8.286 The Early Universe

Themes

Lectures (23 of 23 with pages so far)

1. Lecture 1Inflationary Cosmology: Is Our Universe Part of a Multiverse? Part IMIT ↗
   • The Big Bang and its prequel — an overview of inflationGuth's opening lecture. The standard Big Bang describes only the aftermath of a bang; inflation supplies the bang itself, using two "miracles of physics" — gravity can repel, and gravitational energy is negative — and explains why the universe is uniform, flat and slightly lumpy.→
   • Eternal inflation, dark energy and the landscapeThe inflating material decays, but it expands faster than it decays — so inflation never ends, endlessly spawning pocket universes. Add the 120-orders-of-magnitude mystery of dark energy and string theory's landscape of perhaps 10⁵⁰⁰ vacua, and a multiverse begins to look plausible.→
2. Lecture 2Inflationary Cosmology: Is Our Universe Part of a Multiverse? Part IIMIT ↗
   • The anthropic argument and the multiverse — and where the course beginsWhy might we live in one of the rare pocket universes with a tiny vacuum energy? Guth makes the case for a selection effect — the explanation of last resort — answers questions about the multiverse, and starts the course proper with Hubble's law and the Lemaître controversy.→
3. Lecture 3The Doppler Effect and Special RelativityMIT ↗
   • The Doppler effect and special relativityWhy a moving source shifts the wavelength of sound and light, what redshift z means, and the three effects of special relativity that cosmology relies on.→
4. Lecture 4The Kinematics of the Homogeneous Expanding UniverseMIT ↗
   • The homogeneous expanding universeIsotropy, homogeneity and Hubble's law — and how a single function, the scale factor a(t), describes the whole expanding universe.→
5. Lecture 5Cosmological Redshift and the Dynamics of Homogeneous Expansion, Part IMIT ↗
   • Cosmological redshiftLight stretches with the universe — the redshift of a distant galaxy tells you how much the universe has expanded since the light left it.→
   • Why a static universe cannot workNewton thought an infinite, evenly filled universe could stand still. Gauss's law shows it cannot — gravity forces the universe to expand or collapse.→
6. Lecture 6The Dynamics of Homogeneous Expansion, Part IIMIT ↗
   • The expanding sphere and the equation for a(t)Newton's gravity applied to a uniformly expanding ball of matter gives the equation that governs the scale factor — and a conserved quantity that decides the fate of the universe.→
7. Lecture 7The Dynamics of Homogeneous Expansion, Part IIIMIT ↗
   • The Friedmann equationRewriting the conserved quantity of the expanding sphere gives the Friedmann equation — the equation at the heart of modern cosmology — and a Newtonian derivation that is exact.→
   • Open, closed and flat universesThe sign of k decides the fate of a matter-filled universe. The dividing line is the critical density — about five protons per cubic metre — and a flat universe grows as t to the 2/3.→
8. Lecture 8The Dynamics of Homogeneous Expansion, Part IVMIT ↗
   • The age of the universe and the Big Bang singularityA flat universe of matter alone would be two-thirds of a Hubble time old — younger than its oldest stars. What "age" means when the equations break down at t = 0.→
   • The horizon distanceHow far away are the most distant things we could possibly see? In a flat matter-dominated universe, three times the speed of light times the age — and why it is more than c times the age.→
9. Lecture 9The Dynamics of Homogeneous Expansion, Part VMIT ↗
   • The closed universe as a cycloidSolving the Friedmann equation for a closed universe gives a parametric solution with a surprising shape — the curve traced by a point on a rolling wheel.→
   • The age of a closed universe from H and ΩAstronomers measure H and Ω, not the cycloid's α and θ. Translating gives the age of a closed universe — and shows that Ω climbs from 1 to infinity and back over its life.→
10. Lecture 10Introduction to Non-Euclidean SpacesMIT ↗
    • The open universe and the age of any matter universeThe open universe swaps sines and cosines for their hyperbolic cousins. Together with the flat and closed cases, it gives one smooth curve for the age of every matter-dominated universe.→
    • Non-Euclidean geometryEuclid's parallel postulate turned out to be optional. Dropping it gives curved geometries — and Gauss's idea of a metric, which general relativity uses to describe gravity.→
11. Lecture 11Non-Euclidean Spaces: Closed UniversesMIT ↗
    • The metric of a sphere and of a closed universeMeasuring distance on a sphere with angles, then going up one dimension to the 3-sphere — the shape of space in a closed universe.→
    • Curvature and expansion — the Robertson–Walker metricHow the radius of curvature of a closed universe is tied to its scale factor, why curvature is a relativistic effect, and the Robertson–Walker metric that describes the expanding universe.→
12. Lecture 12Non-Euclidean Spaces: Open Universes and the Spacetime MetricMIT ↗
    • The geometry of open universesLetting k go negative in the Robertson–Walker metric gives the infinite, negatively curved space of an open universe — and the three geometries together are all a homogeneous, isotropic universe can be.→
    • The spacetime intervalThe one combination of space and time separations that every inertial observer agrees on — and how it sorts pairs of events into spacelike, timelike and lightlike.→
13. Lecture 13Non-Euclidean Spaces: Spacetime Metric and Geodesic EquationMIT ↗
    • The spacetime metric of the universeHow time joins the Robertson–Walker metric, what ds² means once gravity is present, and why free-falling observers take over the role of inertial ones.→
    • The geodesic equationHow to find the paths of stationary length in any metric — index notation, a varied path, one integration by parts, and the equation that comes out.→
14. Lecture 14The Geodesic EquationMIT ↗
    • Simplifying the geodesic equationMeasure the path by its own length and the geodesic equation sheds its square roots; solving for the acceleration brings in the inverse metric and the Christoffel symbols.→
    • Falling into a black holeThe geodesic equation applied to the Schwarzschild metric — an object dropped towards a black hole reaches the centre in finite proper time, yet seen from outside never even reaches the horizon.→
15. Lecture 15Black-Body Radiation and the Early History of the Universe, Part IMIT ↗
    • Mass, energy and the dilution of radiationLight has energy, so by E = mc² it has mass density and gravitates — and because each photon is redshifted as well as diluted, radiation's density falls as 1/a⁴, faster than matter's.→
    • Matter–radiation equality and the pressure of lightRunning today's radiation density backwards dates the end of the radiation era to roughly 75,000 years after the Big Bang — and radiation's pressure forces a pressure term into the second Friedmann equation.→
16. Lecture 16Black-Body Radiation and the Early History of the Universe, Part IIMIT ↗
    • The radiation-dominated universePressure gravitates — positive pressure decelerates, negative pressure would accelerate — and a flat universe full of radiation grows as the square root of time, with a density fixed by the clock alone.→
    • Black-body radiationRadiation in equilibrium at temperature T is the same whatever contains it; quantum mechanics rescues its energy density from the classical infinity, giving u ∝ T⁴, n ∝ T³ and s ∝ T³ — and neutrinos, though not massless, count as radiation too.→
17. Lecture 17Black-Body Radiation and the Early History of the Universe, Part IIIMIT ↗
    • Neutrinos and counting particle speciesEvery kind of particle that is effectively massless adds to the black-body radiation — fermions with a factor 7/8 — giving g = 10¾ for photons, neutrinos and electron–positron pairs; today's neutrinos are colder than the photons, by (4/11)^⅓.→
    • The temperature of the early universe and decouplingCombining ρ = 3/(32πGt²) with the black-body formula gives the temperature as a function of time — about 10¹⁰ K one second after the Big Bang — and following it down to 3,000 K dates the moment the universe became transparent.→
18. Lecture 18Cosmic Microwave Background Spectrum and the Cosmological Constant, Part IMIT ↗
    • The spectrum of the cosmic microwave backgroundFrom a single frequency in 1965 to COBE's flawless black-body curve in 1990 — how the CMB spectrum was measured, what the Planck formula predicts, and why a perfect fit confirms the hot, dense early universe.→
    • The cosmological constant and vacuum energyIn 1998 distant supernovae showed that the expansion is speeding up. The simplest explanation is Einstein's cosmological constant, read today as the energy of the vacuum — whose negative pressure drives acceleration and makes the universe older.→
19. Lecture 19The Cosmological Constant, Part IIMIT ↗
    • The age of the universe with vacuum energyWriting every ingredient of the universe as a fraction Ω of the critical density turns the Friedmann equation into one integral for the age — the formula behind the Planck age — and adding vacuum energy makes the age problem disappear.→
    • How bright is a distant supernova?The formula the 1998 supernova teams fitted to their data — the measured intensity of a standard candle as a function of its redshift, for a universe with matter, radiation, vacuum energy and curvature.→
20. Lecture 20Supernovae Ia and Vacuum Energy DensityMIT ↗
    • The supernova evidence for accelerationHow astronomers turned the brightness of type Ia supernovae into distances, why the 1998 data favoured a universe with vacuum energy, why being dimmer means accelerating, and why dust and evolution were ruled out.→
    • The puzzle of the vacuum energy, and Einstein's mistake about FriedmannQuantum field theory easily explains why the vacuum should have energy, but a naive estimate overshoots the observed value by about 120 orders of magnitude. Plus the story of how Einstein wrongly "refuted" Friedmann's expanding universe.→
21. Lecture 21Problems of the Conventional (Non-inflationary) Hot Big Bang ModelMIT ↗
    • The horizon problemThe CMB has the same temperature in every direction to one part in 100,000, yet in the conventional Big Bang the places that emitted it from opposite sides of the sky were about 46 horizon distances apart — too far for anything to have evened them out.→
    • The flatness problemΩ = 1 is an unstable balance point, like a pencil on its tip. For Ω to be anywhere near 1 today, at one second after the Big Bang it must have equalled 1 to about 18 decimal places — and the conventional Big Bang has no reason why.→
    • The Standard Model, gauge theories and grand unificationThe third problem of the conventional Big Bang, magnetic monopoles, only arises in grand unified theories. To get there, Guth sketches the Standard Model of particle physics, why nobody thinks it is final, what a gauge theory is, and how SU(5) contains SU(3) × SU(2) × U(1).→
22. Lecture 22The Higgs Field and the Cosmological Magnetic Monopole ProblemMIT ↗
    • The Higgs field and spontaneous symmetry breakingHow electromagnetism's gauge freedom becomes a U(1) phase in quantum theory, why the weak and electromagnetic symmetries look different today, and how a Higgs field settling into one of infinitely many equivalent minima breaks the symmetry — distinguishing electrons from neutrinos and giving particles mass.→
    • Topological defects and the magnetic monopole problemSymmetry breaking starts independently in causally separate regions, and where regions with different Higgs values meet, defects form. Every grand unified theory predicts point-like defects that are magnetic monopoles of about 10¹⁸ GeV — and the conventional Big Bang makes so many that they would outweigh everything else by an enormous factor.→
23. Lecture 23InflationMIT ↗
    • The false vacuum and the mechanism of inflationInflation runs on a scalar field stuck at a high-energy "false vacuum". Its energy density cannot drop quickly, which forces a negative pressure equal to minus the energy density — and negative pressure makes gravity repulsive. How the original model failed to end, and how new inflation fixed it.→
    • Exponential expansion, de Sitter space and the inflationary scenarioA false vacuum makes the universe grow exponentially — de Sitter space, with an event horizon one Hubble length away that protects the inflating region. With grand-unified numbers, a patch 10⁻²⁷ cm across grows to centimetres, reheats to 10¹⁶ GeV and becomes everything we see.→
    • How inflation solves the problems of the Big BangInflation makes the observed universe grow from a region small enough to reach equilibrium, drives Ω towards 1 exponentially fast, dilutes monopoles to nothing — and turns quantum fluctuations into the seeds of galaxies, whose imprint on the CMB matches the theory beautifully.→

Note: Lecture titles are from the 8.286 Fall 2013 video lectures page. Dark matter and structure formation get their own pages beyond MIT's lecture list; each such page names its own MIT source.