1	Astr 1050 Fri., Apr 22, 2005 Today: Extra Credit Articles HW 11 solutions Finish Ch. 15, Cosmology
2	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
3	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
4	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 ?
5	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.
6	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
7	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.
8	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
9	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
10	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
11	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
12	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” See Science News: http://sciencenews.org/articles/20030802/fob1.asp
13	“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.
14	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
15	Acoustic Peaks in Background
16	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
17	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