Final Exam - Tuesday, May 49:00am to 11:00am

• Closed book

• Will cover all of the lectures, as evenly as possible

• If a topic is in the book, but was not covered in class, it will not be on the exam!

• Exam Format - similar to midterms (mix of questions)

• Equations, constants will all be given

• Standard calculators allowed (but not provided)

• Cell phones, PDAs, computers not allowed

One last chance to complete NL#2

The forecast for tonight is not looking good for NL#2, but it’s looking fabulous for Thursday night.

If it’s reasonably clear on Thursday night, there will be one last opportunity to do NL#2.

Due date for NL#2 is extended to 5:00pm on Friday (hand in using the Homework Box upstairs).

Outline - April 26, 2010

• Dark matter recap (pg. 681-695)

• “Fossil photons” from the Big Bang (pgs. 714-716)

• Dark energy (pg. 698-699)

• The Early Universe (pg. 707-711)

• What don’t we know about the Universe at present?

• Is the Big Bang a “good theory”?

The Universe is really weird…

Assuming that all of the observations (and interpretations) are correct, then we appear to live in a very weird universe. At the present day we think:

• 27% of the energy density is in the form of mass (at present the energy density in light is negligible)

• 73% of the energy density is in the form of dark energy, the nature of which is unknown

• only 15% of the mass is in the form of ordinary chemical elements, the rest is in some type of unknown material that emits no light whatsoever (dark matter)

What’s the evidence for Dark Matter and Dark Energy - should you take this stuff seriously????

A WIMP Universe

WIMP universes reproduce the observed “structure” to the universe, grows the right number of galaxies of the right size, and grows the right number of galaxy clusters of the right size (big success).

Big problem is that WIMPS are currently hypothetical particles!

Should you believe in dark energy??

Two Independent Lines of Evidence for Dark Energy:

• white dwarf supernovae in extremely distant galaxies (lookback times of 7 billion years or so) are too faint to be explained by a universe in which the expansion rate has been decelerating for all time (i.e., the galaxies are much farther away than they ought to be)

• “lumps and bumps” in temperature of the leftover light from the Big Bang (called the CMBR) have a distinct, measurable pattern, and the details of the pattern give us precise measurements of the amount of energy in the form of mass versus the amount of energy in the form of “dark energy”

Supernovae

At its peak brightness, a supernova is typically as bright as the whole galaxy in which it lives.

White Dwarf Supernovae (known as a Type-Ia supernova) can be used to make very accurate measurements of the distances to galaxies.

Type-Ia supernovae are easily identified from details in their spectra and light curves.

HST image of a supernova in a nearby spiral galaxy

Dark Energy from Supernova Measurements

• measurements of distances to supernovae in many different galaxies (measure “Hubble Law” at different times in the history of the universe)

• expansion rate of the universe decelerated for the first 9.5 billion years after the big bang

• for the past 4.5 billion years the expansion rate of the universe has been accelerating (and will continue to accelerate forever)

Fair question: Do we really understand supernovae well enough to make this statement?

Maybe stars blew up very differently in the past than they do today. Maybe something else (not accelerating universe) is causing the distant supernovae to

look fainter than we expect.

Where are the “fossil photons” from the Big Bang?

Answer: Everywhere! (they make up about 90% of the radiant energy of the universe at the present day, but you can’t see them with your eyes…)

MICROWAVE photons (very long wavelength, very low energy)

Cosmic Microwave Background Radiation (CMBR)

If the universe began in an extremely hot, extremely dense state:

• universe would have been opaque initially

• primordial light would have had a continuous, black body spectrum

• primordial light would have been very high energy (very short wavelength)

Expansion of the Universe:

• stretches the wavelengths of the primordial photons

• does not change the shape of the spectrum (i.e., it remains a black body but with a different temperature than it had early on)

• after roughly 14 billion years, the high energy photons will have stretched so much that they will have become microwave photons!

The CMBR should appear as a (nearly) uniform “hiss” of microwave radiation on the sky, and it should have a black body spectrum.

Observations of the CMBR

1964, Arno Penzias & Bob Wilson

• discovered serendipitously

• unable to measure spectrum

• awarded Nobel Prize in Physics (1978)

1992, COBE Satellite

• measured shape of spectrum, nearly perfect black body with T = 2.73 Kelvin

• detected extremely tiny “fluctuations” in the temperature (deviation of only 1 part in 100,000); best proof that the universe is isotropic!

• made low-resolution map of temperature on the sky

• George Smoot & John Mather awarded Nobel Prize in Physics (2006)

2003 to 2005, WMAP Satellite

• made extremely high-resolution map of temperature of CMBR on the sky

Temperatures on the Earth

blue = “cold”, red = “hot”

Note the big temperature range! (100o C)

CMBR Temperature “Fluctuations”MicroKelvin (10-6 K) deviations from universal average temperature

Color scale goes from -3x10-6K (blue) to +3x10-6K (red)

CMBR Temperature Fluctuations

The “lumps and bumps” in the CMBR aren’t random. They’re correlated and the pattern tells us that there is dark energy in the universe.

Neither the CMBR nor the supernovae have anything to do with each other, but they both give the same value of the amount of dark

energy in our universe!!

How did we get from there to here?

The Big Bang concept is that the universe begins in an extremely hot, extremely dense state.

Not only could stars and galaxies not have existed at the beginning, neither could ordinary matter.

Why is the universe that we see around us today so very different from the one that we started with about 14 billion years ago?

“History” of the Universe

Note: except for “the beginning”, the time since the Big Bang (“t”) and the temperature at that time (“T”) are approximate

t = 0 sec

• the “Big Bang” occurs simultaneously throughout the universe

• universe is extremely dense and extremely hot (possibly a “singularity” with infinite temperature)

• atoms and nucleons (p,n) could not have existed under these extreme conditions, but light existed!

• there is no currently known physics to describe this era (requires “unification” of gravity with the other forces of nature)

t = 10-43 sec, T = 1032 K (the “Planck time”)

• from this time onward, the physics is known (but somewhat speculative at the Planck time)

• nucleons and atomic nucleii still did not exist

t = 10-35 sec, T = 1028 K until t = 10 sec, T = 3x109 K

• pairs of particles and their “antiparticles” are produced by pairs of photons (conversion of energy into mass via E = mc2)

• all the building blocks of atoms (p,n,e) are produced from light over this time

• nuclei (other than H = one proton) do not exist yet

• pairs of particles and antiparticles are produced at the same rate at which they annihilate (“thermal equilibrium”)

Simplest Picture: Pure Equilibrium, Symmetrical Production and Annihilation

Problem: We live in a “matter” universe today!

The process must have been very slightly asymmetrical (by about 3 parts in 1 billion) - but how?

photons from annihilation eventually become CMBR photons

t = 1 min to 4 min, T = 109 K (“Primordial Nucleosynthesis”)

• at this time universe is too cool to continue to produce elementary particles (photons don’t have sufficient energy)

• universe hot enough and dense enough to fuse protons and neutrons to produce deuterium (“heavy hydrogen”), helium, and tiny amounts of lithium and beryllium

• after t = 4 min, the universe is no longer sufficiently dense for the fusion to continue (universe is not a star; internal temperature and density of stars is constant for millions to billions of years)

Bottom line: Big Bang only produces VERY LIGHT chemical elements (H, He, Li, Be

Chemical abundance of cosmic objects stars should be roughly 75% H and 25% He

So where did rocky planets, dinosaurs, ferns, and people come from??

t = 400,000 years, T = 3000 K

• neutral atoms form for the very first time! (previously there were “bare nuclei” swimming in a sea of electrons)

• universe becomes transparent to radiation (previously was opaque - like “fog”)

• the farthest back in time that we can “see” (this is where the CMBR photons are coming from)

T = 1 billion years, T = 25 K

• galaxies begin to form by the contraction of cold gas clouds

• stars begin to form shortly after the large clouds of cold gas begin to contract

• if the clouds are sufficiently dense, then gravity alone can overcome the expansion of the universe

t = 13.8 billion years, T = 2.7 K

• “today”

• galaxies have stopped forming, but many galaxies continue to form new stars (spiral and irregular galaxies)

• galaxies are evolving (stars age and die out), and occasionally collide and merge together

t > 13.8 billion years, T < 2.7 K

• the future!

• FATE is going to be cold and dark if the idea of dark energy is correct

Big Things We Don’t Knowbut we’re working on…

• How was more matter than antimatter produced? (There may be some loopholes in the physics; need incredibly tiny asymmetry. For every 1,000,000,000 “quarks” need 999,999,997 “antiquarks” and all will be well.)

• What caused the fluctuations in the density that we see as temperature fluctuations in the CMBR? (And why was the universe so kind as to set things up so that galaxies could grow by gravity alone?)

• What is the nature of the dark energy? (It’s looking like it is is “vacuum energy density”, a quantum mechanical phenomenon that is manifesting on the macroscopic scale.)

• What is the nature of the dark matter? (Most likely “WIMPs”. Works extremely well in computer models, but our particle physicist friends haven’t yet caught a WIMP in a bottle for us yet!)

A Good Theory?

If you randomly stop 1000 cosmologists on the street, 999 of them will tell you that there is no doubt that the Big Bang is the correct theory of the origin of the universe.

But, does the Big Bang qualify as a “good scientific theory”?

Qualities of a good theory:

• able to make specific predictions

• testable in such a way that, in principle, it could be proven false

• should be simple

Big Bang Predictions

• The universe had a specific beginning (night sky is dark; Hubble’s Law; approximate age = 1/H0)

• Initially, the universe was extremely hot, dense, and opaque (Hubble’s Law + CMBR)

• The universe has evolved/changed over time (hints from the CMBR vs. the universe “today” + direct evidence of galaxy evolution over time)

• The universe is expanding (Hubble’s Law)

• Cosmic objects (such as stars) should have a chemical composition that is roughly 75% hydrogen and 25% helium (observed)

All of the observations could be completely disconnected from each other; the Big Bang is the one idea (hypothesis) that ties all of these very different things together.

Midterm Exam #3

Your score on this exam: 79 / 100

Your ranking in the class on this exam: 20 / 40

Approximate letter grade on this exam: B

Curve boundaries for Midterm #3:

A > 90%

A- 86% to 90%

B+ 81% to 86%

B 75% to 81%

B- 72% to 75%

C+ 68% to 72%

C 63% to 68%

C- 56% to 63%

D 50% to 56%

F < 50%

Class letter grade average based on the curve is between B and B- (2.95 / 4.0)

This info is on the last page of your exam.