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The Universe on the Largest
Scales
• No evidence of structure on a scale
larger than 200 Mpc
• On very large scales, the universe
appears to be:
• Homogenous - the same everywhere
• Isotropic - the same in all directions
Cosmology
• The study of the structure and evolution of the universe
• Cosmological principle - twin assumptions of homogeneity and isotropy
• Generally accepted by astronomers
• No edge (violates homogeneity)
• No center (violates isotropy)
Olbers’s Paradox
• Assume that universe is infinite and
unchanging in time
• When you look at sky at night, your line of
sight will eventually encounter the bright
surface of a star
• Entire sky should be as bright as the sun
• But sky is dark at night - Olbers’s Paradox
• From nineteenth century Heinrich Olbers
Olbers’s Paradox
• Since sky is dark at night, either
• universe is not infinite and/or
• universe evolves in time
Hubble’s Law
• Recession velocity = H0 X distance
• How long did it take a galaxy to reach
its current distance from us?
• Distance = velocity X time
• time = Distance/velocity
= Distance/(H0 X distance) = 1/H0
• = 14 billion years (for H0 = 70 km/s/Mpc)
Birth of the Universe
• Hubble’s law implies that 14 billion years ago,
all galaxies were at the same location
• Everything in the universe was confined to a
single point then
• The point exploded - this is the Big Bang
• This was the beginning of the universe and
the beginning of time
Big Bang
• Big Bang explains Olbers’s paradox -
even if universe is infinite, we only see a
finite part within 14 billion light-years
• Light from beyond has not yet reached
us
Where was Big Bang?
• Big Bang was not an explosion of matter into space
• Big Bang was an explosion of the universe itself, or of space itself
• Galaxies don’t rush into empty space -instead space itself expands
• Entire universe was a point - the Big Bang happened everywhere at once
Receding galaxies
• Think of galaxies as coins taped to an
expanding balloon
• Surface of balloon represents universe
• Every coin sees every other coin recede
• No coin is at center
Cosmological Redshift
• For expanding universe, Doppler
interpretation not technically correct
• Galaxies are not moving apart through
space
• Instead, space itself is expanding
• Redshift represents expansion of
wavelength as universe expands
Fate of the Universe
• Will universe expand forever?
• Similar to escape velocity from a planet
• Will object tossed upward rise forever or
fall back?
• Depends on launch speed and mass of
planet
Critical Density
• Low density universe expands forever
• High density universe collapses in a Big
Crunch
• Critical Density is the dividing line
• For H0 = 70 km/s/Mpc, critical density is
9 X 10-27 kg/m3
• 0.1 Milky Way galaxies per cubic Mpc
Geometry of space
• Mass/energy warps space
• The greater the total density, the greater
the curvature
• Density includes mass (visible and dark
matter)
• Also includes all energy
Cosmic density parameter
0 is ratio of actual to critical density
0 > 1.0 is a closed universe
0 < 1.0 is an open universe
0 = 1.0 is a critical universe
Flat space
• Euclidean geometry
• Parallel lines never meet
• Angles in triangle add to 180°
• Circumference of circle is X diameter
0 = 1, critical universe
• Infinite in extent
Positively curved space
• Studied by Georg Riemann
• Like surface of sphere
• “Parallel” lines intersect twice
• Angles in triangle add to more than 180°
• Circumference of circle is < X diameter
0 > 1, closed universe
• Finite in extent
Negatively curved space
• Studied by Nikolai Lobachevsky
• Imagine a saddle shape
• Infinite number of lines through a point
parallel to another line
• Angles in triangle add to less than 180°
• Circumference of circle is > X diameter
0 < 1, open universe
• Infinite in extent
Cosmic density parameter
• Counting all luminous matter gives 0 of
several percent
• Adding in estimated dark matter in
galaxies and clusters gives 0 ≈ 0.25
• On a larger scale distribution of dark
matter not well known
• Overall cosmic density less than critical
Cosmic acceleration
• Use Type I supernovae to measure distances
(independent of Hubble’s law)
• If gravity slowing expansion - universe is
decelerating - objects at great distances -
(long ago) - should be receding faster than
Hubble’s law predicts
• Data seems to show expansion is
accelerating
Cosmic acceleration
• What causes this acceleration?
• Dark energy - exerts repulsive force
• Dark energy may greatly exceed total
mass (luminous and dark) of universe
Cosmological Constant
• “Vacuum pressure” force associated with empty space
• First suggested by Einstein in 1917 - his equations showed universe evolved in time
• Expansion of universe not known then
• When discovered, he discarded Cosmologial Constant as the biggest mistake of his scientific career
• May be making a comeback as a dark energy explanation
Cosmic Composition
• Theoretical studies suggest universe is flat
• A variety of measurements lead to 0 = 1.0
• Density is made of both matter (27%) and
dark energy (73%)
• Gravity tends to slow expansion
• Dark energy tends to increase expansion
• Universe will expand forever
Age of universe
• For H0 = 70 km/s/Mpc,
• Age of critical density universe with no
cosmological constant is 9 billion years
• Age of low density universe > 9 billion y
• Age of high density universe < 9 billion y
• Age of accelerating universe is about 14
billion y
Age of universe
• Globular clusters formed 10 - 12 billion
years ago
• Consistent with 14 billion years age for
universe with 2 billion years for galaxies
to evolve
• Inconsistent with critical density with no
dark energy
Cosmic Microwave
Background• Penzias and Wilson in 1964 discovered a
“hiss” in all directions of space
• Microwave wavelengths - blackbody curve at 2.7 K
• Gamma ray wavelengths in early universe cosmologically redshifted to microwave wavelengths
• Radiation is isotropic (same in all directions)
• Contains far more energy than all of energy emitted by all stars and galaxies
Matter and Radiation
• Currently density of matter much
greater than density of radiation
• Matter-dominated universe
• In past, both radiation and matter more
dense
• But radiation cosmologically redshifted
• Early universe radiation-dominated
Formation of nuclei and atoms
• Early universe almost entirely radiation
• In first minute photons had sufficient
energy to transform into electrons,
protons, neutrons and exotic particles
• Primordial nucleosynthesis - formation
of elements heavier than hydrogen
shortly after Big Bang
Deuterium and helium
• Below 900 million K, about two minutes after Big Bang, protons and neutrons fused into deuterium
• After short while, deuterium fused into heavier elements, mostly He-4
• Almost all neutrons consumed
• By 15 minutes, elemental abundance set
Deuterium abundance
• Not all primordial deuterium converted to He
• Present day density of universe indicated by
deuterium remaining
• Gives density of “normal” matter of 3 to 4
percent of critical
• Total matter density is about 1/3 of critical
• Most of matter is “dark” and not composed of
protons and neutrons
Formation of Atoms
• At age of tens of thousands of years, matter began to dominate over radiation
• Cooled enough for nuclei and electrons to form atoms - known as de-coupling
• Before then, free electrons scattered radiation
• Universe went from opaque to transparent
• After about 400,000 years, temperature fell to 3000 K, and microwave background we see now released when universe was 1100X smaller than today
Horizon Problem
• Observe two regions at opposite
directions in sky
• Microwave background same at both
• Density and temperature same at both
• But not enough time, even at speed of
light, to “connect” them
Flatness Problem
• Universe is very close to being flat
today
• Universe must have been extremely
close to critical in the past
• Why is universe’s density nearly critical,
out of all possibilities?
Horizon and Flatness problems
explained
• Grand Unified Theory (GUT) describes
superforce made up of electromagnetism and
strong and weak nuclear forces
• 3 forces unified at very high temperatures
• Predicts that at 10-34 s after Big Bang, at 1028
K, universe greatly expanded by factor of 1050
until 10-32 s
• Epoch of inflation
Cosmic inflation
• Explains horizon problem
• Inflation took parts of universe that had
“communicated”, then dragged them far
apart
• Explains flatness problem
• Curved space, greatly expanded,
“appears” flat
Formation of large-scale
structure
• Small inhomogeneities in early universe
grew into large scale structures
• Dark matter, unaffected by radiation,
clumped and gravitationally affected
normal matter
COBE map
• Dark matter doesn’t emit or absorb
radiation
• Its gravity affects redshift of cosmic
microwave background radiation
• Measured by COBE satellite
• Map shows universe is of critical density