Astronomy 350 Cosmology 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 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 Group 11 Erin Gress Betsy Moore Christina Willer Give it up for Group 11! April 1, 2003 Lynn Cominsky - Cosmology A350

Cosmological curvature W = density of the universe / critical density < 1 hyperbolic geometry W = 1 flat or Euclidean W > 1 spherical geometry The Pleiades contains over 3000 stars, is about 400 light years away, and only 13 light years across. Quite evident in the above photograph are the blue reflection nebulae that surround the bright cluster stars. Low mass, faint, brown dwarfs have recently been found in the Pleiades. April 1, 2003 Lynn Cominsky - Cosmology A350

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

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 r + 3P r 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 r April 1, 2003 Lynn Cominsky - Cosmology A350

The fate of the Universe As the universe expands, the matter spreads out, with its density decreasing in inverse proportion to the volume. (V = 4pr3/3 for a sphere) The strength of the curvature effect decreases less rapidly, as the inverse of the surface area. (A = 4pr2 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

Geometry is not Destiny WMAP (and others) have determined that the Universe is geometrically flat (Wtot = 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 (L) April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 Views of the Universe April 1, 2003 Lynn Cominsky - Cosmology A350

Cosmological Constant L 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 (Wtot=1), but with only 27% matter and dark matter (WM=0.27), the other 73% must be a different type of mass-energy that we now call “Dark Energy” (WL=0.73). April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 “Anti-gravity”? According to Einstein's equations, this type of matter must be gravitationally self-repulsive. Since G is proportional to r + 3P, repulsive G means G<0 so therefore P < 0 and 3P > r Matter with this type of P and r 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

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/2p  “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 Dx Dp = h/2 April 1, 2003 Lynn Cominsky - Cosmology A350

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 DE Dt = h/2 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Casimir Effect Experimental evidence for virtual particle pairs Pressure is less between the plates due to modification of the vacuum by the pairs Modified vacuum Only integral number of l allowed True vacuum All l allowed April 1, 2003 Lynn Cominsky - Cosmology A350

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

Lynn Cominsky - Cosmology A350 Vacuum Energy The cosmological constant L 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 Gravity and pressure Relativistic G = r +3P P = r/3 G = 4r > 0 Non-relativistic G = r +3P P = 0 G = r > 0 L G = r +3P P = -r < 0 G = - 2r <0 Quintessence G = r +3P P = -2r/3 < 0 G = - r <0 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 Big Bang Timeline We are here Today’s lecture April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

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 theory Horizon problem Flatness problem Alan Guth April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 Horizon problem The 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

Lynn Cominsky - Cosmology A350 Horizon Problem Inflation allows the early Universe to be small enough so that light can easily cross it at early times April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 With inflation Space expands from 3 x 10-25 cm to much bigger than the Universe we see today April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 Flatness Problem Why does the Universe today appear to have W 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 W starts out <1, it will get much lower and vice versa  only values of W very near 1 can persist A value for W =1 also implies the existence of dark matter as well as the cosmological constant April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Planck scale activity Uncertainty Principle DE Dt = h/2 The goal of this activity is to calculate the Planck mass, length, time and energy. Remember Uncertainty Principle DE Dt = h/2 Uncertainty Principle Dx Dp = h/2 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

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

Lynn Cominsky - Cosmology A350 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

Formation of child Universe True vacuum False vacuum wormhole As false vacuum expands, space distorts to form a wormhole This entire region is 10-25 cm April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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

Lynn Cominsky - Cosmology A350 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! April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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/13/11/8 Big 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 April 1, 2003 Lynn Cominsky - Cosmology A350

Lynn Cominsky - Cosmology A350 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 April 1, 2003 Lynn Cominsky - Cosmology A350