April 1, 2003Lynn Cominsky - Cosmology A3501 Professor Lynn Cominsky Department of Physics and...

April 1, 2003 Lynn Cominsky - Cosmology A350

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Professor Lynn Cominsky

Department of Physics and Astronomy

Offices: Darwin 329A and NASA EPO

(707) 664-2655

Best way to reach me: [email protected]

Astronomy 350Cosmology


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Group 11

Erin GressBetsy MooreChristina Willer


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Cosmological curvature

= density of the universe / critical density

hyperbolic geometry

flat or Euclidean

spherical geometry


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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.


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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


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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.


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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 ()


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Views of the Universe


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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).


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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


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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.


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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


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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


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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)


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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


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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


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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


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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


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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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Big Bang Timeline

We are hereToday’s lecture


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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)


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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)?


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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


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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!


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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


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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!


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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!


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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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April 1, 2003Lynn Cominsky - Cosmology A3501 Professor Lynn Cominsky Department of Physics and...

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