27. Exploring the Early Universe Rapid inflation of the early Universe Mass & energy formed during inflation Most matter & antimatter annihilated each other Neutrinos & helium are primordial fireball relics Galaxies formed from early density variations Grand Unified Theories unite all physical forces Cosmic strings & other oddities may be relics Grand Unified Theories suggest 11 dimensions Rapid Inflation of the Early Universe Two fundamental problems The isotropy problem The cosmic microwave background is uniform to 1:10,000 Opposite sides are much too far apart for this to occur The flatness problem What could have made ρ 0 = ρ c to 50 decimal places? This is necessary to produce a flat Universe Too little mass would have ended up with no galaxies Too much mass would have ended up with a Big Crunch One possible cause Rapid inflation very shortly after the Big Bang Possible Causes of Cosmic Inflation One possible solution to the problem of isotropy A very early & very brief period of inflation Lasted only ~ 10 24 seconds Universe expanded by a factor of ~ 10 50 During this time interval, the cosmological constant was huge About 10 120 times larger than Einstein envisioned One possible solution to the problem of flatness We see only a tiny fraction of the Universe Our particle horizon is a sphere This sphere enlarged so much that its surface looks flat Similar to one acre of land on the Earth s spherical surface The Isotropy Problem Inflation & the Observable Universe Inflation Solves Flatness Problem
Mass & Energy Formed During Inflation Matter at two scales Super -atomic scale Everyday experience Location & momentum can be precisely known Accuracy depends on measuring instruments Sub -atomic scale High-energy physics Location & momentum cannot be precisely known Accuracy depends on fundamental nature of matter Quantum mechanics Fundamental nature of matter at the smallest scale Heisenberg uncertainty principle for location & momentum EMR is needed to measure location & momentum of an electron Either location or momentum will be changed by the observation Heisenberg uncertainty principle for energy & time Special relativity asserts that E = m. c 2 Heisenberg uncertainty principle for mass & time Δm. Δt = h / (2. π. c 2 ) Some Aspects of Quantum Mechanics Ambiguity of mass & time Uncertainty regarding mass over very short times Empty space might contain no mass Empty space might containabundant mass Virtual pairs of particles spontaneously appear The more massive they are, the less time they exist Property of particle symmetry Two particles are always produced One particle has + charge & the other charge The overall electrical charge of the Universe does not change Supporting observational evidence Lamb & Retherford detect H spectral irregularities Disturbing effects of virtual particles on H orbital electrons Extremely small shift in spectral line positions Virtual Pairs Can Become Real Pairs Observational evidence Two highly energetic gamma rays collide Photon pairs disappear Particle & antiparticle pairs appear Combined photon energy > m. c 2 More energy produces more massive particles Accepted interpretation of that evidence Photon collisions convert virtual pairs into real pairs Particle accelerators are used to study this phenomenon Annihilation occurs when particles recombine Photon pairs appear Particle & antiparticle pairs disappear Relevance to cosmology Processes active during the inflationary period Virtual Pairs Can Appear & Disappear Annihilation in the Primordial Fireball Mass & energy formed as part of the Big Bang The mass was in the form of matter & antimatter Temperature & pressure were both extremely high Collisions were frequent & energetic A condition of thermal equilibrium existed Mass-to-energy & energy-to-mass processes in balance The primordial fireball cooled quickly By t = 10 4 sec, all protons & neutrons formed Annihilation decreased the Universe s mass content Resulting energy contributed to the primordial fireball By t = 10 0 sec, all electrons & positrons formed Annihilation decreases the Universe s mass content The resulting energy contributed to the primordial fireball A Truly Remarkable Dilemma The symmetry problem Annihilation left an excess of matter over antimatter Perfect symmetry would produce only energy Any remaining antimatter would annihilate matter Gamma rays would be the result Gamma rays observed from some parts of the Universe Number & energy are both inconsistent with annihilation Symmetry-breaking somehow occurred The (proton + neutron) to photon ratio is ~ 1:10 9 The odds were a highly unfavorable one billion to one!
Virtual Pair Production & Annihilation Collision of Relativistic Gold Atoms Neutrinos & Helium Are Fireball Relics Neutron decay Free neutrons are unstable Radioactive Half-life of ~ 630 seconds Daughter products: 1 proton + 1 electron + 1 antineutrino By t = 2 sec, neutron decay had commenced Number of neutrons in the Universe decreased radically Nucleosynthesis The deuterium bottleneck prevented He formation Gamma rays too energetic for the synthesis process By t = 3 minutes, the Universe cooled even more Gamma rays too weak to prohibit the synthesis process Helium quickly formed The proton to neutron ratio stabilized a ~ 6:1 By t = 15 minutes, too cool for nucleosynthesis Only H, He, Li & Be were present in appreciable numbers Nucleosynthesis in the Early Universe Galaxies Formed from Density Variations Recombination ~ 300,000 years after Big Bang The Universe was cool enough for neutral H Photon interactions became very rare Matter decoupled from radiation The Universe thus became transparent The neutral H was very uniformly distributed Very small density variations did exist The characteristics of density variations Gravity & pressure oppose each other The gravity increase tends to contract the gas cloud The pressure increase tends to expand the gas cloud Gravity & pressure balance at some point James Jeans 1902 Density fluctuations larger than the Jeans length grow Density fluctuations smaller than the Jeans length dissipate Globular Clusters & Jeans Length Conditions at recombination T = 3,000 K ρ m = 10 15 g. m 3 Conditions in globular clusters Typical mass of ~ 5. 10 5 M Typical diameter of ~ 100 ly Identical to the Jeans length for typical globular clusters Observations of globular clusters They contain the oldest known stars They may have been among the first structures formed Complicated by the discovery of dark matter Known only by its gravitational effects
Microwave Background Variations The Growth of Density Fluctuations Globular Clusters ~ Jeans Length Cold & Hot Dark Matter The fundamental problem The nature of dark matter is unknown Many models have been suggested Computer models Cold dark matter High mass particles, low speed Galaxies form from the bottom up Initial small clumps of matter coalesce into larger clumps Hot dark matter Low mass particles, high speed Galaxies form from the top down Initial large clumps of matter break apart into smaller clumps Cold Dark Matter Simulation Grand Unified Theories Four basic forces Gravity Weakest of all Only attractive Electromagnetism Second strongest Both attractive & repulsive Strong Strongest of all Only attractive Weak Second weakest Only attractive Thought to be identical at very high energies Weak & electromagnetic join > 10 2 GeV Easily achieved in particle accelerators W / E & strong join > 10 14 GeV W / E / S & gravity join > 10 19 GeV
Table 29-1: The Four Forces The Unification of the Four Forces 7 x 10 3 Unification of Forces: Another View The Early History of the Universe http://physics.angelo.edu/~msonntag/physics1301/forces.jpg Cosmic Strings & Other Oddities Vacuum & symmetry Asymmetric true vacuum Truly empty space Visualize pencils standing on their points The pencils do not point in any direction in XY plane Symmetric false vacuum More energy Visualize pencils fallen on their sides The pencils do point in some direction in XY plane The possibility of cosmic strings Clusters of fallen pencils keep some pencils upright Symmetry remains intact at that location This is analogous to cosmic strings One possibility for dark matter Symmetry Breaking & Cosmic Strings
Distribution of ~ 400,000 Galaxies A Universe With 11 Dimensions? Hidden dimensions of space Einstein joined space & time into spacetime 1905 Four dimensions Theodor Kaluza proposed a fifth dimension 1919 Gravity & electromagnetism both warp spacetime Fifth dimension is curled up too tightly to be observed Oskar Klein 1926 Make Kaluza spacetime compatible w/quantum mechanics Foundations of Kaluza-Klein theory Edward Witten All four forces best explained by 11 dimensions Ten dimensions of space & one dimension of time The seven extra dimensions are curled up very tightly This suggests the existence of very massive particles These have not yet been observed Spatial Dimensions Too Small To See Cosmic inflation The isotropy & flatness problems Can be solved by cosmic inflation Lasted ~ 1 24 sec Universe grew by 10 50 Important Concepts Cosmological constant was huge The role of quantum mechanics Heisenberg uncertainty principle Location-energy & mass-time Virtual pairs of particles Can become real due to gamma-rays Extremely hot Universe Production & annihilation equal Cooling Universe Production & annihilation unequal Nucleosynthesis of H, He, Li & Be Slight excess of matter over antimatter One extra particle per billion Density variations & galaxy formation Extremely delicate mass balance The Jeans length Variations must be quite large Globular clusters formed very early Grand Unified Theories (GUTs) All four natural forces are united Extremely high energies Cosmic strings Remnants of primordial symmetry Extremely massive May help explain dark matter An 11-dimensional Universe Best explains four unified forces Extra 7 dimensions are tightly wound Too small to be directly observed