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Astr 1050 Mon., Nov 12, 2007 Today: Start Ch. 17: The Birth of the

Universe

Reading in Horizons by Bennett: Chapter 17, for Monday

Reminders: New MA HW is posted

Final Exam is NOT Cumulative

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Chapter 17 & 18: The Birth of the Universe, Dark Matter & Dark Energy •  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

GREAT WEB RESOURCE: http://www.astro.ucla.edu/~wright/cosmolog.htm

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Olber’s Paradox: Why is the night sky dark?

•  If we are in a small forest we can see space between trees because some lines of site can extend beyond edge

•  If we are in a large forest then any direction we look will just be looking at the trunk of some tree.

From our text: Horizons, by Seeds

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Olber’s Paradox: Why is the night sky dark?

•  If we are in a universe which extends far enough then any direction we will just be looking at the surface of some star.

If unverse is infinte in extent, why isn’t the night sky as bright as the surface of a star?

From our text: Horizons, by Seeds

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Olber’s Paradox: Answer •  It could be that the Universe doesn’t extend far enough –

but then the universe is finite in size and has an “edge.” •  However a 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!

From our text: Horizons, by Seeds

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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 tested!)

–  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. That is, there is no center of the expansion.

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The Hubble Law and the Age of the Universe Ho = 72 ±8 km/s/Mpc

constant) is (assuming yearsbillion6.13s1029.4 17

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We’ll see it probably isn’t exactly constant

From Freedman et al.

Redshift “Game” at: http://www.astro.ucla.edu/~wright/Zguess.html

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Hubble Law: Everyone sees same expansion

Car d

vr

t0 = 1/H0

d relative to B vr relative to B

t0 = 1/H0

A 30 miles 15 mph 2 hr -70 miles -35 miles/hr 2 hr

B 100 miles 50 mph 2 hr 0 miles 0 miles/hr ----

C 120 miles 60 mph 2 hr 20 miles 10 miles/hr 2 hr

D 140 miles 70 mph 2 hr 40 miles 20 miles/hr 2 hr

You get the same result whether you use “absolute” velocities and distances, or measure velocities relative to any arbitrary car.

Every driver thinks they are at the center of the “car universe” and the other cars are just heading away from them, all having left at some common start time. See http://www.astro.ucla.edu/~wright/nocenter.html

Car “B” is the Highway Patrol – using a radar gun which can find speed and distance to other cars – but can’t see the ground.

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Universal Expansion: Balloon Analogy •  Simulation of a “closed” spherical universe

expanding: •  http://www.astro.ucla.edu/~wright/Balloon2.html •  Analogy of raisin cake •  The points here are that

–  Expansion looks the same from each galaxy –  There is no “center” of the universe –  Galaxies do not fly apart, expansion of space carries them –  Photons are redshifted because space itself is expanding

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Chapter 18: Dark Matter, Dark Energy and the Fate of

the Universe

•  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.

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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 ⇔ (particles + antiparticles)

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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, Antiprotons⇔photons •  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, ρ 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

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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

From our text: Horizons, by Seeds

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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. http://www.astro.ucla.edu/~wright/photons_outrun.html

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Second prediction from Big Bang Model: Abundance of the light elements

•  Big Bang Nucleosynthesis –  T, ρ both high enough at start to fuse protons into heavier

elements –  T, ρ 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 ρnormal matter

•  Suggests ρnormal matter is only 5% of ρcritical •  But we need to also consider “dark matter” and its gravity

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Main Tests of the Big Bang

•  Hubble Expansion (not a test really, more the inspiration)

•  Cosmic Microwave Background •  Abundance of light elements •  Density Fluctuations & the Origin of Galaxies

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 ρ, T fluctuations which lead to galaxies

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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 > vesc ?

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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.

From our text: Horizons, by Seeds

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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

From Voyages through the Universe by Fraknoi et al.

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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 π R)? It goes up slower in a positively curved world.

From Voyages through the Universe, by Fraknoi et al.

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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

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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

Flat universe

“Size” of Universe

Time From our text: Horizons, by Seeds

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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

–  We can test for changing Ho by measuring mv vs. z

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Evidence for Dark Energy •  Evidence for Cosmological Constant or “Dark Energy”

–  Time-scale Test –  High Redshift Supernovae

Measurements of H0 (various methods) and T0 (age of Globular Clusters) in the 1990s showed that the simple, flat, matter-dominated cosmology with Ω =1 was probably ruled out by. That is, H0T0 ~ 0.9 not

2/3. More recent observations of high redshift supernovae (right) have

strongly confirmed this.

The best fit models require a modest matter density (Ωm = 0.24) and a

Dark Energy (ΩΛ = 0.76). Note that ΩT = Ωm + ΩΛ = 1, thus a flat

cosmology (k = 1) and consistent with the CMB.

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“Cosmological Constant”aka Dark Energy •  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.

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Cosmology & High Energy Physics

•  Particle Physics “Grand Unification Models” (GUTS) Attempt to Unify the Fundamental Forces –  GUTS: at higher energies the forces become unified. –  Electricity & Magnetism unified in 19-th century –  Weak nuclear force and Strong force added in 20-th century –  Unification of Gravity is focus of current efforts

•  Next generation of particle accelerators can test some predictions of GUTS (e.g., Higgs particle) but cannot test the highest energy predictions. –  Predictions for the highest energies testable only via the Big

Bang •  Origin of Dark Matter and the Cosmological Constant (Dark

Energy) is currently unknown and may only be addressable via observational cosmological. To date, searches for Dark Matter particles in the lab have failed.

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History of the Universe

Time (sec) Temp. (K) What < 10-43 > 1032 Grand unification (Plank epoch) 10-43 1032 Gravity separates 10-43 – 10-35 1032 – 1027 GUTs 10-35 1027 Spontaneous symmetry breaking of strong nuclear force 10-35 – 10-33 1027 – 1026 Inflation (~ e100) 10-33 – 10-12 1026 – 1015 Quarks, e-e+, baryogenesis, particle-antiparticle annihilation 10-12 1015 Weak nuclear force separates 2 x 1012 Quark-Hadron phase transition (p, n, ν form) 10-4 1012 Neutral current interaction maintain proton, neutron equilibrium 3 x 1011 Neutrinos de-couple 1 1010 Neutrons decouple from protons (n/p ~ 1/6) 180 109 Deuterium forms, nucleosynthesis begins, all n go to 4He (23%) 106 3000 Recombination of Hydrogen, formation of microwave background 109 yrs 100 First globular clusters and galaxies form 1010 yrs 3 Present time

Brief History of the Universe

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Chapter 24: The New Cosmology - IV

Alternative Cartoon Version

•  Planck Epoch: t < 10-43 sec •  4 fundamental forces unified

•  Grand Unification Epoch: 10-43 < t < 10-36

sec •  Inflationary Epoch: t ~ 10-32 sec

•  Quark & Higgs Epoch: 10-12 < t < 10-6 sec •  Hadron (P & N) Epoch: 10-6 < t < 1 sec. •  Annihilation Epoch: 1 < t < 10 sec. •  Nucleosynthesis: 3 < t < 20 min. •  Matter Dominates: 70,000 years •  Recombination: t = 377,000 years •  Dark Ages: 150 < t < 800 x 106 years •  First Galaxies: t ~ 300 x 106 years

•  Reionization: 150 < t < 1000 x 106 years •  Solar System: 9 x 109 years •  Dark Ages II: 1014 years

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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

From our text: Horizons, by Seeds

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Temperature Fluctuations in the Microwave Background

•  Sound Waves Are Frozen into the Microwave Background at Recombination. Tiny density fluctuations: Δρ/ρ ~ ΔT/T < 10-5

–  Power Spectrum Provides Precision Test of Cosmological Models

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Chapter 24: The New Cosmology - II •  The Cosmic Microwave Background (CMB) provides a sensitive test of cosmological models. •  The power spectrum of the acoustic signal in the microwave background.

–  The location of the first peak requires that the universe is flat (k = 0). –  The location of the second and third peak constrain the Baryonic and dark matter density. –  Good web page: www.background.uchicago.edu/~whu

The WMAP satellite provided the first good measurements of

the power spectrum of the CMB.

The figure shows the amplitude of the temperature fluctuations as a function of angular scale on the sky. The first peak at

200 wave-numbers corresponds to ~ 1.8 deg. This features

requires a flat (k = 1) geometry for the universe.

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Acoustic Peaks in Background

Fluctuation structure consistent with Big Bang, Flat Universe

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Problems with the Big Bang Model •  Problems with the Standard Model

–  Isotropy and Homogeneity •  Regions of the universe in causal contact have to be separated by

less than a horizon scale. •  Horizon is defined as DH = cT where T is time since the Big

Bang •  At epoch of recombination DH corresponded to only ~ 40 degrees

on the sky. •  Why are regions of microwave background not in causal contact

so uniform in T (ΔT/T < 10-5)? –  Flatness

•  Density parameter (Ω = ρ/ρcrit) could have any value but is pretty close to 1, the critical density and resulting in a flat cosmology.

•  Measurement of the acoustic power spectrum requires that we have precisely a flat cosmology (zero curvature).

•  Why is the universe so close to flat? –  Origin of Structure

•  Origin of the irregularities that grow to form galaxies is unknown

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Chapter 24: The New Cosmology - V •  Cosmic Inflation:

–  Energy is injected into the universe by the decay of GUTS particles (Axion?). This “inflates” the universe (faster than the speed of light) smoothing out irregularities and solving the horizon problem and the flatness problem.

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Problems with the Big Bang Model

•  Galaxy Formation –  The standard Big Bang model provides no explanation for the

origin or the initial fluctuations that grow to form galaxies. –  Inflation may provide this via quantum mechanical

fluctuations. They provide the required slope for the power spectrum and would be inflated to macroscopic size to then grow via gravity. This is an active topic for current theoretical research.

•  Summary –  Inflationary model provides the best explanation for problems

with the standard Big Bang model. It may ultimately prove incomplete as well but it provides the context within which new ideas are formulated and tested. This is the nature of cutting-edge scientific research.

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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

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Chapter 17 & 18: Cosmology

•  The Hubble Expansion – review+ •  Olber’s paradox •  The Big Bang •  Refining the Big Bang •  Details of the Big Bang •  General Relativity •  Dark Energy (“Cosmological Constant”) •  Origin of Structure