Astronomy 182: Origin

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Astronomy 182 Origin Evolution of the Universe
Lecture 15


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Assignments
For today Essay due on Ferris, Chapter 9 May
23 Final essay due (please discuss your
proposed topic with me in advance) May 30
Final exam in class

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Today
Unification in Particle Physics The Inflationary
Scenario
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Brief History of Unification
1800s electricity magnetism given a unified
description in Maxwells theory of
Electromagnetism 1960s Electromagnetic weak
interactions unified in electroweak theory
(Glashow, Weinberg, Salam) 1970s Electroweak
strong interactions unified in Grand
Unified Theories 1980s-20?? Unify electroweak,
strong, and gravitational interactions in
Superstring Theory
well-tested
speculative
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Higgs field breaks Electroweak Symmetry gives
mass to all particles
Last Undiscovered Ingredient of the
Standard Electroweak Model of Particle Physics
Fermilab or CERN
Beyond the Standard Model
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(Bosons integral spin particles)
Electromagnetic
Grand Unified Theories
Electroweak (Standard Model)
Weak
Strong
Grand Unified Theories (GUTs) unify the first 3
3 interactions into a single symmetry, but leave
out gravity
Gravity
String Theory attempted unification of all 4
interactions
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Supersymmetry (SUSY)
Hypothetical symmetry between bosons (particles
with integer spin 0,1,2) and fermions
(particles with half-integer spin). Pros (1)
can help explain why there is such a huge
disparity in energy between the
electroweak and GUT or Planck scale
(2) grand unification of electroweak strong
forces at GUT scale appears more natural
in SUSY theory (running coupling) Puzzle Like
the electroweak symmetry, SUSY must be a broken
symmetry in Nature (we havent discovered
any of the predicted SUSY partner
particles yet). The mechanism of SUSY breaking
remains a mystery (its not due to a Higgs
field).
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String Theory
Coupling Constants Of the Different
Interactions Unify at 1015 GeV in theory
w/ Supersymmetry
GeV
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Theory of Everything
The Quantum Field Theory marriage of Quantum
Mechanics and (Classical) Fields has
generated an extraordinarily successful model
of Fundamental particles the Standard
(Electroweak) Model and Quantum Chromodynamics
(theory of Strong Interactions). However,
one field has so far resisted Quantization the
gravitational field. We do not yet have a
successful theory that marries Quantum
Mechanics with General Relativity. Quantum
Theory of the Gravitational Field is plagued with
unphysical infinities. As a result, we do
not have a Theory of Everything that unifies
Gravity with the 3 other fundamental
interactions. Superstring Theory is the current
(best) hope for realizing this.
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Spacetime Foam
At a lengthscale LPlanck (hG/c3)1/2 10-33 cm,
the Planck length, the quantum fluctuations
of the gravitational field become large,
and the classical picture of a smooth(ly
distorted) spacetime breaks down (and with
it, our notions of space time). These violent
ultra-small-scale fluctuations lead to
infinities in the equations of quantum
gravity.
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String Theory
Postulates that all particles are, at the
ultra-microscopic scale, not point-like but
instead are excitations of extended
1-dimensional strings. These strings have a
characteristic lengthscale of the Planck
length. The extended nature of the strings
smooths out the violent Planck-length
fluctuations of the gravitational field and
gets rid of the associated infinities. It turns
out that all the matter and charge carrier
particles can be described in terms of string
vibrational modes. String theory is thus a
candidate Theory of Everything that unifies all
the fundamental interactions in a single
theory.
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Photon Gluon
10-31 mm
String
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Features of Superstring Theory
Supersymmetry (SUSY) hypothetical symmetry
relating fermions (spin-1/2 particles) with
bosons (integral-spin particles). This
symmetry predicts existence of many new
particles, which may be discovered at
particle accelerators. SUSY is a natural
outcome of String Theory. Extra Dimensions
Superstring Theory naturally lives in 10
spacetime dimensions. Since we only observe
4, the other 6 must be hidden. Two choices
(a) they are very small, of order the
Planck length, or (b) we are confined to only 3
of the 9 space dimensions (3-d membrane).
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Symmetry breaking Phase Transitions Cosmology

• As in a Ferromagnet, or as in ice ? water, at a
  Temperature
• above 100 GeV, the broken Electroweak
  symmetry should
• be restored the Higgs field is driven to zero
  everywhere, and the
• W,Z and all other matter particles become
  massless. Conversely,
• as Universe cools below 100 GeV, the Higgs
  field
• evolves away from zero to its non-zero
  low-Temperature value.
• Early Universe may have gone through several such
  
• Symmetry-breaking Phase Transitions associated
  with different
• Higgs fields. Depending on the type of
  symmetry broken, such
• transitions can have interesting consequences
  for cosmology
• Topological Defects
• Inflation
• Early Universe as a Laboratory for Symmetry
  Unification

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Potential energy density
High Temp.
High Temperature Symmetry is restored, ?
0. Low Temperature Symmetry is broken ?
or -
Low Temperature
?
Higgs field
Higgs Field
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Cosmological effects of Phase Transitions also
depend on the speed of the transition (relative
to the expansion rate) Second order
transitions are fast (the field evolves
continuously from its high-Temperature to
low-Temp. state) First order transitions are
slower field must quantum tunnel through
an energy barrier and can get hung up in the
wrong
(high-Temperature) state
Potential Energy Density
Second-order transition
Low-Temperature state
High-Temperature state
Higgs field value
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Cosmological effects of Phase Transitions also
depend on the speed of the transition (relative
to the expansion rate) Second order
transitions are fast (the field evolves
continuously from its high-Temperature to
low-Temp. state) First order transitions are
slower field must quantum tunnel through
an energy barrier and can get hung up in the
wrong
(high-Temperature) state
Potential Energy Density
Low-Temperature state
High-Temperature state
Higgs field value
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Inflation
An epoch generally associated with some scalar
field that takes a cosmologically long time
to evolve to its (low-Temperature) ground
state. During this time, the potential energy
density of the Scalar field comes to dominate
over other forms of energy (e.g., in radiation
or massive particles) in the Universe. While the
field is stuck in its high-Temperature
state (or slowly evolving from it), the energy
density of the Universe is approximately
constant (rather than decreasing with time,
as it does during all other epochs). This
implies H constant (approximately) and that the
scale factor grows roughly exponentially in
time. This is the sign of an accelerating
Universe trapped field acts as a (temporary)
cosmological
constant.
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The Inflationary Scenario
Theory arose 1980 (Alan Guth) from thinking
about the cosmological consequences of slow
symmetry-breaking Phase Transitions in the
early Universe. Motivations
horizon/homogeneity, flatness, and structure
problems. Why is the Universe homogeneous,
isotropic, and nearly flat? These are not
robust features of the standard cosmology.
How can large-scale structure form without
violating causality?
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and Horizons
As the Universe ages, we see more and more
galaxies (other observers) at larger
distances Going back in time, we see a
smaller fraction of the Universe Other
observers were outside our horizon
radius a(t1) Cosmic Scale Factor
radius a(t2)
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Horizons the CMB
COBE satellite showed that the Cosmic Microwave
Background radiation is isotropic to 1 part in
105 over the whole sky. This is a puzzle
different regions of the CMB separated by
more than 1 degree or so in angle were, at the
time of Photon decoupling/recombination (105
years after the Big Bang) outside each
others horizon, not yet in causal contact.
Theres no reason these causally disconnected
regions should have been at the same Temperature!
No physical process acting since the Big Bang
could have established this uniformity if it
wasnt there at the beginning. Why then does the
Universe appear isotropic homogeneous on
large scales? HORIZON PROBLEM
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CMB Sky Points A and B separated by more than
few degrees were not in causal contact at
decoupling
Horizon of observer B at time of
decoupling
A
B
45o
Big Bang t0
Us, today
Photon Decoupling (Last Scattering
Surface) t 300,000 yr
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Structure/Causality Problem
Another symptom of the Horizon problem The
Large-scale structures we see today were, at
early times, larger than the horizon. Thus, the
seeds for structure (density perturbations
which were amplified by gravity into
galaxies, etc) could not have been made
causally unless you wait until very late times
(and we have no theory of how to form seeds at
late times).
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Flatness Problem
CMB observations indicate that the observable
Universe (within our present horizon) is nearly
flat ? 1 As the Universe evolves, the spatial
(3D) curvature generally becomes more
important with time Saddle universe (k -1)
rapidly becomes empty Spherical universe (k
1) should recollapse rapidly. Natural timescale
for these rapid events is the Planck time,
tPlanck LPlanck/c 10-43 seconds! But our
Universe still appears almost flat 1017 sec
1060 Planck times after the Big Bang. The
Universe must have been fine tuned to be
very precisely flat at the Planck time for it
still to be roughly flat today.
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Problems of Initial Conditions
Neither flatness nor homogeneity are robust
features of the standard cosmological model
they are unstable conditions. If the early
Universe had been slightly more curved or
inhomogeneous, then it would look much
different today. The present state of the
observable Universe appears to depend
sensitively on the initial state. If we consider
an ensemble of Universes at the Planck
time, only a tiny fraction of them would
evolve to a state that looks like our Universe
today. Our observed Universe is in some (hard
to quantify) sense very improbable.
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God may not play dice, but perhaps S/He throws
darts...
Each point in the green dart board represents
the initial condition for a possible Universe
Us, now
today
time
Big Bang t tPlanck
Most Universes look less less like ours does as
they age God must have been extremely lucky or
able to have made our Universe.