Cosmic Microwave Background

• The Cosmic Microwave Background (CMB) is the radiation remnant of the primeval hot Big Bang fireball.
• Observationally, the Cosmic Microwave Background:
  • Has an exquisite thermal (black body) spectrum, with a temperature of 2.725 Kelvin.
  • Is almost uniform on the sky.
  • Shows a “dipole” distortion from the motion of the Sun through the CMB, at 365 km/s.
  • After subtraction of the dipole distortion, the residual temperature fluctuations are tiny, a few parts in 10⁵.
  • The power spectrum of fluctuations shows a pattern of acoustic peaks in remarkable agreement with the predictions of the Standard ΛCDM Model of Cosmology.
• Theoretically, the Cosmic Microwave Background:
  • Supports the idea that there was a hot Big Bang.
  • The CMB cools as the Universe expands, the wavelengths of CMB photons being stretched (redshifted) by the expansion of the Universe.
  • Its uniformity and thermal (blackbody) spectrum tell us that the Universe used to be much simpler when it was young.
  • Comes to us from the Epoch of Recombination, when the Universe was 380,000 years old, and the temperature was 3000 Kelvin.
  • At Recombination, hydrogen and other elements combined from an ionized plasma of nuclei and free electrons to a neutral gas of atoms. As a result, the Universe changed from being opaque to transparent, allowing the CMB to propagate freely to us from that time.
    

    Before Recombination	After Recombination
    ionized	neutral
    opaque	transparent
    vibrating photon-baryon fluid	baryons start collapsing into galaxies

  • The peak in the power spectrum, about 1° on the sky, corresponds to the cosmological horizon size at Recombination, about 400,000 lyr.

Week 13 (Apr 5): Large Scale Structure, Dark Matter

• Redshift surveys of galaxies reveal a “cosmic web” of structure.
• The large scale structure shows a characteristic scale of about 100 Mpc (300 million lightyears), a supercluster scale. This is the imprint of the scale of the cosmological horizon at Recombination.
• Computer simulation of the formation of a supercluster (TNG 2019)

• The Local Group is about 1 Mpc across.
• The Local Group contains about 100 galaxies:
  • M31, the Andromeda galaxy;
  • The Milky Way;
  • M33, the Triangulum galaxy;
  • various smaller irregular and dwarf spheroidal galaxies.
• M31 is approaching the Milky Way at 100 km/s, and they will collide in 5 billion years time. Simulation.

• The Local Supercluster is about 100 Mpc across.
• It contains thousands of bright galaxies.
• The Local Group is on its outskirts.
• At the center of the Local Supercluster is the Virgo cluster of galaxies.

• When galaxies collide, they feel each other’s gravity, but the stars do not collide.
• A compilation of simulations versus observations.
• The Antennae galaxy.
• The Cartwheel galaxy.

Dark Matter

• Dark Matter (as opposed to gravitationally repulsive Dark Energy) is unseen matter which is detected by its gravitational effects.
  • The composition of the Universe is measured from the Cosmic Microwave Background, galaxies, and other supporting evidence to be 70% Dark Energy, 25% Dark Matter, 5% Baryonic Matter.

• Most of the Dark Matter is thought to be some mysterious “non-baryonic” particle whose interactions are so weak as to have escaped detection in the laboratory (so far — go physicists!).
  • The most compelling evidence that Dark Matter is non-baryonic comes from comparing the amplitude of fluctuations in the CMB to those in galaxies today. How can tiny fluctuations in the CMB grow by gravity into today's galaxies and galaxy clusters in “only” the age of the Universe? Baryons are not enough because before Recombination, baryons were tightly coupled to photons, and could not start clustering gravitationally. But non-baryonic dark matter could start clustering before Recombination. And the power spectrum of the CMB requires non-baryonic cold dark matter.
    

• Dark Matter in spiral galaxies. The rotation of the galaxy reveals the total mass of gravitating matter in the galaxy. The mass of dark matter relative to luminous matter grows more and more at greater distances from the center of the galaxy.

• Dark Matter in the Local Group of galaxies.
  • For the Andromeda galaxy (M31) to be approaching us (at 300 km/s) requires that the M31-Milky Way system (the Local Group) contain ten times as much matter as is visible in stars.

• Dark Matter in clusters of galaxies.
  • The temperature of x-ray emitting hot gas reveals the depth of the gravitational potential well, hence the amount of gravitating matter. Again, typically the total mass is ten times the luminous mass.
  • Gravitational lensing of background galaxies (bluish arcs) by a foreground cluster (yellowish galaxies). Once again, typically the total mass measured from lensing is ten times the luminous mass.

• The Bullet Cluster shows two colliding clusters whose dark matter halos have passed through each other while their hot gas has not.

Weeks 14 & 15 (Apr 12 & 19): The Birth of the Universe

Evolution of the Universe

• The Cosmic Scale Factor \(a\)
  • a measure of the size of the universe, with the defining property that it expands with the Universe.

• Wavelengths of light stretch with the expansion of the Universe

  \(\lambda\) \(\propto\) \(a\) Wavelength is proportional to cosmic scale factor

  Given astronomers' definition of redshift \(z\), it follows that

  \( 1 + z = \displaystyle {\lambda_{\rm obs} \over \lambda_{\rm em}} = {a_{\rm obs} \over a_{\rm em}} \)

  • True in a full general relativistic description of the Universe.
  • Another way of thinking about the redshift of distant objects in the Universe.

• Emmy Noether's (1918) theorem says that with every symmetry of nature is associated a conserved quantity.
  • Today, each of the four forces of nature is recognized as being associated with a symmetry of nature.

• Gravity, governed by Einstein's General Relativity:
  • Is the force associated with symmetries of spacetime.
  • Unites space and time into a single 4-dimensional spacetime.

    Symmetry Conserved quantity Time translation Energy Space translation   Momentum Rotation Angular Momentum

  • Because general relativity unites time and space, not only energy (density), but also momentum (pressure), gravitates.

    Gravitational acceleration \(\propto\) \(- ( \rho + 3 p )\)  is proportional to  minus ( density + 3 \(\times\) pressure )

    
    

    Form of energy  \(p/\rho\) \(\rho + 3 p\) Radiation \(\frac{1}{3}\) \(2\) attractive Matter \(0\) \(1\) attractive Curvature \(-\frac{1}{3}\) \(0\) neutral Vacuum \(-1\) \(-2\) repulsive

  • The factor of 2 for radiation is the famous factor of 2 for the deflection of light by the Sun, confirmed by the eclipse expedition of 1919.

• General Relativity relates the age and fate of the Universe to its mass-energy content.

Inflation

• Schematic evolution of the Universe
  • Evolution of different kinds of mass-energy with the expansion of the Universe.

• The cosmological horizon of the observable Universe
  • The edge from which a signal created at the Big Bang could just reach us.
  • The distance to the horizon is approximately the age of the universe times the speed of light.
  • The CMB, released at Recombination, is the most distant thing that we can see in electromagnetic radiation; but it was emitted just inside our horizon (not at our horizon).
  • The horizon size at Recombination, when the Universe was about 400,000 years old, was about 400,000 lightyears. This corresponds to about 1 degree of angle on the CMB sky today.
  • What lies beyond our horizon?

• Problems of the Universe
  1. Why is the Universe expanding?
  2. Why is the Universe at large so smooth (CMB fluctuations are tiny)?
  3. Why is the Universe so flat (Boomerang, WMAP, Planck)?
  4. The horizon problem: How can regions of the Cosmic Microwave Background more than 1 degree apart, which were causally disconnected at the time of Recombination, know to have the same temperature today?
  5. Where did matter in the Universe come from?
  6. What caused ripples in the smoothness?

  Remarkably, the theory of Inflation (Alan Guth 1981) offers a solution to all of these problems.

• Inflation is a hypothesized epoch in the very early Universe when the mass-energy of the Universe was dominated by vacuum energy.
  • Vacuum energy is the quantum zero-point energy of the vacuum.
  • Vacuum energy is gravitationally repulsive, according to General relativity.
  • Consequence: the Universe inflates, doubling in size each “tick of the clock”.
    If the vacuum energy was that of GUT (Grand Unified Theories; see below), then
    • each tick was a GUT time, about \(10^{-38}\) seconds, long;
    • inflation took place over perhaps \(10^{-35}\) seconds altogether;
    • the Universe grew from perhaps 1000 GUT lengths, about \(10^{-29}\) meters, to perhaps a meter in size;
    • the temperature was about \(10^{26}\) Kelvin;
    • the vacuum density was about \(10^{80}\) times the density of water.

• Solution to Problem 1: Why is the Universe expanding?
  • The repulsion of the vacuum accelerated the Universe into tremendous exponential expansion — inflation.

• Solution to Problem 2: Why is the Universe so smooth?
  • Any initial fluctuations in density were stretched (redshifted) into smoothness.

• Solution to Problem 3: Why is the Universe so flat?
  • Inflation made the Universe so huge that today we see only a small patch of it, which looks flat. On a much huger scale, well beyond our horizon, the Universe might not be flat at all.

• Solution to Problem 4: The horizon problem.
  • Before inflation, the different parts of the Universe were causally connected.
  • Inflation caused different parts of space to accelerate away from each other, eventually faster than the speed of light, so that they became causally separated.
  • So the solution is: Causally disconnected regions of the CMB were once causally connected, before Inflation.
  • The peaks in the power spectrum of fluctuations in the CMB require that the fluctuations were initially synchronized (like the initial pluck of a guitar string) as predicted by inflation.
  • Probably the most compelling observational reason in favor of inflation.

• Solution to Problem 5: Where did matter in the Universe come from?
  • The observed vacuum energy today is tiny, about \(10^{-26}\) kg/m³, far less than the \(10^{84}\) kg/m³ GUT density.
  • Therefore, inflation must have ended at some point.
  • Theory:

    Vacuum energy \(\rightarrow\) Matter + radiation energy.

• Solution to Problem 6: What caused ripples in the smoothness?
  • Tiny quantum fluctuations in the inflationary vacuum energy produced ripples,
  • which later grew by gravity into galaxies, stars, and you.
  • Inflation predicts a “scale-invariant” spectrum of fluctuations at the largest scales (larger than the horizon size at Recombination) in agreement with the observed power spectrum of fluctuations in the CMB at scales much greater than 1°.

• What is this vacuum energy that drove inflation?
  • It’s energy associated with the Unification of forces — specifically, with the unification of the electroweak and strong forces into a hypothesized GUT (Grand Unified Theory) force.
  • The interactions of all particles appear to be governed by just four forces:
    • Gravity
    • Electromagnetism
    • The strong, or nuclear, or color force
    • The weak force
  • Glashow, Salaam, and Weinberg won the 1979 Nobel prize for their theory of the unification of the electromagnetic and weak forces into a combined electroweak force.
    • Electroweak unification appears only at high energy, above about 10¹⁵ Kelvin, which is about the highest energy accessible in particle accelerators today.
    • Electroweak unification correctly predicts various experimentally observed phenomena — such as that, at high energy, neutrinos (which interact only by gravity and the weak force) interact similarly to electrons (which interact by gravity, the weak, and electromagnetic forces).
  • Extrapolating, physicists predicted that at even higher energies the electroweak force may unite with the strong force into a single GUT force.
    • But the GUT energy is too high, about 10²⁸ Kelvin, to be reached in particle accelerators, so the theory is not well understood and is not experimentally tested.
  • The (de)unification of forces is like a phase transition (like steam \(\leftrightarrow\) water). Vacuum energy is the “latent heat” of the transition.

• In summary, inflation offers an enticing and observationally consistent picture that suggests how the Universe today could have come from almost “nothing”.

• Inflation does not explain how the laws of physics that govern our Universe were laid down, nor why those laws are so beautifully adapted to life.

• What happened before inflation? An unanswered mystery.

  ASTR 2010 Spring 2022 Homepage

Updated 2022 Apr 19