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April 1, 2003 Lynn Cominsky - Cosmology A350
1
Professor Lynn Cominsky
Department of Physics and Astronomy
Offices: Darwin 329A and NASA EPO
(707) 664-2655
Best way to reach me: lynnc@charmian.sonoma.edu
Astronomy 350Cosmology
April 1, 2003 Lynn Cominsky - Cosmology A350
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Cosmological curvature
= density of the universe / critical density
hyperbolic geometry
flat or Euclidean
spherical geometry
April 1, 2003 Lynn Cominsky - Cosmology A350
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Geometry and Curvature of Space
Let’s make some quantitative measurements of the angles in a triangle for the different geometries – flat, sphere and hyperbolic (saddle) – and see how the angles compare for different size triangles.
April 1, 2003 Lynn Cominsky - Cosmology A350
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The shape of the Universe
The shape of the Universe is determined by a struggle between the momentum of expansion and the pull of gravity.
The rate of expansion is determined by the Hubble Constant, Ho
The strength of gravity depends on the density and pressure of the matter in the Universe. G is proportional to + 3P is the density and P is the pressure
For normal matter, P is negligible, so the fate of the universe is governed by the density
April 1, 2003 Lynn Cominsky - Cosmology A350
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The fate of the Universe
As the universe expands, the matter spreads out, with its density decreasing in inverse proportion to the volume. (V = 4r3/3 for a sphere)
The strength of the curvature effect decreases less rapidly, as the inverse of the surface area. (A = 4r2 for a sphere)
So, in the standard picture of cosmology, geometry (curvature) ultimately gains control of the expansion of the universe.
April 1, 2003 Lynn Cominsky - Cosmology A350
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Geometry is not Destiny
WMAP (and others) have determined that the Universe is geometrically flat (tot = 1)
In the standard picture, this would mean that the Universe would expand more slowly with time, eventually coasting to a stop
However, the Type 1a supernova measurements show that the universe is actually accelerating
This implies the existence of a form of mass-energy with a strong negative pressure, such as the cosmological constant ()
April 1, 2003 Lynn Cominsky - Cosmology A350
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Cosmological Constant
was introduced by Einstein in his theory of General Relativity, in order to keep the Universe stable – otherwise his equations predicted either expansion or contraction (depending on the density of matter)
In order for the Universe to be geometrically flat (tot=1), but with only 27% matter and dark matter (M=0.27), the other 73% must be a different type of mass-energy that we now call “Dark Energy” (=0.73).
April 1, 2003 Lynn Cominsky - Cosmology A350
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Dark Energy Evolution
Dark Energy, however, must have been insignificant not too long ago, otherwise its gravitational influence would have made it almost impossible for ordinary matter to form the stars, galaxies and large-scale structure that we see in the universe today.
It must therefore have a density that decreases much more slowly with time than the (normal and dark) matter density, so it can dominate as the Universe expands
April 1, 2003 Lynn Cominsky - Cosmology A350
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“Anti-gravity”?
According to Einstein's equations, this type of matter must be gravitationally self-repulsive.
Since G is proportional to + 3P, repulsive G means G<0 so therefore P < 0 and 3P >
Matter with this type of P and will cause the expansion of the universe to accelerate.
If this exotic type of matter-energy plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever.
April 1, 2003 Lynn Cominsky - Cosmology A350
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Uncertainty Principle
The uncertainty principle states that you cannot know both the position x and the momentum p of a particle more precisely than Planck’s constant h/2“h-bar”
When dimensions are small, particles must therefore move in order to satisfy the uncertainty principle
This motion creates a “zero point energy” > 0
Uncertainty Principle x p = h/2
April 1, 2003 Lynn Cominsky - Cosmology A350
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Uncertainty Principle
Another version of the uncertainty principle relates the energy of a particle pair to lifetime
This version explains the “virtual particles” that appear as quantum fluctuations
They do not violate the uncertainty principle as long as their lifetimes are very short, and they are created in pairs which conserve charge, spin and other quantum properties
Uncertainty Principle E t = h/2
April 1, 2003 Lynn Cominsky - Cosmology A350
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Quantum fluctuations
Virtual particle pairs continually emerge and disappear into the quantum vacuum
If you observe the particles (hit them with a photon), you give them enough energy to become real
The particles can also get energy from any nearby force field (like a BH)
April 1, 2003 Lynn Cominsky - Cosmology A350
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Casimir Effect
Experimental evidence for virtual particle pairs Pressure is less between the plates due to modification
of the vacuum by the pairs
True vacuum
All allowed
Modified vacuum
Only integral number of allowed
April 1, 2003 Lynn Cominsky - Cosmology A350
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Negative Energy Density
Pressure difference between the true vacuum and the modified vacuum drives the plates closer together
Pressure of the true vacuum is zero The energy density between the plates is
negative, because the pressure between the plates is less than zero
Negative energy density exerts a repulsive force, keeping the plates apart, despite the force from the pressure gradient
April 1, 2003 Lynn Cominsky - Cosmology A350
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Vacuum Energy
The cosmological constant is related to the “zero-point energy” of the Universe which comes from the quantum fluctuations of the vacuum.
However, the vacuum energy density is 10120 too high to allow structure formation to occur
Something must be canceling almost all of the vacuum energy in order for us to be here
And that something must have arranged for the exact 73% of critical density to be left over at our current time, 13.7 billion years later
April 1, 2003 Lynn Cominsky - Cosmology A350
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Quintessence
Quintessence is another theory for dark energy that involves a dynamic, time-evolving and spatially dependent form of energy.
It makes slightly different predictions for the acceleration
It’s name refers to a “fifth essence” or force
April 1, 2003 Lynn Cominsky - Cosmology A350
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Gravity and pressure
RelativisticG = +3PP = /3 G = 4> 0
Non-relativistic
G = +3P
P = 0
G = > 0
QuintessenceG = +3P P = -2/3 < 0
G = -
G = +3P P = -< 0
G = - 2
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What is inflation?
Inflation refers to a class of cosmological models in which the Universe exponentially increased in size by about 1043 between about 10-35 and 10-32 s after the Big Bang (It has since expanded by another 1026)
Inflation is a modification of standard Big Bang cosmology
It was originated by Alan Guth in 1979 and since modified by Andreas Albrecht, Paul Steinhardt and Andre Linde (among others)
April 1, 2003 Lynn Cominsky - Cosmology A350
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Why believe in inflation?
Inflation is a prediction of grand unified theories in particle physics that was applied to cosmology – it was not just invented to solve problems in cosmology
It provides the solution to two long standing problems with standard Big Bang theoryHorizon problem Flatness problem
Alan Guth
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Horizon Problem
The Universe looks the same everywhere in the sky that we look, yet there has not been enough time since the Big Bang for light to travel between two points on opposite horizons
This remains true even if we extrapolate the traditional big bang expansion back to the very beginning
So, how did the opposite horizons turn out the same (e.g., the CMBR temperature)?
April 1, 2003 Lynn Cominsky - Cosmology A350
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Horizon problemThe Universe at t = 300,000 y after the
Big Bang (when the CMBR was formed)A and B are sources of photons that are now arriving on Earth
Horizon distance is 1/100 of the distance between A and B
Horizon distance is 3 x 300,000 y because the Universe is expanding – tells you how far light could travel
April 1, 2003 Lynn Cominsky - Cosmology A350
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Horizon Problem
Inflation allows the early Universe to be small enough so that light can easily cross it at early times
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No inflation
At t=10-35 s, the Universe expands from about 1 cm to what we see today
1 cm is much larger than the horizon, which at that time was 3 x 10-25 cm
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With inflation
Space expands from 3 x 10-25 cm to much bigger than the Universe we see today
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CMBR vs. Inflation
Inflation also predicts a distinct spectrum of fluctuations for the CMBR which arise from the original quantum fluctuations in the pre-inflation bubble
Everything we see in the Universe
started out as a quantum fluctuation!
April 1, 2003 Lynn Cominsky - Cosmology A350
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Flatness Problem
Why does the Universe today appear to have between 0.1 and 1 – the critical dividing line between an open and closed Universe?
Density today will differ greatly from density of early Universe, due to expansion – if starts out <1, it will get much lower and vice versa only values of very near 1 can persist
A value for =1also implies the existence of dark matter as well as the cosmological constant
April 1, 2003 Lynn Cominsky - Cosmology A350
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Flatness Problem
Density of early Universe must be correct to 1 part in 1060 in order to achieve the balance that we see
April 1, 2003 Lynn Cominsky - Cosmology A350
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Flatness Problem
Inflation flattens out spacetime the same way that blowing up a balloon flattens the surface
Since the Universe is far bigger than we can see, the part of it that we can see looks flat
April 1, 2003 Lynn Cominsky - Cosmology A350
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Big Bang Revisited
Extrapolating back in time, we conclude that the Universe must have begun as a singularity – a place where the laws of physics and even space and time break down
However, our theories of space and time break down before the singularity at a time known as the Planck time
The Planck scale refers to the limits of mass, length, temperature and time that are what can be measured using the Uncertainty principle
April 1, 2003 Lynn Cominsky - Cosmology A350
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Planck scale activity
The goal of this activity is to calculate the Planck mass, length, time and energy.
Remember
Uncertainty Principle x p = h/2
Uncertainty Principle E t = h/2
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Quantum Universe
Edward Tryon (1970) suggested that the Universe has a total E=0 because in a flat Universe, the negative energy of gravity is exactly balanced by the positive energy of matter
With E=0, there is no time limit on the Universe’s existence from the Uncertainty Principle
The quantum fluctuation Universe will collapse again due to the gravity of the singularity, unless it is given a sudden surge of energy
Spontaneous symmetry breaking of the previously unified forces provides this energy
April 1, 2003 Lynn Cominsky - Cosmology A350
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Unified Forces
The 4 forces are all unified (and therefore symmetric) at the Planck scale energy
Planck scale
The phase transition which splits off the strong nuclear force is what triggers inflation
April 1, 2003 Lynn Cominsky - Cosmology A350
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Symmetry Breaking
Here is an example: it is unclear which glass goes with which place setting until the first one is chosen
April 1, 2003 Lynn Cominsky - Cosmology A350
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Broken Symmetry
At high T, the Universe is in a symmetrical state, with a unique point of minimum energy
As the Universe cools, there are many possible final states – but only one is chosen when the symmetry breaks
April 1, 2003 Lynn Cominsky - Cosmology A350
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False Vacuum
The unified (symmetric) state of the very early Universe is a state of negative energy called the false vacuum
It is a modified vacuum like that between the plates in the Casimir experiment, because not all types of particles can exist in this state
A phase transition turns the false vacuum into the true vacuum and provides the surge of energy that drives inflation – similar to the energy released when water freezes into ice
April 1, 2003 Lynn Cominsky - Cosmology A350
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False Vacuum
During inflation, the Universe is stuck in a state of false vacuum which decays very slowly
When it reaches the true vacuum state, inflation will stop and particles will form
The shallow slope near the false vacuum allows the Universe to keep the energy density almost constant as it expands
April 1, 2003 Lynn Cominsky - Cosmology A350
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Old vs. New Inflation
There were a few problems with Guth’s original formulation of inflation that have been solved by newer theoretical models The ball represents the Higgs field
April 1, 2003 Lynn Cominsky - Cosmology A350
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Pocket Universes
As the false vacuum decays, particles are created in “pocket universes”
In each time slice, the original pocket universe expands by a factor of 3 while new ones are created out of the false vacuum in a fractal pattern
April 1, 2003 Lynn Cominsky - Cosmology A350
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Formation of child Universe
As false vacuum expands, space distorts to form a wormhole
True vacuum
False vacuum
wormhole
This entire region is 10-
25 cm
April 1, 2003 Lynn Cominsky - Cosmology A350
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Child Universe
The child universe disconnects from the original space
True vacuum
False vacuum
Child Universe
Observers in the parent universe see a black hole form!
April 1, 2003 Lynn Cominsky - Cosmology A350
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Multiverses
Universe was originally defined to include everything
However, with inflation, the possibility exists that our “bubble universe” is only one of many such regions that could have formed
The other universes could have very different physical conditions as a result of different ways that the unified symmetry was broken
New universes may be forming with each gamma-ray burst that makes a black hole!
April 1, 2003 Lynn Cominsky - Cosmology A350
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A Humbling Thought
Not only do we not occupy a preferred place in our Universe, we don’t occupy any preferred universe in the Multiverse!
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Web Resources
Cosmic Background Explorer http://space.gsfc.nasa.gov/astro/cobe/cobe_home.html
George Smoot’s group pages http://aether.lbl.gov/
University of Washington Curvature of Space http://www.astro.washington.edu/labs/clearinghouse/labs/Curvature/curvature.html
Lindsay Clark’s Curvature of Space http://www.astro.princeton.edu/~clark/teachersguide.html
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Web Resources
Ned Wright’s CMBR pages http://www.astro.ucla.edu/~wright/CMB-DT.html
Bell Labs Cosmology Archives http://www.bell-labs.com/project/feature/archives/cosmology/
Physics Web quintessence http://physicsweb.org/article/world/13/11/8Big Bang Cosmology Primer http://cosmology.berkeley.edu/Education/IUP/Big_Bang_Primer.html
Martin White’s Cosmology Pages http://astron.berkeley.edu/~mwhite/darkmatter/bbn.html
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More Resources
Inflationary Universe by Alan Guth (Perseus) A Short History of the Universe by Joseph Silk (Scientific American Library) Before the Beginning by Martin Rees (Perseus) Inflation for Beginners (John Gribbin) http://www.biols.susx.ac.uk/Home/John_Gribbin/cosmo.htm
Ned Wright’s Cosmology Tutorial http://www.astro.ucla.edu/~wright/cosmolog.htm
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