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 r0 = rc 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 ~ 1050
– During this time interval, the cosmological constant was huge
– About 10120 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 . c2
• Heisenberg uncertainty principle for mass & timeDm . Dt = h / (2 . p . c2)
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 contain abundant 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 . c2
• 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 & positronsformed• 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 ~ 1:109
• 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 rm = 10–15 g . m3
• Conditions in globular clusters– Typical mass of ~ 5 . 105 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 > 1014 GeV– W / E / S & gravity join > 1019 GeV
Table 29-1: The Four Forces
7 x 10–3
The Unification of the Four Forces
Unification of Forces: Another View
http://physics.angelo.edu/~msonntag/physics1301/forces.jpg
The Early History of the Universe
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 1050
• 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
Important Concepts
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