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Transcript
Lecture 25
Problems with the Big Bang
Inflation
ASTR 340
Fall 2006
Dennis Papadopoulos
The cosmic concordance
• What is our universe like?
– Matter content?
– Geometry (flat, spherical, hyperbolic)?
– Anything else strange?
• Remarkable agreement between different
experimental techniques:
“Cosmic concordance” parameters
Measurements of the matter content of
the Universe (recap)
• Primordial nucleosynthesis
– Theory predicts how present light element
abundances (4He, 3He, D, 7Li) depend on mean
baryon density
– Observed abundances  B0.04
• Galaxy/galaxy-cluster dynamics
– Look at motions of stars in galaxies, or galaxies in
galaxy clusters…
– Infer presence of large quantities of “dark matter”
which gravitationally affects observed objects but
cannot be seen with any telescope
Nucleosynthesis
• Analysis of galaxy
motions suggests a total
matter density of
Matter0.3
• Same conclusion from
gravitational lensing by
clusters (light from
background objects is
bent due to GR effects)
• First stunning conclusion:
– Compare B0.04 and Matter0.3
– Normal matter only accounts for about 1/8 of
the total matter that’s out there!
– Dark matter provides DM0.26
– We’re made of the minority stuff!
• Can be confirmed by taking
an inventory of a cluster,
where diffuse gas is hot and
emits X-rays…
– Find that about 1/8 of a
cluster’s mass is in baryons
– We believe that clusters
should be representative
samples of the universe…
– Confirms DM0.26
MEASURING THE GEOMETRY OF
THE UNIVERSE
• Recall that universe with different curvature has
different geometric properties
• Adding up the angles in a triangle,
– Flat universe(k=0): angles sum to 180
– Spherical universe (k=+1): angles sum to >180
– Hyperbolic universe (k=-1): angles sum to <180
• Similarly, for a known length L at a given distance D,
the angular size on the sky varies depending on the
curvature of space
– Flat universe (k=0): angular size =L/D
– Spherical universe (k=+1): angular size >L/D
– Hyperbolic universe (k=-1): angular size <L/D
L
L
k=0
k=+1
L
D
k=-1
Angular size of fluctuations in the CBR
• Remember the cosmic microwave
background…
• It has fluctuations, with average separations
corresponding to a known scale L at the
distance where light last interacted with
matter (matter/radiation decoupling)
• Distance D to this “surface of last scattering”
is also known
• Can use apparent angular separations of
fluctuations compared to L/D to infer
geometry of Universe
Surface of last
scattering
us
D
L
Flat universe!
• Result:
– The universe is flat
– In terms of omega curvature parameter,
k=0, i.e k=0
– Recall that the sum of all three omega parameters
as measured at present time must be 1:
1 M    k
– How do we reconcile k=0 with our measurement
of the matter density, which indicates M=0.3?
– There must be a nonzero cosmological constant,
=0.7!


0
M  0 
crit (3H02 /8G)

 
3H 0 2
kc 2
k   2 2
R0 H 0
Non-zero 
• Recall that with a non-zero, positive value of
 the universe expands more rapidly than it
would if it contained just matter
• Are there other indications of nonzero ?
• Yes, from direct measurement of “deceleration
parameter” q0
• Recall q0 = (d2R/dt2 )/(RH2) measures the rate of
change of the Hubble parameter (expansion rate)
• The relation between q0 , , and M is
q0 =0.5 M  
• If M =0.3 and =0.7, would expect q0 =-0.55
• More generally, any negative q0 means acceleration
rather than deceleration in the cosmic expansion
rate, and would imply  > M /2=0.15
• Direct measurement of q0 would be able to confirm
finding that  is nonzero…
The accelerating Universe
• Huge clue came from observations of
Type-1a Supernovae (SN1a)
– Very good “standard candles”
– Can use them to measure relative
distances very accurately
Type 1A Supernovae
• In the normal life of a star
(main sequence)…
– nuclear fusion turns
Hydrogen into Helium
• In the late stages of the
life of a massive star…
– Helium converted into
heavier elements (carbon,
oxygen, …, iron)
– At end of star’s life, get an
onion-like structure (see
picture to right)
• What’s special about iron?
– Iron has the most stable nucleus
– Fusing hydrogen to (eventually) iron releases energy
(thus powers the star)
– Further fusion of iron to give heavier elements
requires energy to be put in…
– Can only happen in the energetic environment of a
supernova explosion
– So, all heavier elements are created during
supernova explosions
Supernovae
• What produces a SN1a?
– Start off with a binary star system
– One star comes to end of its life – forms a “white
dwarf” (made of helium, or carbon/oxygen)
– White Dwarf starts to pull matter off other star… this
adds to mass of white dwarf (accretion)
– White dwarfs have a maximum possible mass… the
Chandrasekhar Mass (1.4 MSun)
– If accretion pushes White Dwarf over the
Chandrasekhar Mass, it starts to collapse.
• White Dwarf starts to collapse…
– Rapidly compresses matter in white dwarf
– Initiated runaway thermonuclear reactions – star
turns to iron/nickel in few seconds
– Liberated energy blows star apart
– Resulting explosion briefly outshines rest of
galaxy containing it… these are the SN1a events
• SN1a
– No remnant (neutron star or black hole) left
– Since white dwarf always has same mass when it
explodes, these are “standard candles” (i.e.
bombs with a fixed yield, hence fixed luminosity)
H0 and q0 with SN1a’s
• The program:
– Search for SN1a in
distant galaxies
– Compare expected
power with observed
brightness to determine
distance
– Measure velocity using
redshift
• “Low redshift” galaxies
give measurement of H0
• “High redshift” galaxies
allows you to look for
deceleration of universe
The results…
• This program gives
accurate value for
Hubble’s constant
– H=72 km/s/Mpc
• Find acceleration, not
deceleration, at large
distance!
– Very subtle, but really
is there in the data!
– Profound result!
• What does the future hold? Increasingly rapid
expansion!
Dark Energy
• There is an “energy” in the Universe that is
making it accelerate
– Call this “Dark Energy”
– This makes up the rest of the gravitating energy in the
Universe, and causes it to be flat!
– Completely distinct from “Dark Matter”
• Remember Einstein’s cosmological constant…?
– Dark Energy has precisely the same effect as
Einstein’s cosmological constant
– So, he was probably right all along!
What is “dark energy”?
• An “energy” that is an inherent component
of space…
• Consider a region of vacuum
– Take away all of the radiation
– Take away all of the matter
– What’s left? Dark energy!
– But we have little idea what it is…
The Age of the Universe
• Using this cosmological model, we can figure
out the age of the Universe.
– Answer – 13.7 billion years
• Prediction…
– There should be no object in the Universe that is
older than 14 Gyr.
– This agrees with what’s seen!
– This was a big problem with old cosmological
models that didn’t include dark energy:
• e.g age of the universe in M =1, k =0, =0 model is 9
billion years
• But there are globular star clusters whose estimated ages
are 12-14 billion years!
• This was troubling since universe must be at least as old
as the oldest stars it contains!
Concordance model
In summary, the parameters for our Universe,
using best available data…
• Hubble constant: H0=72 km/s/Mpc
• Geometry: k =0 (flat)
• Deceleration parameter: q0=0.55
• Baryon density: B=0.04
• Dark matter density: DM=0.26
• Cosmological constant: =0.7
• Age: t0=13.7 billion years
Deceleration –Acceleration
The Saga Continues
…although we are far from understanding all
the properties of the Universe, recent
observations are bringing us to the “era of
precision cosmology!”
Observing the Big Bang for Yourself
• Olber’s Paradox
• Why is the darkness of the night sky
evidence for the Big Bang?
Why is the darkness of the night
sky evidence for the Big Bang?
Olbers’ Paradox
If universe were
1) infinite
2) unchanging
3) everywhere
the same
Then, stars would
cover the night sky
Olbers’ Paradox
If universe were
1) infinite
2) unchanging
3) everywhere
the same
Then, stars would
cover the night sky
Night sky is
dark because
the universe
changes with
time
As we look
out in space,
we can look
back to a
time when
there were no
stars
Night sky is
dark because
the universe
changes with
time
As we look
out in space,
we can look
back to a
time when
there were no
stars
• Why is the darkness of the night sky
evidence for the Big Bang?
– If the universe were eternal, unchanging,
and everywhere the same, the entire
night sky would be covered with stars
– The night sky is dark because we can see
back to a time when there were no stars
What aspects of the universe
were originally unexplained with
the Big Bang theory?
Inflation
• What aspects of the universe were
originally unexplained with the Big Bang
theory?
• How does inflation explain these features?
• How can we test the idea of inflation?
What is Inflation
• Power law expansion – rate of change R gets
longer as the Universe expands. i.e. if R was
50% smaller 10 Gyars ago it will be a factor of 2
bigger 30 Gyears later
• Rate of change of R constant – expansion
exponential- Universe could expand by a factor
of 1050 in a fe10-30 seconds
• In GR rate of expansion~1/2(doubling
time~1/1/2)
Mysteries Needing Explanation
1) Where does structure come from?
2) Why is the overall distribution of matter so
uniform?
3) Why is the density of the universe so close
to the critical density?
Mysteries Needing Explanation
1) Where does structure come from?
2) Why is the overall distribution of matter so
uniform?
3) Why is the density of the universe so close
to the critical density?
An early episode of rapid inflation can solve
all three mysteries!
How does inflation explain these
features?
1 meter
Inflation can
make all the
structure by
stretching tiny
quantum ripples
to enormous size
These ripples in
density then
become the
seeds for all
structures
How can microwave temperature be nearly identical on
opposite sides of the sky?
Regions now on opposite sides of the sky were close
together before inflation pushed them far apart
Density = Critical
Density > Critical
Density < Critical
Overall
geometry of the
universe is
closely related
to total density
of matter &
energy
Inflation of
universe flattens
overall
geometry like
the inflation of a
balloon, causing
overall density
of matter plus
energy to be
very close to
critical density
How can we test the idea of
inflation?
Patterns of structure observed by WMAP show us the
“seeds” of universe
Observed patterns of structure in universe agree (so far)
with the “seeds” that inflation would produce
“Seeds” Inferred from CMB
• Overall geometry is flat
– Total mass+energy has critical density
• Ordinary matter ~ 4.4% of total
• Total matter is ~ 27% of total
– Dark matter is ~ 23% of total
– Dark energy is ~ 73% of total
• Age of 13.7 billion years
“Seeds” Inferred from CMB
• Overall geometry is flat
– Total mass+energy has critical density
• Ordinary matter ~ 4.4% of total
• Total matter is ~ 27% of total
– Dark matter is ~ 23% of total
– Dark energy is ~ 73% of total
• Age of 13.7 billion years
In excellent agreement with observations of present-day universe
and models involving inflation and WIMPs!
What have we learned?
• What aspects of the universe were originally
unexplained with the Big Bang theory?
– The origin of structure, the smoothness of the
universe on large scales, the nearly critical density
of the universe
• How does inflation explain these features?
– Structure comes from inflated quantum ripples
– Observable universe became smooth before
inflation, when it was very tiny
– Inflation flattened the curvature of space, bringing
expansion rate into balance with the overall density
of mass-energy
What have we learned?
• How can we test the idea of inflation?
– We can compare the structures we see in
detailed observations of the microwave
background with predictions for the
“seeds” that should have been planted by
inflation
– So far, our observations of the universe
agree well with models in which inflation
planted the “seeds”