Big Bang Black Holes No Math ASTRPHYS 109
Big Bang, Black Holes, No Math ASTR/PHYS 109 Dr. David Toback Lectures 30 & 31 Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 1
Was due Today – L 31 • • • Reading: – Unit 5: Was due before class Pre-Lecture Reading Questions Quiz: – Unit 5 Quiz: Will assign today End-of-Chapter Quizzes: – Chapter 13 • Do worksheet on class homepage to help prepare for EOC quizzes – Does not need to be turned in • Chapter 13 parts A-D: Due date extended to next class • Chapter 13 Parts E-F: Will assign today • Help quizzes available – Chapter 14 • Chapter 14 Parts A-D: Will assign after that • Chapter 14 Parts E-G: Will assign after that Feynman Diagram Drawing Assignment – Assignment 1 & 2 grades done, working on revisions and 3 – Assignment 4: Will assign today – Many people seem to be getting the answers from “not the instructions”. If you need help let us know and we’ll make the instructions better (and give you extra credit) – (Feynman Diagram Assignment 1, 2 & 3) Papers – Papers 1 & 2: • Can submit Revisions at any time. Make sure to do all stages – Paper 3: • Paper 3 due date pushed again to Wednesday April 14 th • Rough draft assignment available again Honors Section: – “Stage 3 Final Draft”: Due Monday before class – Need to hear from you at least once every 7 days Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 2
Was due Today – LX • • • Reading: – Unit 5: Was due before class Pre-Lecture Reading Questions Quiz: – Unit 5 Quiz: Due before next class End-of-Chapter Quizzes: – Chapter 13 • Do worksheet on class homepage to help prepare for EOC quizzes – Does not need to be turned in • Chapter 13 parts A-D & Parts E-F: Due MONDAY before class – Chapter 14 • Chapter 14 Parts A-D: Will assign after that • Chapter 14 Parts E-G: Will assign after that Feynman Diagram Drawing Assignment – Quiz to help people get better at them in same folder. Can also do Revisions. – (Feynman Diagram 3) Papers – Papers 1 & 2: • Can submit Revisions at any time. Make sure to do all stages – Paper 3: Due tonight, Wednesday Nov 4 th Honors Section: – You should have Stage 2 Approved, and be working on Stage 3 – Need to hear from you at least once every 7 days Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 3
A Big Bang Occurs… Then What? Universe goes through a phase of being hot and small As the universe evolves it gets bigger, older and colder Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 4
Various Times Explain what happens during each of a number of different periods in time – The VERY early universe Chap 13 – The first three Minutes – The next 300, 000 years Chap 14 – The next billion years – ~13 billion years later (now) } Chaps 15 -17 – The ultimate fate } Unit 6 of the universe? • The first four will take a couple of lectures } } Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 5
More detail Photons no longer energetic enough to bust apart protons Photons no longer energetic enough to bust apart nuclei Photons no longer energetic enough to bust apart atoms Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 6
Where are we now in the history? 3 Minutes: Photons can no longer break up nuclei Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 7
After the First Three Minutes • At about the 3 minute mark the temperature of the Universe is about 1 billion degrees • Electrons and positrons have mostly annihilated each other – No particles energetic enough to produce new ones ~1 electron for every proton Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 8
What else? • The temperature drops so much that the photons, on average, can’t even break up deuterium –Easier to start building up the heavier nuclei Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 9
Forming Heavy Nuclei in the Early Universe Proton + Proton Deuterium + Electron + Neutrino Electron Nuclear Reaction Proton Deuterium Neutrino Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 10
Nuclei and Low Energy Photons At the 3 minute mark, low energy photons only “bump” nuclei Deuterium Low Energy Photon Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 11
Can Now Build Heavier Nuclei Deuterium Proton + Deuterium 3 He + Photon Nuclear Reaction Photon 3 He Proton Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 12
Creating Stable Helium 3 He + 3 He 4 He + 2 Protons Replenishes the hydrogen in the Universe Nuclear Reaction Proton 4 He 3 He Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes Proton 13
Why so few atoms Heavier than Helium? Nuclear Physics Can build up Hydrogen and Helium one at a time Next possibility, 5 He or 5 Li, isn’t stable 4 Li lifetime = 9 x 10 -23 sec 5 Li lifetime = 4 x 10 -22 sec Big Bang, = Black 5 He lifetime 7 x 10 -22 sec So What? Since 5 He and 5 Li decay quickly they don’t have enough time to find another proton to become 6 Li and be stable Almost no elements heavier than helium are produced in the early Universe • Will happen much later, and in stars Evolution of the Universe Holes, No Math Topic 2: After The First Three Minutes 14
Time marches on… • Universe continues to expand cool • Number of protons goes up and number of neutrons goes down – Why? Any neutron not in a nucleus will decay into a proton (about 15 minutes) Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 15
Neutron Decay Neutron Proton + Electron + Neutrino Electron Decay Proton Neutrino Neutron Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 16
The End of an Era • For the next couple hundred thousand years things don’t change much • Nuclear processes eventually stop making helium since the Universe gets too big • Still MUCH too hot for atoms to form – Any formed quickly get busted apart Evolution of the Universe Big Bang, Black 17 Holes, No Math Topic 2: After The First Three Minutes
The beginning of a new Era • From 200, 000 -700, 000 years the universe expands and cools • All the nuclei and electrons combine to form atoms – Said differently: Universe cools until the photons in the universe can’t knock all the electrons out of the atoms any more Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 18
Atoms in a Lower Temperature Universe Proton At these lower temperatures photons can’t easily break up atoms Electro. Magnetic Reaction Electron Hydrogen Atom Photon Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 19
Where are we now in the history? 200, 000 -700, 000 years Photons can no longer break apart atoms Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 20
The Transition From a Hot Universe to a Cool Universe Some Time Passes Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 21
The Universe at ~700, 000 Years Old • At a temperature of about 3000 K photons, on average, can’t knock apart atoms • Stable atoms can form and most electrons become part of atoms • The atoms are now free to form into stars and galaxies Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 22
Give this special time in history a name Call this time “Recombination” Crappy Word! Atoms are combining for the first time, not recombining! Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 23
Atoms in the Universe Early Universe A couple hundred Thousand Years Later These days Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 24
Before and After the Creation of Atoms After: Protons and electrons combine to form atoms Universe becomes transparent for photons Before: Lots of free electrons and protons in the Universe Photons scatter from charged particles Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 25
Transparent Universe The Universe now LOOKS different! • The light (photons) have no free electrons to interact with • Since all the electrons are in atoms, because of Quantum Mechanics, they largely ignore the photons • Photons just travel in a straight line Like traveling through glass Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 26
Atoms in the Universe Early Universe Photons bust apart atoms Hydrogen A couple hundred Thousand Years Later Photons can only excite atoms These days Universe is transparent to photons High energy photon Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 27
A Cartoon… + + + + After Before Recombination: Photonsignore Atoms interact withphotons the charged particlestravel in Photons Scatter and straight lines change directions forever Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 28
Cosmic Background Radiation • The photons we see in the cosmic background radiation are essentially the photons AFTER they interacted with their last charged particle • Well… they’ve been traveling for awhile so they’ve changed a bit Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 29
Photons in the Universe After recombination, photons can travel freely through space Their wavelength is only stretched (red shifted) by cosmic expansion Observe most photons as the cosmic background radiation! Also can observe photons emitted from Galaxies a billion years ago (just reaching us now) as being red -shifted Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 30
A Neutral Universe • After the electrons and protons combine to form atoms the Universe is almost completely neutral i. e. , neutrally charged • Why is this so important? All the particles in the Universe stop attracting each other due to their electric charge – Not completely true, just true outside the atoms – Basically can ignore electric charge from here on out Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 31
The Transition From a “Charged” Universe to a “Neutral” Universe Some Time Passes Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 32
Aside on Dark Matter • Dark matter is a BIG part of this story because there is 5 times more mass in the Universe in dark matter than in atoms – Will come back to this in Chapter 15 • However, the story doesn’t change much with Dark Matter since we think it is just another neutral particle Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 33
A Gravity Dominated Universe • The only thing left is gravity! • The gravitational attraction between massive things ONLY makes them move towards each other through space • Any single atom would be most attracted to the closest place with lots of mass Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 34
Wait a Half Billion Years • As the years go by, mass clumps together • By a half a billion years after the bang, most of the mass is in one of a large number of “clumps” • Huge numbers of these clumps, each becomes part of a galaxy! Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 35
The Next Few Billion Years After less than ~0. 5 billion years, the first stars form Stars produce heavy elements (“Stellar Cooking”) Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 36
Fast Forward… • Fast forward 13 billion years – Temperature of space is now ~3 Kelvin – Cosmic Background Radiation • We get people… • More on Stellar and Galaxy Formation next Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 37
Lecture on Chapter 14 now complete Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 38
Looking Forward • Finished Unit – Evolution of • Starting Unit – From half a until today – Big Objects 4 the Universe 5 billion years and Black Holes Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 39
For Next Time – L 30 • • • Reading: – Unit 5: Due before next class Pre-Lecture Reading Questions Quiz: – Unit 5 Quiz: Will assign next time End-of-Chapter Quizzes: – Chapter 13 • Do worksheet on class homepage to help prepare for EOC quizzes – Does not need to be turned in • Chapter 13 parts A-D Due before class • Chapter 13 Parts E-F: Will assign next time • Help quizzes available – Chapter 14 • Chapter 14 Parts A-D: Will assign after that • Chapter 14 Parts E-G: Will assign after that Feynman Diagram Drawing Assignment – Assignment 1 & 2 grades done, working on revisions and 3 – Many people seem to be getting the answers from “not the instructions”. If you need help let us know and we’ll make the instructions better (and give you extra credit) – (Feynman Diagram Assignment 1, 2 & 3) Papers – Papers 1 & 2: • Can submit Revisions at any time. Make sure to do all stages – Paper 3: • Paper 3 due date pushed again to Monday April 12 th • Rough draft assignment available again Honors Section: – “Stage 3 Draft”: Was due Monday before class – Need to hear from you at least once every 7 days Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 40
For Next Time – L 30 • • • Reading: – Unit 5: Due before next class Pre-Lecture Reading Questions Quiz: – Unit 5 Quiz: Will assign next time End-of-Chapter Quizzes: – Chapter 13 • Do worksheet on class homepage to help prepare for EOC quizzes – Does not need to be turned in • Chapter 13 parts A-D Due before next class • Chapter 13 Parts E-F: Will assign next time • Help quizzes available – Chapter 14 • Chapter 14 Parts A-D: Will assign after that • Chapter 14 Parts E-G: Will assign after that Feynman Diagram Drawing Assignment – Assignment 1 & 2 grades done, working on revisions and 3 – Many people seem to be getting the answers from “not the instructions”. If you need help let us know and we’ll make the instructions better (and give you extra credit) – (Feynman Diagram Assignment 1, 2 & 3) Papers – Papers 1 & 2: • Can submit Revisions at any time. Make sure to do all stages – Paper 3: • Paper 3 due date pushed again to Monday April 12 th • Rough draft assignment available again Honors Section: – “Stage 3 Draft”: Was due Monday before class – Need to hear from you at least once every 7 days Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 41
For Next Time – L 31 • • • Reading: – Unit 5: Was due already Pre-Lecture Reading Questions Quiz: – Unit 5 Quiz: Due before next class End-of-Chapter Quizzes: – Chapter 13 • Do worksheet on class homepage to help prepare for EOC quizzes – Does not need to be turned in • Chapter 13 parts A-D: Due date extended to next class • Chapter 13 Parts E-F: Also due next class • Help quizzes available – Chapter 14 • Chapter 14 Parts A-D: Will assign after that • Chapter 14 Parts E-G: Will assign after that Feynman Diagram Drawing Assignment – Assignment 1 & 2 grades done, working on revisions and 3 – Assignment 4: Will assign today – Many people seem to be getting the answers from “not the instructions”. If you need help let us know and we’ll make the instructions better (and give you extra credit) – (Feynman Diagram Assignment 1, 2 & 3) Papers – Papers 1 & 2: • Can submit Revisions at any time. Make sure to do all stages – Paper 3: • Paper 3 due date pushed again to Wednesday April 14 th • Rough draft assignment available again Honors Section: – “Stage 3 Final Draft”: Due Monday before class – Need to hear from you at least once every 7 days Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 42
Full set of Readings So Far • Required: – BBBHNM: Chaps. 1 -15 • Recommended: – TFTM: Chaps. 1 -5 – BHOT: Chaps. 1 -7, 8 (68 -85), 9 and 11 (117 -122) – SHU: Chaps. 1 -3, 4(77 -93), 5(95 -114), 6, 7 (up-to-page 159) – TOE: Chaps. 1 -3 Evolution of the Universe Big Bang, Black 43 Holes, No Math Topic 2: After The First Three Minutes
Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 44
Clicker Question How far back in time can we “see” (clear line of sight from light) when we look into space? a) To ~0. 5 billion years after the bang (time of creation of the first stars) b) To ~250, 000 years after the bang (time of “recombination”, creation of atoms) c) To ~3 minutes after the bang (creation of heavy nuclei) d) To ~microsecond after the bang (creation of protons) Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 45
Clicker Question: Part 1 Why are there many free protons at a thousandth of a second after the big bang? Select all the correct statements that are both true and relevant. (i. e. , is one of the CAUSES of why we have lots of free protons at a thousandth of a second). Hint: Some of the options are the same/similar reasons but described in different ways. Click A for Yes and E for No. 1) One of the reasons we have lots of free protons at a thousandth of a second after the bang is because there were lots of free quarks before a millionth of a second, and since they existed they could/would combine into protons. Any protons that had been created from quarks would not be broken apart at a thousandth of a second. 2) One of the reasons we have lots of free protons at a thousandth of a second after the bang is because at a thousandth of a second after the bang, we will have lots of free protons and electrons. Since there are lots of free protons and electrons they *will* combine to form neutral hydrogen atoms. However, at a thousandth of a second after the bang, the temperature is too high for neutral atoms to *stay* bound. Since any neutral hydrogen atoms that would be created would quickly be broken apart again into free protons and electrons, we would have lots of free protons at a thousandth of a second. Said differently, the neutral hydrogen atoms that are forming keep getting broken up by high energy collisions, this results in free protons, and therefore one of the causes of why we have free protons. 3) One of the reasons we have lots of free protons at a thousandth of a second after the bang is because protons are fundamental particles and all fundamental particles are stable. Thus, we have them at a thousandth of a second after the bang. Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 46
Clicker Question: Part 2 Why are there many free protons at a thousandth of a second after the big bang? Select all the correct statements that are both true and relevant. (i. e. , is one of the CAUSES of why we have lots of free protons at a thousandth of a second). Hint: Some of the options are the same/similar reasons but described in different ways. Click A for Yes and E for No. 4. One of the reasons we have lots of free protons at a thousandth of a second after the bang is because protons are stable. Since they are stable they can live forever unless they get broken apart or combine with other particles and form a bound object, like a nucleus or an atom (if they are in a composite object they are still protons, but they aren't considered free anymore). Thus, since a large number of protons are created before a thousandth of a second, an abundance of free protons will still be around at a thousandth of a second. Said differently, since protons are stable, the same protons created after a millionth of a second after the bang will still be around at a thousandth of a second after the bang. 5. One of the reasons we have lots of free protons at a thousandth of a second after the bang is because protons are no longer broken apart by high energy photons after a millionth of a second. Any proton that exists at a thousandth of a second will stay as a proton. 6. One of the reasons we have lots of free protons at a thousandth of a second after the bang is because there are very few particles of any type that are high energy enough to break a proton into free quarks after a millionth of a second. Thus, we will have lots of protons at a thousandth of a second. 7. One of the reasons we have lots of free protons at a thousandth of a second after the bang is because at a thousandth of a second, since we have lots of free protons, they will collide and form nuclei heavier than hydrogen. However, the average energy of the particles at a thousandth of a second is high enough that any nuclei-heavier-than-hydrogen (e. g. deuterium or helium) that gets formed will quickly be broken apart again. When nuclei are broken apart we are left with free protons and neutrons. Said differently, the abundance of free protons will create atoms heavier than hydrogen (i. e. deuterium, helium) but the high energy particles at this time will break them apart which makes the protons free again. Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 47
Clicker Question Was the following present in large amounts at about a minute after the bang? Select A for Yes, and E for No 1. Free quarks 2. Free muons 3. Photons 4. Free electrons 5. Free neutrons 6. Free protons 7. Completely ionized hydrogen nuclei (no electrons) 8. Completely ionized helium nuclei (no electrons) Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 48
Clicker Question Was the following present in large amounts at about a minute after the bang? Select A for Yes, and E for No 9. Completely ionized nuclei heavier than helium (no electrons) 10. Neutral hydrogen 11. Neutral helium 12. Neutral atoms heavier than helium Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 49
Clicker Question Why can we only see so far back into space? a) Because before recombination the light in the universe was scattering off of the charged particles b) Because there are too many things in the way which block our ability to see Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 50
Clicker Question Other questions to help with the EOC Chapter 14 quiz? a) What is the difference between ionized atoms and neutral atoms b) When do we start getting an abundance of nuclei-that-are-heavier than helium in the universe? c) Do we ever have lots of ionized heavy nuclei? Re-ionization here is a bugger detail Evolution of the Universe Big Bang, Black 51 Holes, No Math Topic 2: After The First Three Minutes
Looking Back at the Early Universe The more distant the objects we observe, the further back into the past of the universe we are looking Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 52
Part II In class Quiz for Next Time: What is happening in each region? { Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 53
Why not much Heavier than Helium? Nuclear Physics Can build up Hydrogen and Helium one at a time Next possibility, 5 He or 5 Li, isn’t stable So What? Since 5 He and 5 Li decay quickly they don’t have enough time to find another proton to become 6 Li and be stable Almost no elements heavier than helium are Evolution of the produced Universe 54 Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes
Aside on Helium Why is Helium important to the story? Explains two things: 1. Why the atoms in the Universe are mostly Hydrogen and Helium, and not much else 2. Why the Helium, like the photons is evenly distributed around the universe Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 55
The Reading So Far and For Unit 5 Reading for Unit 5: • BBBHNM: Chaps. 15 -17 • SHU: 4(87 -93) • TOE: 3 • BHOT: 8(76 -85) Full reading so far for Unit 5: • BBBHNM: Chaps. 1 -17 • TFTM: Chaps. 1 -5 • BHOT: Chaps. 1 -7, 8 (68 -85), 9 and 11 (117 -122) • SHU: Chaps. 1 -3, 4(77 -93), 5(95 -114), 6, 7 (up-to -page 159) • TOE: Chaps. 1 -3 Lecture prep: Turn in on e. Learning Two questions from Chapter 15 you want to Evolution know the answer to of the Universe Big Bang, Black 56 Holes, No Math Topic 2: After The First Three Minutes
The Transition From a Hot Universe to a Cool Universe Electrons Atoms Photons Protons Electrons Some Time Passes Protons Photons Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 57
Before 700, 000 years: Summary Photons are incessantly scattered Photons-electron soup have the same by free electrons; photons are in temperature (energy) equilibrium with matter Radiation dominated era Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 58
After 700, 000 Years: “Recombination” Protons and electrons combine to form atoms universe becomes transparent for photons Transition to matter dominated era Crappy Word! Atoms are combining for the first time, not recombining! Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 59
A cartoon of an atom and a photon Mostly this is happening now since the photons are low energy Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 60
The Cosmic Background Radiation After recombination, photons can travel freely through space Their wavelength is only stretched (red shifted) by cosmic expansion This is what we can observe today as Evolution of the Universe Bang, the Blackcosmic background radiation! Big Holes, No Math Topic 2: After The First Three Minutes 61
Wait a Billion Years After less than ~ 1 billion years, the first stars form Produce Heavy Elements in Stellar Cooking Formation of the first stars Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 62
The First Three Minutes http: //bigbang. physics. tamu. edu/Figures/Stolen. Animations/first 3 minutes. swf Evolution of the Universe Big Bang, Black Holes, No Math Topic 2: After The First Three Minutes 63
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