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 MSun

– 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