Lecture 23:
The Big Bang
Astronomy 111
Monday November 21, 2016
Reminders
• No homework assigned this week
– Happy Thanksgiving!
• Homework #11 will be assigned next
Monday
– Due Monday December 5 at 3pm
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Expansion of the Universe
• Universe is expanding today.
– Observational Evidence: Hubble’s Law
• As the Universe expands, it cools.
• In the past, it must have been:
– Smaller
– Denser
– Hotter
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The Big Bang
• The Universe has expanded to its
present observed state from an initially
very hot, very dense state.
• This initial state must have existed at
some finite time in the past.
• We call this hot, dense state the “Big
Bang”
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Foundations
• The Big Bang model for the Universe
follows from three basic assumptions:
– General Relativity is correct on cosmic
scales.
– The Universe is homogeneous and
isotropic on large scales.
– The energy of the vacuum is either zero or
very small (the Cosmological Constant: Λ)
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Testable model
• These basic assumptions are plausible:
– Empirical support for the most part.
– Reasonably sound physical basis.
• But, they are not required to be true.
• Real Test:
Does the Big Bang model explain the
properties of the observed Universe?
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Expansion & Hubble’s Law
• As the Universe expands:
– Space gets stretched in all directions.
– Matter is carried along with space.
– Distances between galaxies get larger.
• Big Bang predicts Hubble’s Law exactly,
provided that the speeds are small
compared to the speed of light.
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Expansion and redshifts
• Expansion of space also stretches
photons:
– Wavelengths get stretched = longer = redder.
– More distant the object, the greater the
stretch.
– Result: redshift gets larger with distance.
• Light moves at a finite speed:
– More distant objects seen in the past.
– “look-back” to when the universe was smaller
& younger.
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Critical density
• All galaxies attract each other via gravity.
– Gravitational attraction slows the expansion.
• How it behaves depends on the density:
– High Density: Expansion slows, stops, &
reverses.
– Low Density: Keeps expanding forever.
• Dividing Line = “Critical Density”
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Density parameter: Ω
average density of Universe
Ω=
critical density
Ω>1: High Density Universe
Ω<1: Low Density Universe
Ω=1: Critical Density Universe
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Geometry of the Universe
• If Ω>1:
– positive curvature (“spherical”)
– finite yet unbounded Universe
• If Ω<1:
– negative curvature (“hyperbolic”)
– infinite Universe
• If Ω=1: Universe is Flat and infinite.
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2-D examples of curved spaces
Closed
Open
Flat
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Fate of the Universe
• If Ω>1: “Closed” Universe
– Expansion slows to a maximum size &
stops
– Collapses into a Big Crunch
• If Ω<1: “Open” Universe
– Expands forever at a near-constant rate.
• If Ω=1: “Flat” Universe
– Expands forever at an ever slowing rate.
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Back to the beginning
• The Universe is expanding now
• In the past:
– Universe was smaller
– Galaxies were closer together in space
• If we go back far enough in time:
– All galaxies (matter) in one place
• How far back = “Age of the Universe”
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Analogy
• Road trip: you leave College Station by car
for South Padre, but leave your watch
behind.
• How long have you been on the road?
– your average speed = 100 km/h
– odometer reads: distance = 230 km
• Time since you left: t = distance ÷ speed
– t = 230 km ÷ 100 km/h = 2.30 hours
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The Hubble time
• Hubble’s Law says
– a galaxy a distance “d” away has a recession
speed, v = Hd
• If v, locally, is about its average speed,
then:
–t=d/v
– but since, v = Hd,
– t = d/Hd = 1/H
• Hubble Time = 1/H
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In-class assignment
• Calculate the age of the Universe in
years using the Hubble time
• Assume H=75 km/s/Mpc
• 1 pc = 3 x 1013 km
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The age of the Universe
• Example:
– For H = 75 km/sec/Mpc
– t = 1/H = 13 Billion Years
• But
– Universe does not expand at a constant rate.
– Different expansion rate in past.
• The Hubble Time is an approximation of
the age of the Universe.
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Complications
• Need three numbers we do not know
exactly:
• Hubble Constant, H:
– Tells us how fast the universe is expanding
now
• Density Parameter, Ω:
– Tells us how the expansion has slowed down.
• Cosmological Constant, Λ:
– Counteracts the slowing effect of gravity.
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Best estimate of the age
About 13.8 Gyr
• Problems:
– Close to age of oldest stars in Globular
Clusters
– Makes the margin for forming galaxies
somewhat close (formation had to be very
fast)
• Subject of on-going research &
discussion
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The Hot Big Bang
• Now:
– the Universe is cold & low density.
– as it expands, it cools
– matter (galaxies) gets further apart.
• In the past:
– Universe was smaller, hotter, & denser
• Is there any evidence of this early
hot, dense phase in the past?
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Where did Helium come from?
• Pop I Stars (and the Sun):
– 70% H, 28% He, and ~2% metals
– Pop I metals from Pop II star supernovae.
• Metal-poor Pop II Stars:
– 75% H, 25% He, and <0.01% metals
• Where did the He in Pop II stars come
from?
– If from the first stars, where are all the metals?
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Primordial nucleosynthesis
• When the Universe was only ~1 second
old:
– Temperature: ~10 Billion K
– Too hot for atomic nuclei:
– Only protons, neutrons, electrons, & photons
• General hot, dense soup of subatomic
particles & photons.
• As it expanded, it cooled off.
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Primordial Deuterium formation
• When the Universe was ~2 minutes old:
– Temperature: ~1 Billion K
• Neutrons & Protons fused into Deuterium
(2H)
– All free neutrons go into Deuterium
– Leftover protons stay free as Hydrogen
“nuclei”
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Primordial Helium formation
• Some Deuterium fused to form 4He nuclei
– Other reactions made Li, Be, and B in very tiny
quantities.
• By the time the Universe was ~4 minutes
old:
– Much of the Deuterium turned into 4He
– Universe cooled so much that fusion stops
and no heavy elements get formed.
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Aftermath
• After Primordial nucleosynthesis stops:
• Theory predicts:
– 4He/H = 20−26%
– D/H = 0.0001−0.1%
• Observations:
– 4He/H = 22−25%
– D/H = 0.001−0.02%
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Current status
• Predictions of primordial nucleosynthesis
look good compared to observations
• Observations:
– Need refinement of the primordial abundances
– Very difficult observations to make
• Theory:
– Need to know average density of p & n
– light-element reactions need some refinement
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Hot Early Universe
• After nucleosynthesis, the Universe
stays hotter than 3000 K for a long time:
– electrons & nuclei cannot combine to form
neutral atoms
– Universe remains fully ionized.
– Free electrons easily scatter all photons.
• Universe is opaque to light during this
time.
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Blackbody radiation
• Universe is filled at this time by a hot,
dense, opaque ionized gas.
– Has a perfect blackbody spectrum.
– Characteristic temperature, T
• As the Universe expands & cools:
– photons redshift
– peak of the spectrum shifts redward
– Blackbody temperature drops
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Epoch of recombination
• When the Universe is ~300,000 years old:
• Temperature drops below 3000 K:
– electrons & nuclei combine to form atoms
– not enough free electrons to scatter photons
• Universe suddenly becomes transparent:
– Photons stream out through space
– Photon Spectrum: 3000 K Blackbody
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Cosmic background radiation
• After Recombination, the Universe is filled
with diffuse, “relic” blackbody radiation.
• As the Universe expands further:
– Blackbody photons redshift.
– Spectrum peak shifts to redder wavelengths,
hence cooler temperatures.
• By today, spectrum is redshifted by a
factor of ~1000 down to ~3K
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Discovery
• 1965: Penzias & Wilson (Bell Labs)
– Mapping sky at microwave wavelengths.
– Found a faint microwave background noise.
– First thought it was equipment problems (noisy
amplifiers, pigeon poop in the antenna).
– Finally determined it was cosmic in origin.
• Won the Nobel Prize in 1978 for
discovering the Cosmic Background
Radiation.
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But, is it blackbody radiation?
• The Big Bang model makes very specific
predictions:
– the spectrum is a perfect blackbody
– characterized by a single temperature.
• 1965-1990:
– Experiments with balloons, rockets, & radio
antennas showed a rough blackbody spectrum
– Temperature ~2.7 K
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COBE: Cosmic Background
Explorer Satellite
• Launched in Nov 1989:
– Mapped the entire sky at Near-IR to
Microwave wavelengths.
– Searched for fluctuations in the
background as evidence of early largescale structure.
– Far-IR spectrometer mapped the spectrum
in detail from 0.1 to 10 mm.
• Spectacular Blackbody with T=2.726 K
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COBE Cosmic Background
Spectrum
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Spectacular confirmation
• The COBE results confirm and greatly
strengthen the Big Bang Model:
– Perfect blackbody spectrum - as predicted
– Characterized by a single temperature - as
predicted
– Uniformly fills the Universe - as predicted
• Details:
– Fine structure at part in 105 level is related to the
large-scale structure we see in the galaxies.
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Evidence for the Big Bang
• Expansion of the Universe: CONFIRMED
– Hubble’s Law
– Age is consistent with the oldest stars
• Primordial Nucleosynthesis: CONFIRMED
– Deuterium & Helium in about right amounts
• Cosmic Background Radiation:
CONFIRMED
– Perfect blackbody with a single temperature
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Summary
• Big Bang model of the Universe
– Starts in a hot, dense state
– Universe expands and cools
• Expansion and redshift
• Critical density
– Geometry of the Universe
• Hubble time = maximum age of the
Universe
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Summary
• Fundamental tests of the Big Bang
• Primordial nucleosynthesis
– Primordial Deuterium & Helium
– Primordial light elements (Li, B, Be)
• Cosmic background radiation
– Relic blackbody radiation from Big Bang
– Temperature: T = 2.726 K
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