| Today: Go over exam (briefly!) | |
| Ch. 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 | |
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. |
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. |
| 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 |
| 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. | ||
The Hubble Law and the
Age of the Universe
Ho = 72 ±8
km/s/Mpc
Hubble Law: Everyone sees same expansion
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 | ||
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. | |
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) | ||
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 1014 K 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 |
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 |
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. |
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| 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. | |||
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 rnormal matter | |||
| Suggests rnormal matter is only 5% of rcritical | |||
| But we need to also consider “dark matter” and its gravity | |||
| Hubble Expansion (not a test really, inspiration) | |||
| Cosmic Microwave Background | |||
| Abundance of light elements Refinements of Big Bang Still Being Tested |
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| 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 | |||
| 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 > vesc ? | ||
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. |
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 |
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. |
| 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 | |||
| 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=vescape (flat universe – curvature forced to zero) | ||
| Also solves horizon problem – everything was in causal contact | ||
Implications of Slowing Expansion Rate
| Our calculation of age T=1/Ho = 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/Ho) = 9.3 billion years | ||
| contradiction with other ages if T is too small | ||
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 “Ho” for very distant objects, compare that to “Ho” for closer objects | ||
| Remember – we found Ho by plotting velocity (vr) vs. distance | ||
| We found velocity vr from the red shift (z) | ||
| We found distance by measuring apparent
magnitude (mv) of known brightness objects |
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| We can test for changing Ho by measuring mv vs. z | ||
Measuring deceleration using supernovae
| Plot of mv 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 |
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| Surprise results from 1998 indeed do suggest accelerating expansion | ||
| May be due to “cosmological constant” proposed by Einstein | ||
| AKA “Dark energy” or “Quintessence” | ||
| 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. | ||
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 | ||
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 |
| 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 | |