Introduction to Cosmology

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The History and Fate of the Universe
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The History and Fate of the Universe

• Will the Universe expand forever?
• Or will it stop expanding and collapse (a Big
  Crunch)?
• What was there before the Big Bang?
• Is the Universe infinite or just really, really
  big?

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The Microwave Background

• The microwave background is extremely uniform
  over the whole sky. This is what demonstrates
  that it must be from the early Universe and not
  from, for example, hot dust in intergalactic
  space.

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The Microwave Background

• When we look at the variations in temperature
  over the sky, we find first that, because the
  Earth is moving through space, the microwave
  background is redshifted in one part of the sky,
  and blueshifted in the opposite part of the sky.

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The Microwave Background

• When the Earths motion is removed, the
  distribution of microwaves on the sky becomes
  more uniform again. Here we see that sources in
  the plane of the Galaxy are emitting microwaves
  that interfere with the cosmic signal.

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The Microwave Background

• With emission from cold gas in the Milky Way
  removed, the remaining distribution becomes very
  (but not perfectly) smooth. The remaining
  fluctuations you see here are primordial  dating
  from the time when the Universe was just 380,000
  years old.

The fluctuations are only a few parts in 10,000!
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The Microwave Background

• Higher temperatures means higher densities and
  pressures. The red areas are over-dense by a
  factor of 1.00004.

From these primordial density fluctuations come
todays galaxies and clusters.
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Formation of Structures

• Over time, the very small density fluctuations of
  the early universe have been amplified many times
  by gravity. The galaxies and clusters we see
  today grew from the very small fluctuations in
  the microwave background.

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Formation of Structures

• Over time, the very small density fluctuations of
  the early universe have been amplified many times
  by gravity. The galaxies and clusters we see
  today grew from the very small fluctuations in
  the microwave background.

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Formation of Structures

• Over time, the very small density fluctuations of
  the early universe have been amplified many times
  by gravity. The galaxies and clusters we see
  today grew from the very small fluctuations in
  the microwave background.

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History of the Universe

• The Big Bang occurred 13.7 billion years ago.
  Since then
• 10-43 seconds ???? Grand unification
• 10-35 seconds Quarks form gravity begins to
  exist
• 10-12 seconds Particles form and annihilate
• 0.00001 seconds Protons, neutrons form
• 3 minutes Fusion of hydrogen to helium ends
• 380,000 years Release of the microwave
  background
• 400,000,000 years Milky Way begins to form
• 2,000,000,000 years Era of galaxy
  formation/interaction
• 9,000,000,000 years Birth of the Sun

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Formation of Galaxies

• The hot gas of the early universe cools and, with
  the aid of gravity, gets turned into galaxies and
  clusters of galaxies.

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Formation of Galaxies
Over time, the very small density fluctuations of
the early universe have been amplified many times
by gravity.
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The Fate of the Universe

• Will the Universe expand forever?
• Or will it stop expanding and collapse (a Big
  Crunch)?

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The Fate of the Universe

• The Universe was once small now it is large.
  The only force slowing the expansion is gravity
  the more mass, the more gravity, and the more
  deceleration that will occur.

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The Fate of the Universe

• The Hubble Law implies 3 possible fates for the
  universe
• The universe expands forever unbound, or open
  universe

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The Fate of the Universe

• The Hubble Law implies 3 possible fates for the
  universe
• The universe stops expanding and collapses
  bound, or closed universe

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The Fate of the Universe

• The Hubble Law implies 3 possible fates for the
  universe
• The universe is exactly balanced between closed
  and open marginally bound, or flat universe

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• Each of these possibilities corresponds to a
  certain geometry for the Universe as a whole
• A bound Universe has the geometry of a
  four-dimensional sphere
• A marginally-bound Universe is flat, like a plane
• An unbound Universe is like a four-dimensional
  saddle

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Empty Universe Constant Expansion Rate
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Open Flat Universe Slowing Expansion Rate
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The Deceleration of the Universe

• The fate of the Universe depends on both its
  expansion rate (the Hubble Constant) and its
  density. Measuring density directly is hard,
  since 90 of the mass is invisible (dark matter).
  But by looking into the past, we can see how the
  Universe has decelerated. For either a closed or
  open Universe, the Universe should have expanded
  faster in the past than today.

now
past
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The Deceleration of the Universe?
Type Ia supernovae can be used as standard
candles to look across the universe and measure
the deceleration via a Hubble Diagram. This was
done in 1998. The answer was
The Universe was expanding more slowly, not more
rapidly, in the past. The Universe is not slowing
down at all, in fact, its speeding up!!! We
live in an accelerating Universe! Its as if
theres another force pushing the universe apart
some sort of anti-gravity  its like throwing
a baseball into the air, and finding that it
accelerates as it moves upward!
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Deceleration Acceleration of the Universe
Actually it is a bit more complicated than that.
When the Universe is smaller, matter has more of
an impact on how it grows (recall gravitys
inverse square law). So for a few billion
years, the expansion was decelerating due to the
influence of gravity. But as gravity weakened
with time, thanks to the expansion of the
Universe, the anti-gravity began to win out. The
expansion began to accelerate. And this is the
state we find ourselves in today
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The Decelerating-Accelerating Universe
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The Age of the Universe

• If there were no mass (i.e., no gravity) in the
  universe, the Hubble expansion would proceed at a
  constant speed. The age of the universe would
  then just be given by 1 / H0.

In a real universe with mass, gravity must have
(over time) slowed the Hubble expansion. In the
past, the galaxies must have been moving apart
faster. The age must therefore be less than
1/H0. If you can measure H0, you can estimate the
age of the universe.
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The Age of the Universe

• Our current measurements give a value of the
  Hubble Constant of H0 72 ? 8 km/s/Mpc. This
  implies an age for the Universe of lt13 billion
  years.

But the stars in globular clusters are at least
13 billion years old. How can some stars be
older than the Universe? Did we do something
wrong ?
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The Age of the Universe

• Our current measurements give a value of the
  Hubble Constant of H0 72 ? 8 km/s/Mpc. This
  implies an age for the Universe of lt13 billion
  years.

Our estimate of the age of the Universe was based
on the current expansion rate of the universe and
an assumption that the universe expanded more
rapidly the past. But the universe is actually
accelerating and was expanding more slowly in the
past, which produces an older age of 13.7 billion
years that agrees with globular cluster ages.
But the stars in globular clusters are at least
13 billion years old. How can some stars be
older than the Universe? Did we do something
wrong ?
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The Accelerating Universe

• Einstein postulated the existence of a
  Cosmological Constant, an anti-gravity force
  present with the same strength everywhere in the
  Universe, for all time. He postulated it to
  prevent the gravitational collapse of the
  Universe, and went to his death thinking that he
  had been wrong, and that the Cosmological
  Constant was unnecessary because the observed
  Hubble expansion of the universe would keep it
  from collapsing.

But he was right after all!
32
The Accelerating Universe
Today, Dark Energy is the name given to the
anti-gravity force (we are not sure it is truly
constant). Dark Energy is currently the dominant
component of the Universe, dwarfing even Dark
Matter. Regular matter (stars, planets, iPods,
etc.) makes up a tiny fraction of the Universe.
And it will only get worse as the Universe
expands, it fills with more and more Dark Energy.
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What is the Dark Energy?
Were clueless. One traditional theory,
consistent with the Cosmological Constant model,
holds that the particles and anti-particles
constantly being created and annihilated in empty
space (due to the uncertainty principle) give the
vacuum ground state a finite energy density. But
theorists estimate of this energy density is off
by a factor of 10122.
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Summary History Fate of the Universe

• Origins of Structure
• Slight variations in density were present in the
  Universe when it was very young, 0.1 its current
  size
• We observe and measure those variations in the
  cosmic microwave background
• Those density variations collapsed under the
  influence of gravity to form the structures we
  see today  galaxies, clusters of galaxies, and
  the cosmic web
• Expansion History of the Universe
• The Hubble expansion of the Universe implies
  three possible fates collapse (bound), endless
  expansion (unbound), or perfect balance
  (marginally bound)
• We can get an idea of the density and fate of the
  Universe by measuring its expansion history using
  type Ia supernovae
• Dark Energy and the Accelerating Universe
• The Universe was decelerating when it was young,
  due to the gravitational pull of all the matter
  in the Universe
• The Universe has since begun an accelerating
  expansion due to the rapidly growing influence of
  Dark Energy
• The properties of the Dark Energy are consistent
  with Einsteins Cosmological Constant, and give
  the Universe its age of 13.7 billion years
• The true nature of the Dark Energy is a deep
  mystery

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Before the Big Bang
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The History and Fate of the Universe

• What was there before the Big Bang?
• Is the Universe infinite or just really, really
  big?

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The Dark Energy supernova measurements, combined
with maps of the Cosmic Microwave Background
radiation, have measured the geometry of the
Universe on the largest scales.
Of the nearly infinite number of possibilities
for its curvature  almost any positive or
negative number  it turns out to be almost
exactly
Flat!
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Improbable Flatness

• This flatness seems very odd  as if Earths
  orbit around the Sun had ended up being a perfect
  circle.
• Even worse, flatness represents a point of
  unstable equilibrium  like a pencil balanced on
  its point, its not expected to last long.
• If the Universe seems flat now, its must have
  been exponentially flatter  almost perfectly
  flat  just after the Big Bang.

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Improbable Uniformity

• The microwave background is extremely uniform
  over the whole sky  this is one of its most
  important properties.
• But how can this be? The patches of the early
  Universe that we see in opposite directions were
  millions of light-years apart when the photons we
  see were emitted! The Universe at that time was
  too young to be like a single well-mixed pot of
  soup, with a single well-defined temperature.

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Improbable Uniformity

• According to standard Big Bang theory, these two
  patches of the early Universe could not have
  communicated with each other.
• Thus they could not have known to reach the
  same temperature at the same time.
• Is there any way of explaining the extreme
  (improbable) flatness and homogeneity of the very
  young Universe?

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The Inflationary Universe

• Yes!
• When the Universe was less than 1035 seconds old
  it was governed by extremely high-energy physics
  very different from today probably all of the
  forces (except gravity) were unified at that
  time.
• Under the right conditions it could have expanded
  by an enormous factor before reaching the ripe
  old age of 1032 seconds.

From smaller than a proton to much larger than
everything we see around us today (expansion by a
factor of 1050, or more).
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Inflation explains flatness
The nature of this expansion is that it drives
the Universe exponentially towards flatness  by
the same factor of 1050 or more. Imagine
inflating a curved balloon Universe by a factor
of 1050 on any reasonable scale it will no
longer look curved at all!
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Inflation explains uniformity
At the same time, the fact that the Universe had
its origin in a sub-microscopic patch of space
means that it would very naturally have been at
only a single temperature Except for tiny
quantum fluctuations, which are present always
and everywhere. These quantum fluctuations are
the original seeds of structure!
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The History and Fate of the Universe

• What was there before the Big Bang?
• A tiny, sub-microscopic patch of space-time that
  happened to enter the right state to undergo
  cosmic inflation. Inflation then leads naturally
  to a very large (flat, uniform) Universe in a hot
  Big Bang state, and even provides the seeds of
  cosmic structure ultimately giving everything
  we see around us today.

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Is the Universe Infinite?

• Not infinite in age! (13.7by)
• Also not infinite in space  according to Cosmic
  Inflation
• Finite-sized region entered the inflationary
  state
• Thus Universe was finite-sized at exit, as well
• Certainly Large in size, gt100b light years
• Possibly Very Large in size  101012 cm?
• Not infinite

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Is the Universe Infinite?

• BUT!
• The Universe is actually 4-dimensional (time and
  space not separate)
• Whether the Universe is infinite is really a
  question of geometry
• Observations suggest the Universe is flat
  ultimately, however, it is either open (infinite)
  or closed (finite)
• Dark Energy seems to be powering infinite
  acceleration suggesting the open (infinite) case
  holds
• But can it really last forever? (quoting Prince
  thats a mighty long time)

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Is the Multiverse Infinite?

• Even the Universe (everything) may not actually
  be all there is
• Various problems with the theory of Cosmic
  Inflation are resolved in a Multiverse picture
   if one patch can undergo Cosmic Inflation,
  why not others?
• Eternal Inflation theory posits that Inflation
  starts once and lasts forever
• In that case the Multiverse would be infinite,
  even if our Universe is not
• Possibly different physical laws in different
  Universes

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The History and Fate of the Universe

• Is the Universe infinite or just really, really
  big?
• Finite in age, and finite in size (today)
• Potentially infinite, in a four-dimensional sense
• Potentially part of an infinite Multiverse