# The Beginning and the End

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```					The Beginning
and the End
Encompassing material from
Seeds, Chapter 18
A Brief History of Beginnings
   Non mythological beginnings, that is
   Georges Lemaître and his primordial atom
   Vatican Astronomer
   Alexander Friedman: Big Bang
   Russian Mathematician
   He didn’t name the beginning ‘The Big Bang’
   It wasn’t remotely big and it didn’t go BANG!
   A pejorative term given by Sir Frederick Hoyle
   Einstein wasn’t comfortable with either theory, although he did
verify the correctness of Friedman’s mathematics
   N.B. We will have to think in very, v-e-r-y short times scales
here!
The Evidence
Hubble’s Law
   Edwin Hubble found that,
the more distant the galaxy,
the faster it was receding
from us
   Ho is the slope of this line
   Currently is thought to be ~ 73
   Ho is in units of
km/sec/Mpc
   Ultimately units of time
   Gives us the age of the
Universe!
   13.75 +/- 0.12 Gyr
The Rationale:
   According to the Red Shift of distant galaxies, the
Universe is expanding
   If the Universe is expanding, we can run the clock
backwards and find the starting point (whatever that
means)
   Important! Wrap your minds around this:
   By the beginning we don’t mean that all the matter and energy
exploded into an existing space.
   We mean that all matter, energy, SPACE and TIME all
began at this singular point.
Definitions

123rf.com
Homogeneous                  Isotropic
 The same everywhere at a    The same in every direction
certain scale
Light Cones
   A way to plot space and time
   It tells you how much
information you can have at
a certain time, limited by the
speed of light
   The x-y plane represents
space and the z axis
represents time
   Now is 0, past is -, future is +
   Not far in the past (white
arrow) only nearby events
can be known
   Events that happened long
ago (gold arrow) can be
known even if they were far
away
String-Theory
   Stems from the transition from continuum
Physics to quantum Physics at the turn of the
20th C
   Starting in the ‘80’s the notion arose that strings
were a better model for the basic constituents of
matter
   Strings were on the Planck length scale
 10-35m
 Since we can’t see detail at that scale, particles would
naturally be the first approximation
   First applied to describe strong interaction, but
the theory generated gravitons, much to
everyone’s surprise
   And strings demanded 10 dimensions!
   Feynman diagrams too convoluted to
incorporate these extra dimensions
   “Branes” are introduced to explain interactions
Dimensions
M-Theory
   String theory required 9+1 dimensions
   However, this produced 5 equally valid
variations! Unacceptable!
   A lesser known theory, Supergravity, postulated
10+1 dimensions
   Merging the two ideas resolved the 5 variations
   However, the addition of the 11thdimension
caused the strings to weave into Membranes
Insane in the
(mem)Brane
   A theory of the
“trigger”
   Multidimensional
Universe or
multiverse
   Gravity is the
weakest force
because it stretches
between branes and
is diluted
   Intersection of
branes initiates a BB
   So time didn’t have
to begin with the
BB
Other Dimensions
   Flatland, a Romance in
Many Dimensions
   Edwin Abbott Abbott,
1885
   A square and his wife in
Flatland

   An introduction to
greater dimensions
Lisa Randall
   Astrophysicist at
Harvard
proponent
   Warped Passages:
Unraveling the Universe's
Hidden Dimensions
Hugh Everett…
How the Universe Got Its Spots
Jenna Levin and others
propose a more
topological description
of cosmology than
String Theory
However it started…
Epochs
   We divide the early history of the Universe up
into epochs:
   Planck Era: unknown by present theory
t <10-43sec
 GUT Epoch 10-43 < t < 10-36sec
 Inflationary Epoch 10-36 < t < 10-34sec

 Electroweak Epoch 10-34 < t < 10-12 sec

 Particle Epoch 10-12 < t < 1 second
Continued…
 Nucleosynthesis Epoch 1 sec < t < 3 min
 Nucleii Epoch 3 min < t < 380,000 years

 Atom Epoch 380,000 < t < 1 Gyr

 Galaxy Epoch 1 Gyr until now and beyond

   All times approximate 
Planck Epoch
   No Physics exists to describe the cosmos previous to
this time: 10-43 seconds (unless M-theory bears out)
   Impossibly high temperatures (1032K), inconceivably
tiny universe (10-35m) at the end of this brief epoch
   All four fundamental forces—strong, weak,
electromagnetic, and gravity-–were expressed as one.
   Unified by the high energy/temperature into a single force
GUT Epoch
   GUT stands for Grand Unified Theory
   It was during this epoch that the electro
magnetic* force and gravity separated from the
strong force
   Also known as symmetry breaking during a phase
transition, (like water to ice)
   1027K
   Ending around 10-36 seconds
*AKA the electroweak force
TOE: Theory of Everything
GUT: Grand Unified Theory
Inflation occurred here, when gravity split from the other forces.
   Proposed by Alan Guth of MIT in the early 1980s, Inflation
does a good job of explaining the Universe as we see it today
   During this era the early Universe expanded faster than the
speed of light
   Not a violation of SR since nothing is actually moving > c
   It solves the flatness problem, the horizon problem, and the
monopole problem
   Flatness: why W (total energy density of the universe) is so close to Wcrit
   Horizon: why the CMB varies so little
   Monopoles: N or S magnetic pole w/o the other
   However, and this is a strong however, it is merely the best current
theory, not to be considered written in stone
   Theories like Newton’s Law of Gravitation and
Einstein’s General Theory of Relativity are
testable and have been verified many, many times
   Inflation is not yet testable because the energies
are too high to be currently reproduced in the
laboratory
   Furthermore, direct evidence supporting
primordial inflation is not visible because it
happened long before the Universe was
transparent
   Therefore, if you google inflation times,
temperatures, and other parameters, you will
find a variety of values, all depending upon
which ‘flavor’ of inflation they were derived
   There are limits to when events could begin and end,
and maximum and minimum energies involved, but
the numbers presented here are not immutable
   And the true nature of dark matter / dark energy
is at best fuzzy
Inflationary Epoch
   As the name implies, a period of enormous expansion
   The Universe grew from 10-28 m to 1016 m
   To put this in perspective, think of the size of a proton
compared to a parsec!
   The Universe cooled, as any expanding system of
particles would, then reheated shortly after inflation
ended.
   The energy used to ‘push’ the Universe outward was released
as heat
You
are
here
Where Inflation Comes From
   Current theory holds that a different value of the
cosmological constant, Linflation , was present during
this epoch
   This formed an inflaton field, a type of scalar field
   You can think of a scalar field like gravity near the ground—
the higher you go the more potential for falling fast you have
   Invoking a scalar field is common in theoretical physics,
and perfectly legal, but it doesn’t make a theory true.
For that, real evidence is required
   And from observation, the Universe is in a period of
inflation now, with the current scalar field being dark
energy (whatever that is)
How Inflation Fixes Flatness
   The Flatness problem: the ratio of the current energy
density (W) of the Universe to the critical density is 1
   Doesn’t seem like much, but when you allow for
expansion and run the clock backwards, the ratio
differs from 1 (perfectly flat) by one part in 1060!
   This is about as likely as everyone in the world winning the
California lottery every time 1035 in a row!!
   Inflation fixes this by essentially flattening all the
‘bumps’ in the Universe, much like inflating a balloon
smoothes out all the wrinkles
k is currently very close to zero; 0 means flat
How Inflation Fixes Horizons
   The temperature of the Universe is remarkably uniform
on a large scale

COBE, predecessor to WMAP
Horizons
   Think of a horizon as the furthest distance than
can be seen for which there is time for light to
travel
   If an event happens in one region that would
affect another region, then there must be
sufficient time for the effect to travel that
distance
   Remember the light cone!
   Run the clock backwards. It turns out that, given the
short time scales involved, there was insufficient time
for energy to travel from one region to another, a
necessary condition for a near-uniform temperature
   The same smoothing function that inflation provided to
solve the flatness problem also inhibited any thermal
inhomogeneities that may have existed by pushing the
horizon father away
   In other words, regions flew apart too fast and could
not communicate with each other
   Events that occurred before inflation were wiped from
the cosmic record
   You can almost say the Big Bang started with inflation!
   What Physicists call “Initial Conditions”
Better than COBE…WMAP
   The red regions are where
CMB photons, losing energy
as they climb out of a
gravitational potential, are
red-shifted
   And the reverse, of course
   VERY small differences in T,
a result of inflation
   The CMB predates stars and
galaxies, but shows the
boundaries of gravitational
potentials where they can be
expected to form
Dark Matter/Energy
   Horizons and Flatness are
inter-related
   The geometry of the
Universe is determined by
the amount of dark energy*
   Left: the scale of the CMB
fluctuations in the WMAP
picture indicate curvature
   Open if the fluctuations < 1/2o
   Flat if ~1o, closed if > 1o
   Ultimately determines the             *perhaps it’s Vacuum Energy, the energy allowed
fate of the Universe                  in an empty void by quantum mechanics
A More Familiar Negatively-
Curved Shape
WMAP Tells the Tale
If the Universe is flat, the angle is 1o

If it is curved inward (closed) the
angle is > 1o

If it is curved outward (open) the
angle is < 1o
Current Mix of Cosmological
Stuff
   W is very close to Wcrit
   Or, if you prefer, CMB
fluctuations very nearly 1o
   Small changes in the
proportions will change
the shape of the
Universe
   L just might be Dark
Energy
   A constant density
   Part of space-time itself,
not residing within
Vacuum and/or Dark Energy

   Very low energy density
   1X10-8 ergs/m3
   If the whole Earth volume were V.E. it would be about 1 day’s worth of
electricity for 1 person
   The Quintessence (L) is B-A-C-K!
   If true, then constants evolve
How Inflation Fixes Monopoles
   A monopole is like a single-pole magnet, only as a
North pole or a South pole, not a pair
   Quantum Mechanics predicts their formation from
‘topological defects’ in the divergence of the four forces
as the Universe cooled, part of the phase transition
mentioned before
   Because inflation pushed the Universe to be so big so
quickly, the few monopoles that may have formed are
e-x-t-r-e-m-e-l-y rare.
   You may find 1 monopole in 1061 Mpc3!
   The Universe is only 1011 Mpc3 in volume
Electroweak Epoch:
after inflation
   During this time the Universe cooled enough
for so-called symmetry breaking
   This is when the four forces fully divided
 Strong Nuclear Force
 Weak Nuclear Force

 Electromagnetism

 Gravity

   Epoch sometimes called quark soup
You
are
here
Particle Epoch
   Quarks cool and form more massive particles
 Two up and one down = p+
 Two down and one up = N
   Interactions abound
   mN > mp so more p than N
   Heavy decays to lighter
   6p for 1N
   Too hot for nuclei to form
   Universe has cooled to 109K by end of era
   The “Freeze Out”; baryons cease to perish in the
high temperature
You
are
here
Nucleosynthesis Era
   Universe cools to 3000K
   1s < 3 min
   Atoms formed (ionized):
   N half-life ~ 15 minutes
   By 3 minutes, 14p for 2N
   Some neutrons had decayed into protons
   2p + 2N = He
   So out of 16 nucleons, 1 He for 12 H
   Hydrogen, including deuterium (75% by mass)
   Helium (25% by mass)
   Lithium (109 < He)
Standard Model verifies Big Bang
Cosmology!
   1948: Ralph Alpher and George Gamow did these
calculations
   Alpher’s Ph.D dissertation
   Tried to get all the elements from this process, but
expansion prohibited the formation of heavier elements
   The exact ratios of H, 4He, 3He, Li, D were
determined by the total number of baryons at t = 1
minute
   We can therefore tell just how many baryons there
are, i.e., 4% of all matter
   The blue strip
is in the range
of observed
abundances
   See how 4He is
right round
25%
   So knowing the
density and the
size of the
universe, we
can calculate
the mass of
baryons (just like
the CAPER  )

CalTech
Atom Epoch
   3 min < t < 380,000 years
   Universe cools enough for electrons to attach to
atoms
   Down to 18 K by end of era
   Universe becomes transparent, photons free to
travel
   The “Last Scattering”
   CMB starts now!
   ½ of 1% of radio noise is CMB
Stelliferous Era
   From about 380,000 years A.B.B (after the Big Bang) until now
   Galaxies at about 1 billion A.B.B
   Average temp = 3K
   The era of stars, galaxies, and us
   What we’ve talked about most of the semester!
   Top down vs. bottom up
   Did massive clouds of gas form first, generating the stars (top down) or
did stars form first, collecting into galaxies (bottom up)?
   Probably a combination
   Where gas was dense enough, stars formed first
   Where gas was rarefied, dark galaxies formed, later yielding stars
   Era will continue until the year 100 trillion A.B.B

Youngest object ever imaged @ 800MYr A.B.B 
The First Stars
The Universe at 2 Gyr Old
Hubble Ultra Deep Field
   1 million second
exposure
   Red shifts allow for
dating and therefore 3D
imaging
   Looking back to 700
million years A.B.B.
   The last image shows a
red galaxy, the earliest
object ever imaged
And here we are today…

What will happen in the distant future?
Fate
The Friedmann Equation

   A way to predict the future!
   See H, the Hubble parameter?
   r is the average density of the Universe
   a is the scale factor, in essence, the distance scale
   k is the curvature of the Universe (-1,0,1)
   L is Einstein’s revived cosmological constant:
Entropy vs Gravity (curvature)
   Entropy: a thermodynamic law dictating the
inevitable march to disorder
 Simple disorder, like breaking glass
 Thermodynamics disorder: concentrations of energy,
as in a star
 The ‘arrow’ of time

   Gravity (curvature) pulls together (order),
entropy corrupts (disorder) over time
Expansion
   The Universe continues to
expand
   Expansion occurs from dark
energy
   Where matter is closely
spaced, gravity (curvature)
overwhelms L
   Elsewhere L wins
   And ultimately L will win!
The Future:
   The most likely* outcome will be the open Universe
   AKA The Big R.I.P.
   The actual density of the Universe is less than the
critical density
   W/Wc ~ 1
   *Actually too small to ever measure accurately for proper
prediction
   The Universe will expand forever
   Three Foreseeable Epochs (after the Stelliferous Era):
   The Time of Degeneracy
   The Time of Black Holes
   The Time of Photons
But first…
   A way to get a handle on these massive time scales
   Remember from our first lectures, the idea of powers of 10?
   101 = 10
   102 = 100
   103 = 1000, etc
   Let’s define a cosmic decade, 10t years
   101 years is the first cosmic decade, 102 is the second, and so on
   Like stairs where every next step is 10X the height of the last
   We are in the 10th cosmic decade
   The Stelliferous Era will last to the 14th cosmic decade
The Time of Degeneracy
   Not about deplorable behavior: how matter behaves
   Quantum Claustrophobia
   From cosmic decade 14 to 37
   How do we know?
   From the mean half-life of a proton, 1037 years
   Few stars, only when two Brown Dwarfs collide
producing a red dwarf
   Once in a while, two White Dwarfs may collide and
produce a supernova
   Pop quiz: which type?
   If not, all WDs will shine away all their energy
   The End of Structure
The Time of Black Holes
   Cosmic Decade 37 to 100
   How do we know?
 Steven Hawking determine the rate of black hole
evaporation, now know as Hawking radiation
 Particle pair production near the event horizon
 Due to the stretching of space-time
 One particle falls in, the other escapes

   ‘Cooling’ time can be calculated
The Time of Photons
   Cosmic Decade 100 until ???
   Very long wavelength photons
   Cold, dark
   Entropy wins
   Or does it?
   Very difficult to make predictions 10100 years in the future
   Could be that new complexity begins
   From other ‘branes’
   Via processes we can’t imagine
But this will all happen after the final exam 

THANK YOU FOR YOUR
INDULGENCE!

```
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