Cosmology

1. Cosmology Does the universe have an edge? A center? What is the “big bang?” How can the universe expand if it has no edge? Why is the universe the way it is?

2. The edge-center problem: • Suppose the universe has an edge… • It wouldn’t be an edge to the distribution of matter – it would be an edge to space itself! • You couldn’t just reach past it and feel around… • Seems to violate common sense… • We assume it has no edge • No edge => no center • If the universe is infinite  no center problem. • What is the universe is finite… (more on this in a moment…)

3. What about the beginning (if there is one…)?: • When you look at the night sky, what do you see? • Well… for one thing, it’s dark! • What if the universe were infinitely old, and infinite in extent? • Then no matter where you looked, your eyes would fall on a star/galaxy. • The night sky would be bright (Why couldn’t dust block the light?) (Or, why is the universe so cold?) • “Olber’s paradox” • Either the universe is finite in extent… • or finite in age (or both…)

4. “Universe” vs. “observable universe”: Minor distinction… Universe = all that exists Observable universe = all that we can “see” The former could be infinite The latter is most definitely finite “All of astronomy is reasonably unreasonable.”  Reasonable assumptions often lead to unreasonable results…

5. Cosmic expansion: • Recall Hubble’s observation in 1929… • Z ~ distance  everything is receding from everything else (on the whole) • The universe is expanding In reference to the balloon, where is the edge? The center? Keep in mind that it’s a 2-D analogy…

6. The big bang: Okay… so the universe is expanding… What if we trace the expansion backward in time? What would we expect? Would we reach a “beginning?” Is there a beginning? This “beginning” is what cosmologists call the “big bang”

7. So what is this big bang? • If no edge, then no center • The big bang did not happen at some “spot,” it happened everywhere… …and is still happening…

8. The age of the universe: Okay… if there was a beginning, then we can ask the question, “how old is the universe?” (Based on what we observe that is…) For starters, we can use the definition of velocity: v = d / t In this simple form, we can take the distance between two galaxies & divide by their velocity of recession (from each other) and solve for the time…

9. The Hubble time: Using H0 = 70 km/s/Mpc  14 billion years Where does 1012 come from? Units of H0 are km/s/Mpc… Convert Mpc to km, and then s to years

10. A side road tour… the CMBR: CMBR = “cosmic microwave background radiation Picture it: 1960s, two physicists (Penzias & Wilson) studying the sky in radio wavelengths, Their measurements showed a “peculiar noise” They thought it was bird droppings… After cleaning the antennae, the “noise” remained…

11. A side road tour… the CMBR (part II): • 1948 • Gamov  early universe should be hot & dense • Should radiate as a black body 1949 Alpher and Herman  large redshift would stretch the wavelength into the IR and radio

12. A side road tour… the CMBR (part III): Back to the ’60s… Princeton physicist Robert Dicke realized that, with the technology available, we should just now be able to detect this radiation (the CMBR)… When Penzias & Wilson heard of Dicke’s work, they realized that’s what they saw! Still… as scientists, we don’t like to jump to conclusions… We would like to have other observations confirm or reject this…

13. A side road tour… the CMBR (part IV): This CMBR should be all over the sky & come from everywhere… Specifically, theory predicted that it should look like the radiation coming from a black body at a temperature of ~ 3K (in the IR…) 1990, COBE satellite Measured black body radiation with a temp. of 2.725 +/- 0.002 K

14. A side road tour… the CMBR (part V): Wait a minute! You’re going to tell me that this “hot big bang” only had a temp. of 2.725 +/- 0.002 K !?! Keep in mind that it is redshifted by 1100. Theory predicted that this stuff was emitted when the universe had cooled to ~ 3000K More on this in a moment…

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16. Back to the highway, the story of the big bang: • Redshifts  expansion • + dark night sky & CMBR • Big bang As yet, we can’t trace the universe to time t = 0, The physics is not understoodwell enough yet… But we can come pretty darn close! (10 millionths of a second old!)

17. The timeline of the big bang: • T = 10-6 s: • High energy photons, T > 1012 K, density > 5 x 1013 g/cm3 (close to that of an atomic nucleus!) • (T for a photon means, the temp. of a blackbody that would radiate such a photon) • (density of photons means, from E = mc2, express the energy of the photons as if they had mass) • Two high-energy photons can collide and create a particle-antiparticle pair – which would then annihilate back into photons • The early universe was a flickering soup of this stuff • As the universe expanded, it cooled. The photons lost some of that energy…

18. The timeline of the big bang: • T = 10-4 s: • High energy photons, T ~ 1012 K • The energy of the photons was not high enough to create n & p particle-antiparticle pairs • The remaining n’s and p’s annihilated back into photons, but… For some reason, there were more particles than antiparticles! • (For every billion pairs, one regular particle survived…) • While the photons didn’t have enough energy to create p/anti-p pairs, they still had enough energy to create electron-positron pairs. • This continued until…

19. The timeline of the big bang: • T = 4 s: • T < Tc where Tc corresponds to the temp. that the photons had enough energy to create electron-positron pairs • All the n, p, e in the universe were created in the first 4 seconds! Meanwhile, the universe continued to expand and cool…

20. The timeline of the big bang: • T = 2 minutes: • Before this time, photons still had enough energy to break apart atomic nuclei • No nuclei before t = 2 minutes T > 2 minutes, deuterium could form (heavy hydrogen)

21. The timeline of the big bang: T = 3 minutes: He began to form (but hardly anything heavier since no stable nucleus with atomic weights of 5 or 8 exist) A tiny amount of lithium formed, but nothing heavier…

22. The timeline of the big bang: T = 30 minutes: T cooled enough to where nuclear reactions stopped ~ 25% of the universe was He nuclei and ~ 75% was H nuclei (protons) (This matches the abundances seen in the oldest stars…)

23. The timeline of the big bang: • T < 50,000 years: • The universe was dominated by radiation (opaque) • Photons couldn’t travel far without hitting matter • Radiation and matter were locked together in a “dance” • Nuclei couldn’t capture electrons to form atoms (and hence, couldn’t emit light…) • The gas was ionized…

24. The timeline of the big bang: T ~ 50,000 years: Around this time, the density of radiation was just about equal to the density of matter Before this, matter couldn’t clump together because the photons kept everything “smoothed out” The universe was becoming “matter dominated” Now, matter could start to clump under the influence of gravity…

25. The timeline of the big bang: • T ~ 105 years: • As the universe expanded, things continued to spread out… • Photons could travel a few kpc’s without bumping into an electron… • The universe became more transparent Around the same time… T cooled to about 3000K. At this temp., protons could capture electrons to form hydrogen! This epoch is referred to as “recombination” The photons could now travel without being scattered, and hence, retained this blackbody temp. of ~ 3000K (which is what we see as the CMBR!) The universe glowed with the temp of 3000K, but as it expanded and cooled, that glow gradually shifted to the IR  The universe became dark – the “dark age”

26. The timeline of the big bang: • T < 109 years: • Darkness lasted until the first stars were formed • Models suggest that these first stars were very massive, very luminous, and very short-lived… • They gave off enough UV light to start to ionize the gas in the universe… • This “reionization” marks the end of the dark age and the beginning of the age of stars and galaxies…. (Looking at quasars reveals gas that has not yet been ionized – observational support of the theory…)

28. The shape of space and time: • On the whole, the universe looks the same in every direction (with the exception of local variations) – “isotropic” • And also uniform – “homogeneous” • Isotropy + homogeneity  “cosmological principle” • Any observer sees the same general features If you accept this, then there can be no edge, and no center (The redshifts of very distant objects are produced, not by the Doppler effect, but by space itself expanding…) This leads us to ask what is the shape of space-time, i.e., the curvature

29. The curvature of space and time: With a certain curvature, the universe can be finite, yet have no edge or center… And we can make measurements to determine the curvature! (specifically, the density…)

30. Open, closed, or flat?: • Curvature: • Three possibilities: • Open • Negative curvature • Infinite in extent • Will expand forever • Closed • Positive curvature • Finite • Will collapse (big crunch/oscillate?) • Flat • In essence, no curvature • Infinite  Expansion will stop at t = infinity

31. The critical density: How the universe is “curved” depends on the density… The density which would make the universe flat is called the “critical density” ρc ρc ~ 9 x 10-30 g/cm3 ρ < ρc => open ρ > ρc => closed All observable matter  ~ 5% of ρc Hubble time revisited: If flat  But clusters are older than this!

32. Dark matter again: From gravitational lensing, rotation curves, etc., we it appears that galaxies contain much more matter than we can “see” Since we can’t seem to detect it, we call it “dark matter” Consider the density of the early universe…

33. Dark matter & early isotopes: Both 2H and 7Li are easily destroyed, in fact, stars tend to destroy them, not create them  When we observe these isotopes at large redshifts, we have very strong reason to believe that they were produced only in the big bang The early universe was a soup of photons, protons, neutrons, and electrons… Deuterium (heavy hydrogen, 2H) was created in this soup of particles If ρ was high, p’s and n’s would have collided with 2H and created He If ρ was low, more 2H would survive Lithium (6Li & 7Li) was also created in trace amounts (but nothing heavier)… If ρ was high, more7Li would be created

34. Dark matter – limits on what it’s made of: The result is that neutrons and protons only make up ~ 4% of the critical density Yet we know that ~ 26% of the critical density is made up of “stuff” that attracts other “stuff” (from gravitational lensing etc.)  Much of the dark matter must be non-baryonic, i.e., not made of normal matter (exotic) Measure the abundance of deuterium and lithium-7 at large look-back times (near quasars)… We have good reason to believe that they were produced only in the big bang… If the density of n, p was low enough, more deuterium would survive If the density of n, p was high enough, more lithium-7 would be created  2H sets a lower limit on the density of normal matter (neutrons and protons- “baryonic matter”), and 7Li sets an upper limit on the density of normal matter!

35. Dark matter candidates: • Only 4% of DM is baryonic (made of normal matter like protons and neutrons) • Neutrinos?  they do have mass… 108 neutrinos for every normal particle… • However, they move at near the speed of light… (they would be considered “hot dark matter”) • The most successful models of galaxy formation require slower dark matter (“cold dark matter”)  neutrinos not the complete answer… • Plus, DM doesn’t interact easily with other particles except through gravity • photons don’t interact with DM • DM not subject to the radiation pressure which hindered the clumping of normal matter Still, adding up the normal matter and the dark matter, we only get ~ 30% of the critical density. It would seem we live in a open universe… Not so fast…

36. Modern cosmology (inflation): The big bang had two problems… The flatness problem: It couldn’t explain why the universe seems to be nearly flat (even a small departure in the early universe would have a dramatic effect on the present universe, 1 part in 1049) The horizon problem: When we look at two parts of the sky separated by only 1o, we see two parts which weren’t causally connected (couldn’t communicate due to the speed of light), yet, these parts (and all others) seem to share the same temperature and properties Inflation provides the solutions…

37. Modern cosmology (inflation): In fact, quantum fluctuations could be the reason for the big bang – “The reason there is something instead of nothing is because nothing is unstable.” The beauty of inflation gives us confidence that we’re on the right track. What is inflation? In essence, the universe underwent a sudden expansion at about time t = 10-35 s, from the size of an atom to the size of a cherry pit What caused this expansion? At this time, the four forces decoupled from each other, releasing a tremendous amount of energy which inflated the universe That sudden inflation would have forced the curvature to be nearly flat (think of a balloon, the flatness problem)… And before inflation, the universe was small enough to have equalize its temperature (the horizon problem)

38. Modern cosmology (acceleration): • The universe seems to be flat, yet matter makes up only 30% of the critical density… • In the 1990’s, two teams of astronomers set out to measure how the universe is slowing down using distant Type Ia supernovae… • They observed that the SNs were fainter than expected • They are farther than expected • The universe is speeding up! Note: And it doesn’t seem to be a problem with how the measurements are taken or dust extinction etc….

39. Modern cosmology (dark energy): • If the universe is accelerating, then there must be some repulsive force accelerating it… • 1916, Einstein, GR • Einstein realized that his theory predicted that the universe should either expand or contract… But at the time, it was thought the universe was in a steady state… So Einstein introduced a “fudge factor” into his theory called the “cosmological constant” When, in 1929, Hubble observed that the universe was indeed expanding, Einstein commented that inserting the cosmological constant was his “greatest blunder” – his original theory predicted the expansion!

40. Modern cosmology (dark energy): • Okay… so reinserting the cosmological constant into GR, we have a working theory of this dark energy… • But need it be constant…? • Quintessence: • “Vacuum energy” • Even seemingly empty space has energy… Quintessence is a theory that allows the cosmological “constant” to vary with time Since the ’90’s, more measurements of Type Ia’s were taken… Some even more distant seem to be too bright! ( they are closer than expected…) Problem for dark energy…? No! DE actually predicts that when the universe was much smaller, gravity would overpower the DE and hence, these extremely distant objects should be closer!

41. Age and fate of the universe: Problem: The universe seems to be flat  age ~ 9 billion years… But we observe clusters that are older than this! But if the universe has been accelerating, expanding slower in the past, then the universe would be older than 9 Gry. (Solves the age problem) The ultimate fate of the universe depends on the nature of dark energy Cosmological constant  will expand forever Quintessence  big rip

42. The cosmological constant vs. quintessence :

43. Age and fate of the universe: Chandra X-ray observatory: Measured hot gas & dark matter in galaxy clusters Compare results with known clusters  solve for distance Results confirm that of the Type Ia’s (that the universe is indeed accelerating) and also seems to almost rule out quintessence (i.e., the cosmological constant indeed seems to be constant)  No big rip…

44. Origin and structure of the curvature: Study the distribution of galaxies, “large scale structure” Measure distance & position and plot the results (i.e., create a map of the universe) Seems like the universe tends to cluster along filamentary structures… This presents a puzzle… The CMBR seems to be uniform (corresponds to the time of recombination – the universe was uniform then)… The look-back time to the farthest galaxies is 93% of the way back to the beginning… How did this uniform gas coagulate so quickly to form galaxies and the structure we see? Why filaments? The Two-Degree-Field (2DF)survey mapped the position and distance of ~ 250,000 galaxies and 30,000 quasars Analysis of the distribution also confirms the acceleration independent of the Type Ia’s and that of Chandra…

45. Theoretical models of large-scale structure: Quantum fluctuations in space would have been stretched and enhanced at the time of inflation  filaments

46. Origin and structure of the curvature: Inflation makes very specific predictions about the sizes of the fluctuations we on Earth should see in the CMBR… WMAP mapped the CMBR at high accuracy  reveals small irregularities If these irregularities were produced by inflation, then the size of them depends on the sound speed of the universe at the time of recombination… Inflation predicts these irregularities to be about 1o if the universe is flat, smaller if open, and larger if closed…

47. Origin and structure of the curvature: Predictions of inflation in the three panels to the left, the observed CMBR in the last panel Observations fit well with a flat universe (which is exactly what inflation did… it “flattened” the curvature of space-time!) This also indirectly confirms dark energy and acceleration…

48. Origin and structure of the curvature: Graphically, the data also fit well with predictions of a flat universe…

49. The abundance of “stuff” in the universe:

50. The modern picture: