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Fromm Institute for Lifelong Learning University of San Francisco. Modern Physics for Frommies IV The Universe - Small to Large Lecture 8. Agenda. Administrative matters Corrections and / or Clarifications to Lecture 7. Astrophysics / Cosmology Rotation Curves and Dark Energy

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Fromm Institute for Lifelong Learning

University of San Francisco

Modern Physics for Frommies IV

The Universe - Small to Large

Lecture 8

Modern Physics IV Lecture 8

  • Administrative matters
  • Corrections and/or Clarifications to Lecture 7
  • Astrophysics / Cosmology
    • Rotation Curves and Dark Energy
    • Expansion of the Universe
    • Hubble’s Law, the Big Bang and the age of the Universe
    • Epochs in the History of the Universe
    • Dark Energy

Modern Physics IV Lecture 8

Corrections and/or Clarifications to Lecture 7

Lec. 7 Slides 15, 22:

Hydrogen Fusion: 411H  24He + 2e+ + 2n + 2g + 26.7 MeV

Fission: Initial mass per reaction ≈ 236 amu

Fusion: Initial mass per reaction ≈ 4 amu

=> Same fuel mass

Fusion gives more energy per mass of fuel by almost an order of magnitude

Modern Physics IV Lecture 8

Rotation Curves and Dark Energy

What is a rotation curve?

Rigid disk rotating with angular velocity w:

Tangential linear velocity v = wr





Plot of tangential linear velocity vs. radius

Modern Physics IV Lecture 8

Planets in the Solar System:

Newton’s mechanics applied to a central 1/r2force → Kepler’s laws.

Modern Physics IV Lecture 8

Can we explain this?

The dominant mass in the solar system is the sun and is distributed spheroidally.

From outside a spherical mass the gravitational field looks like that due to a point mass at the center.

For a circular orbit

Modern Physics IV Lecture 8

What about orbits inside a mass distribution?

Mass is uniformly distributed, density r


For Rorbit > Rdist we have the previous case.

If Rorbit < Rdist we can show that the mass outside the orbit does not contribute to the gravitational force on the planet.


Modern Physics IV Lecture 8




Now, let’s look at a spiral galaxy, e.g. NGC3198

Measure velocities from Doppler red and blue shifts.

Modern Physics IV Lecture 8

Dark Matter; what is this stuff?

Accounts for a large part of the mass-energy of the universe

83% of matter and 23% of mass-energy of the universe

Neither emits nor scatters electromagnetic radiation.


Massive Compact Halo Objects (MACHOs)

Black holes, neutron stars, black dwarfs, brown dwarfs , etc.

Such things as searches for microlensing, Hubble Space Telescope serches and Big Bang nuleosynthesis studies rule these out.

Modern Physics IV Lecture 8

Weakly Interacting Massive Particles (WIMPs)

Axions, lightest supersymmetric (SUSY) particles (neutralinos). Non SUSY sterile neutrinos, other weirdoes from beyond the Standard Model.

Lightest SUSY particle is current favorite,

People are looking at and for all of these things. Difficult experiments!

Modified Gravity Laws

Corrections toGeneral Relativity for different distance scales

So far ruled out by observations

Quantum Gravity

Some theories =>G varys over astrophysical scales.

There are many theories but no experiments.

Modern Physics IV Lecture 8

Expansion of the Universe

Until the 20thcentury the Universe, as a whole, was thought to be static (steady state).

1912 Vesto Slipher observed that the spectra of most galaxies appear to be redshifted, suggesting that they are moving away from the Earth.

1927 Georges Lemaitre proposed the theory of the expansion of the Universe, widely misattributed to Edwin Hubble . Lemaître also proposed what became known as the Big Bang theory of the origin of the Universe (“hypothesis of the primeval atom”).

1929 Edwin Hubble completed systematic studies of the apparent receding motion of galaxies.

Modern Physics IV Lecture 8

The expansion of the Universe can be described as the expansion or stretching of space over cosmological distances. When space “expands,” it carries or drags all the matter and energy along with it. As a result, all clusters of galaxies appear to be receding away from each other. This apparent motion of galaxy clusters is known as the Hubble flow and satisfies Hubble’s law.

Analogy with an expanding baloon.

Modern Physics IV Lecture 8

Viewpoint Point A

Viewpoint Earth

Modern Physics IV Lecture 8

What General Relativity Tells Us About the Expansion:
  • The expansion is not really due to the motion of galaxies, but it is an expansion of space itself. Cosmological effect caused by the stretching of space, does not represent the independent motions of galaxies.
  • The Cosmos is not expanding into an existing vacuum, but is just “expanding within itself,” there is nothing outside the Universe.
  • The expansion has no center, observers in all galaxy clusters will see exactly the same scenario: galaxies receding away from each other.
  • Individual systems or objects do not expand, only the distance between them stretches. Objects are held and bound by forces but are free from the forces of the other clusters, so they just appear subject to the overall cosmological expansion
  • Photons or electromagnetic waves are subject to the expansion, as they are not tightly bound objects. Electromagnetic radiation is redshifted: the photon wavelength is stretched along with space. Thus, the observed redshift is due to the expansion of space rather than due to the motion of galaxies! This is known as the cosmological redshift, physically distinct from the Doppler redshift (due to the motion of ordinary objects).

Modern Physics IV Lecture 8

Hubble’s Law:

All spectra are shifted to the red and that redshift, z, in the spectrum is proportional to the distance, d, from the Earth.

17 Mpc

210 Mpc

310 Mpc


870 Mpc

Modern Physics IV Lecture 8

Determine the recessional velocity

Slope H0≈ 71 (km/s)/Mpc


1 pc ≈ 3.3 ly

Modern Physics IV Lecture 8

Age of the Universe:

Units of H0= (km/s) /(Mpc) = (km/Mpc)/(second)

Thus units of 1/H0= (Mpc/km) (second) = units of time

Convert Mpc to km and seconds to years. One year is approximately 3  107 seconds, (3600 s/hr)(24 hr/day)(365 day/yr), and one parsec is approximately 3  1013 km.

Modern Physics IV Lecture 8

Hubble’s law suggests that in the beginning the universe must have been much smaller (perhaps even a singularity) which ha expanded to today’s condition

=> Big Bang Theory: Origen of the Universe in a great explosion.

Determination of Earth’s age from uranium decay

≈ 4 billion years but Earth was formed late in Universe’s history

Determination of age of oldest stars from stellar evolution theories

≈ 15 billion years

Competitor: Steady state model, infinitely old and on average unchanging.

Expansion with energy conservation requires continuous creation of mass-energy to keep the density constant

Modern Physics IV Lecture 8

Cosmic Microwave Background Radiation:

1964 Arno Penzias and Robert Wilson (Bell Labs)

Background noise or static that “just wouldn’t go away”

Modern Physics IV Lecture 8


Made measurements at l =7.35 cm (microwave)

No time (day-night or seasonal) variation.

No directional variation.

Measured emission at other wavelengths

T = 2.73 K

Modern Physics IV Lecture 8

Extremely high temperature electromagnetic radiation at time of Big Bang

Universe expands, temperature drops. Equivalently, expansion lengthens wavelength.

Small inhomogeneities, arising from quantum fluctuations, provided “seeds” around which galaxy formation could have started. Such small (~ ppm) inhomgeneities detected in 1992.

Modern Physics IV Lecture 8

The early universe must have been extremely hot and dense

The temperature at the earliest times is more than we can create

in particle accelerators. Cosmology at the earliest times is

explored via particle physics!

Photons can be converted into particle-antiparticle pairs and vice-versa

E = mc2

Early universe was full of particles and radiation because of its high temperature

Planck Era

Before Planck time (~10-43 sec)

We can’t say much.

No theory of quantum gravity

Do forces unify at high temperatures?

Four known forces

in universe:

Strong Force


Weak Force


Who knows?

(String Theory,

Loop Quantum Gravity,… )






(Grand Unified Theory)

Lasts from Planck time (~10-43 sec) to end of GUT force (~10-38 sec)

Electroweak Era

Lasts from end of GUT force (~10-38 sec) to end of electroweak force (~10-10 sec)

Particle Era

(particle soup)

Amounts of matter and antimatter nearly equal (roughly 1 extra proton for every 109 proton-antiproton pairs!).


This tiny difference in matter-antimatter gave rise to us and everything we know!!

Today, about 1 billion photons for every particle of matter.

Era of Nucleo-synthesis

Begins when matter annihilates remaining antimatter at

~ 0.001 sec.

Matter now free to interact with itself rather than photons and antimatter.

Free neutrons get snapped up into atomic nuclei

Nuclei begin to fuse, starting with hydrogen to helium

Era of Nuclei

Helium nuclei form at age

~ 3 minutes, with tiny amounts of lithium and deuterium.

Then this stops, as universe runs out of neutrons and becomes too cool to shatter nuclei

Era of Atoms

Atoms can finally form at age ~ 380,000 years.

Cosmic Background radiation “released”: photons go from crawling to flying, and the universe goes from opaque to transparent.

Era of Galaxies

First stars and galaxies form at age ~ 0.1-1 billion years (about redshifts


did the big bang really happen
Did the Big Bang Really Happen?
  • How can we tell what happened so long ago?
  • 14 billion years ago
  • Mostly unobservable before time of 400,000 years; not a repeatable experiment
  • Some of it occurs at temperatures beyond our ability to even understand how physics works!
primary evidence for the big bang the three pillars
Primary Evidence for the Big Bang (the Three Pillars)

We have detected the leftover radiation from the Big Bang. Remarkably uniform in all directions, observed all around us – truly universal

The Big Bang theory correctly predicts the abundance of helium and other light elements. Minimum universal amount of helium of 25% : argues whole universe was millions of degrees for a short time

And of course – the Hubble expansion of the universe – run time backwards….


what does this mean for the shape of our universe when just dark matter is present
What does this mean for the SHAPE of our universe when just dark matter is present?

Ωo is the mass-energy

content of the universe.

Ωo = 1 for a critical universe.


CLOSED universe



↔ CRITICAL orFLAT universe

Problems that Add Complications to this Simplest Model:

Where does structure come from?

Why is the overall distribution of matter so uniform?

Why is the density of the universe so close to the critical density?

An early episode of rapid inflation can solve all three mysteries!

Modern Physics IV Lecture 8

Inflation can make all the structure by stretching tiny quantum ripples to enormous size. The energy for inflation arises when the strong force separates from the GUT force at

t=10-36 sec. in cosmic time.

These ripples in density then become amplified to become the tiny seeds for all structures – stretching factor of 1030 !!

Regions now on opposite sides of the sky were close together before inflation pushed them far apart
Overall geometry of the universe is closely related to total density of matter & energy

Density = Critical

Density > Critical

Density < Critical

Inflation of universe flattens overall geometry like the inflation of a balloon, causing overall density of matter plus energy to be very close to critical density
But expansion appears to be speeding up!

Dark Energy?

In a universe with both dark matter and dark energy, it can have any of the 3 previous shapes, depending on the relative “mix” of dark matter/dark energy.

Not enough dark matter

a history of dark energy
A History of Dark Energy
  • First incarnation: the cosmological constant, introduced by Einstein as a fudge factor to balance out universe’s own gravity, because he believed that the universe must be static and unchanging. He later called it his “greatest blunder”, after Hubble discovered that the universe’s expansion provides the balance for its gravitational force.
  • Today, we believe that such a quantity exists, not as a constant, but rather as a dynamic changing repulsive force that opposes gravity and accelerates the expansion of the universe.



Estimated age of universe depends on both dark matter and dark energy.

The more dark matter we have, the faster the universe and the process of

galaxy formation evolve.

Brightness of distant white-dwarf supernovae tells us the universe’s expansion history since the supernovae exploded
What astronomers saw to their great shock and surprise was that the cosmic Hubble expansion, instead of slowing down with time, was actually SPEEDING UP - faster today than in the past!
Accelerating universe is the best fit to supernova data.

Note also that this tests the age of the universe for the

different models.

some ideas on what dark energy is
Some ideas on what dark energy is:
  • Has to have NEGATIVE pressure in order to oppose gravity up to the largest scales
  • A large-scale form of quantum vacuum energy? (related to the vacuum energy of empty space)
  • Quintessence: dynamic energy field on large scales that varies in time and/or space (unlike the cosmological constant)
  • Something entirely new and unknown?
  • Whatever it is, it will be crucial in unifying our theories of particles and forces
two important questions for any theory of dark energy
Two important questions for ANY theory of dark energy:
  • WHY NOW?
  • And… WHY THIS MUCH? i.e., why is the amount of dark energy (70% critical density) close to amount of dark matter (25% critical density), a seemingly unrelated component of the universe?
  • Both of these referred to as the Cosmic Coincidence problem regarding the nature of dark energy
and which universe do we live in
And which universe do we live in?
  • Latest results from distant supernovae and the microwave background and lots of other data - space in our universe overall appears to be very flat
  • With the current inventory of dark matter and dark energy, it looks like our universe will indeed expand forever and ever…