): exact soln of GR for point-like star

gravity so intense in vicinity, light can’t escape

Chandresekar (1930s): theory of stellar evolution

“stars of large mass cannot evolve into white dwarfs”

Oppenheimer (1939): calculated collapse of star to body of extreme density that swallows everything in vicinty

Wheeler (1950): Black Holes

“regions of space-time in state of extreme gravitational collapse”

Penrose (1965): collapse of any massive star must end in singular space-time point (BH): proof

Hawking and Penrose (1970): Grand Cosmological Theorem

U begins where BH ends: spacetime singularity

1970s: Evidence of BH

Cygnus X-1: BH paired with star

2000: many BH detected

Supermassive BH at center of our galaxy

Inflation

  1. Particle physics and cosmology (1980s)
  1. Flatness problem

Ω originally ≈1, now Ω= 0.3?

  1. One solution: cosmic inflation

Hugely accelerated expansion during at start of BB

Phase transition accompanied by vacuum energy

Ω →1

(Huge balloon is flat)

  1. New evidence: U speeding up

cosmic repulsion

  1. New cosmological const in GR

Energy density of vacuum

  1. Exactly what is need to cause inflation

Reconciles inflation with Ω= 0.3

Modern measurements and GR

  1. Ripples in microwave background (1992)

fluctuations in density, amplified by gravity

2. Gravity waves (1990s)

shock waves from cataclysmic event

-indirect evidence

3. Gravitational lensing (1980s)

gravity of galaxy splits light from star

rejoins when galaxy past

ring of light seen

used as lens system in astonomy

4. Acceleration of U (1998)

Not predicted by Friedmann (GR)

Soln: new cosmological constant in GR

5. U has flat geometry (2000)

Measurements of angular variations of CMB

Ω =1

Acceleration of U

Experimental measurements (1998-)

Not predicted by Friedmann solns (GR)

Suggests: dark energy- new cosmological constant

Most likely:energy density of vacuum = ρ

Gμν + = 8ΠG (Tμν + ρgμν)

predicted by quantum theory

particle-antiparticle creation/annihilation

virtual particles

causes gravity to push instead of pull

could cause flat U with acceleration

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