1	Astr 1050 Wed., Nov. 20, 2002 Today: Chapter 15, Cosmology Leonids reports A great webpage tutorial on cosmology. Recommended! http://www.astro.ucla.edu/~wright/cosmolog.htm
2	Chapter 15: Cosmology Olber’s paradox The Hubble Expansion – review+ The Big Bang Refining the Big Bang Details of the Big Bang General Relativity Cosmological Constant Origin of Structure
3	Olber’s Paradox: Why is the night sky dark? If we are in a forest which extends far enough then In any direction we will just be looking at the trunk of some tree.
4	Olber’s Paradox: Why is the night sky dark? If we are in a universe which extends far enough then In any direction we will just be looking at the surface of some star.
5	Olber’s Paradox: Answer It could be that the Universe doesn’t extend far enough – but that doesn’t seem to be the right answer The finite age of the universe limits how far we can see: If it has age T, we can only see out as far as d=c´T The light from farther stars hasn’t had time to reach us yet
6	Basic Cosmology Assumptions Homogeneity – matter is uniformly spread across the universe on large scales Isotropy – the universe looks the same in all directions, again strictly true on large scales Universality – laws of physics apply everywhere in the universe (being challenged!) These lead to the “cosmological principle” which says that any observer in any galaxy in the universe should see essentially the same features of the universe.
7	The Hubble Law and the Age of the Universe H_o = 72 ±8 km/s/Mpc
8	Hubble Law: Everyone sees same expansion
9	Universal Expansion: Balloon Analogy Simulation of a “closed” spherical universe expanding: http://www.astro.ucla.edu/~wright/Balloon2.html The points here are that Expansion looks the same from each galaxy There is no “center” of the universe Galaxies do not expand Photons are redshifted because space itself is expanding
10	Early History of Universe? Run time “backwards” to understand Density goes up as expansion “reverses” Temperature goes up as material is compressed The early universe was very hot and dense. This is the essence of the “Big Bang” model, which has numerous testable predictions.
11	Consider a molecular H₂ , He gas as it gets hotter H₂ molecules break apart into H atoms H atoms loose their electrons He atoms lose their electrons He nuclei break apart into protons, neutrons Protons and neutrons break apart into quarks More exotic massive unstable particles are created You get more and shorter wavelength photons You get a quasi-equilibrium between photons and matter High energy photons Û (particles + antiparticles)
12	Critical points with time running forward 10^-45 sec Quantum gravity? Physics not understood 10^-34 sec 10²⁶ K Nuclear strong force/electro weak force separate (inflation, matter/antimatter asymmetry) 10^-7 sec 10¹⁴K Protons, AntiprotonsÛphotons 10^-4 sec 10¹² K Number of protons frozen 4 sec 10¹⁰ K Number of electrons frozen 2 min Deuterium nuclei begins to survive 3 min 10⁹ K Helium nuclei begin to survive 30 min 10⁸ K T, r too low for more nuclear reactions (frozen number of D, He -- critical prediction) 300,000 yr 10⁴ K Neutral H atoms begin to survive (frozen number of photons – critical prediction) 1 billion yr Galaxies begin to form 13 billion yr Present time
13	First prediction from Big Bang model: Cosmic Background Radiation Look out (and back in time) to place where H became neutral Beyond that the high density ionized H forms an opaque “wall” Originally 3000 K blackbody radiation The material that emitted it was moving away from us at extreme speed That v produces extreme redshift (z=1000), so photons all appear much redder, so T appears cooler With red shift, get 2.7 K Planck blackbody Should be same in all directions
14	Cosmic Microwave Background Observations First detected by Wilson and Penzias in 1960’s Serendipitous detection – thought is was noise in their radio telescope but couldn’t find cause. Only later heard of theoretical predictions Best spectrum observed by COBE satellite Red curve is theoretical prediction 43 Observed data points plotted there error bars so small they are covered by curve. it is covered by curve. Isotropy also measured by COBE T varies by less than 0.01 K across sky Small “dipole” anisotropy seen Blue = 2.721 Red = 2.729 Caused by motion of Milky Way falling towards the Virgo supercluster.
15	Second prediction from Big Bang Model: Abundance of the light elements Big Bang Nucleosynthesis T, r both high enough at start to fuse protons into heavier elements T, r both dropping quickly so only have time enough to fuse a certain amount. Simple models of expansion predict 25% abundance He 25% is the amount of He observed Abundance of ²H, ³He, ⁷Li depends on r_{normal matter} Suggests r_{normal matter} is only 5% of r_critical But we need to also consider “dark matter” and its gravity
16	Main Tests of the Big Bang Hubble Expansion (not a test really, inspiration) Cosmic Microwave Background Abundance of light elements Refinements of Big Bang Still Being Tested Possible “cosmological constant” Very early history: particle/antiparticle asymmetry “inflation” -- Details of very early very rapid expansion small r, T fluctuations which lead to galaxies
17	Will the expansion stop? Is there enough gravity (enough mass) to stop expansion? Consider an simple model as first step (full model gives same answer) Treat universe as having center Assume only Newtonian Gravity applies Does a given shell of matter have escape velocity? Is v > v_esc ?
18	General Relativistic Description What we call “gravity” is really bending of our 3-d space in some higher dimension. Bending, or “curvature of space” is caused by presence of mass. More mass implies more bending. If bending is enough, space closes back on itself, just like 2-d surface of earth is bent enough in 3rd dimension to close back on itself.
19	Mass and the Curvature of Space First consider case with little mass (little curvature) Ant (in 2-d world) can move in straight line from point A to point B. Add mass to create curvature in extra dimension invisible to the ant. In trying to go from point A to point B, fastest path is curved one which avoids the deepest part of the well. Ant will be delayed by the extra motion in the hidden third dimension. Both effects verified in sending photons past the sun: Bending of starlight during solar eclipse Delay in signals from spacecraft on opposite side of the sun
20	How to test the amount of curvature Measure the circumference of a circle as you get farther and farther from the origin: Does it go up as expected from (2 p R)? It goes up slower in a positively curved world.
21	How high is the density? Not nearly enough normal matter to provide critical density We keep seeing effects of gravity from “dark matter” Higher rotation speeds in our own galaxy Higher relative velocities of galaxies in clusters Rate at which matter clumps together to form galaxy clusters Gravitational lensing from galaxies, clusters May be 10 to 100 times as much “dark matter” as visible matter What might make up the “dark matter”? Possibilities include MACHOs (massive compact halo objects) http://www.astro.ucla.edu/~wright/microlensing.html but ²H, Li, Be abundance suggest no more than 5% can be “baryonic” WIMPs (weakly interacting massive particles) predicted by some GUT’s Mass of neutrinos Mass equivalent of “cosmological constant” energy
22	Refining the Big Bang Flatness Problem – why so close to a critical universe? Horizon Problem – why is background all same T? SOLVED BY AN “INFLATIONARY UNIVERSE” “Grand Unified Theories” of combined Gravity/Weak/Electric/Nuclear forces predict very rapid expansion at very early time: “inflation” When inflation ends, all matter moving away with v=v_escape (flat universe – curvature forced to zero) Also solves horizon problem – everything was in causal contact
23	Implications of Slowing Expansion Rate Our calculation of age T=1/H_o = 13.6 billion years assumed constant rate Gravity should slow the expansion rate over time If density is high enough, expansion should turn around If expansion was faster in past, it took less time to get to present size For “Flat” universe T = 2/3 * (1/H_o) = 9.3 billion years contradiction with other ages if T is too small
24	Is the expansion rate slowing? Look “into the past” to see if expansion rate was faster in early history. To “look into the past” look very far away: Find “H_o” for very distant objects, compare that to “H_o” for closer objects Remember – we found H_o by plotting velocity (v_r) vs. distance We found velocity v_r from the red shift (z) We found distance by measuring apparent magnitude (m_v) of known brightness objects We can test for changing H_o by measuring m_v vs. z
25	Measuring deceleration using supernovae Plot of m_v vs. z is really a plot of distance vs. velocity If faint (Þdistant Þearlier) objects show slightly higher z than expected from extrapolation based on nearby (present day) objects, then expansion rate was faster in the past and has been decelerating Surprise results from 1998 indeed do suggest accelerating expansion May be due to “cosmological constant” proposed by Einstein AKA “Dark energy” or “Quintessence”
26	“Cosmological constant” General Relativity allows a repulsive term Einstein proposed it to allow “steady state” universe He decided it wasn’t needed after Hubble Law discovered Is the acceleration right? Could it be observational effect – dust dims distant supernova? Could it be evolution effect – supernova were fainter in the past? So far the results seem to stand up Still being determined: 1) density, 2) cosmological constant With cosmological constant included, can have a “flat universe” even with acceleration. Given “repulsion” need to use relativistic “geometrical” definition of flatness, not the escape argument one given earlier. Energy (and equivalent mass) from cosmological constant may provide density needed to produce flat universe.
27	Tests using the Origin of Structure Original “clumpiness” is a “blown up” version of the small fluctuations in density present early in the big bang and seen in the background radiation. We can compare the structure implied to that expected from the “Grand Unification Theories” Rate at which clumpiness grows depends on density of universe Amount of clumpiness seems consistent with “flat universe” density That means you need dark matter to make clumpiness grow fast enough
28	Acoustic Peaks in Background
29	Cosmology as a testing ground for physics Extremely high energies and densities in early Big Bang test “Grand Unification Theories” which combine rules for forces due to gravity, weak nuclear force, electric force, strong nuclear force Extremely large masses, distances, times, test General Theory of Relativity
30	Chapter 15: Cosmology The Hubble Expansion – review+ Olber’s paradox The Big Bang Refining the Big Bang Details of the Big Bang General Relativity Cosmological Constant Origin of Structure