Jacco Vink

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Large Scale Structure of the Universe
Lesson 4 Horizons, the early Universe and
inflation
Jacco Vink
Utrecht University
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How to visualize growing angles?
Consider the CMB light we receive today comes
from a surface that when emitted was 4p (aCMB
rCMB)2 . Today the distance to this surface has
increased by a0/aCMB. So things seems larger than
they at emission.
Present day radius when observed ao rCMB
Radius at emission aCMB rCMB
How it was emitted
How we perceive it
Therefore structures in the CMB look gigantic,
since light was emitted from far away when
z1400. Actual size acmb rcmb ?, perceived size
a0 rcmb ? Or ? perceived size/d (1z)
actual size/d
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Is energy conserved in an expanding Universe?
No not really. E.g. take radiation u C x T4,
E u (a/a0)3 , T/T0 (a/a0)-4 So for radiation E
C (a/a0)-1 . However, in GR we are not dealing
with energies, but with the energy Tensor T,
which contains both terms of ?c2 and p. It turns
out what is conserved is entropy S, defined as
From the Friedman equations we obtain
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The Planck Mass/Time/Energy
The following combination of fundamental
constants,G, h, c, have units of mass, length,
time, energy
The idea is that General Relativity and quantum
physics is not sufficient to describe a Universe
with kT 1.22x1019 GeV. Instead a theory of
quantum gravity is needed.
The idea is that our current physics, e.g.
Friedman equations, are adequate for t gt tPlanck
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The Hubble Radius
The typical time scale for evolution is This is
called the Hubble time.
We can associate a length scale with this, the
Hubble radius
For H0 70 km/s/Mpc we have dH 4286 Mpc.
Information can only travel within the,
so-called, particle horizon
(In most cases)
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The early Universe
For the early Universe we have to take into
account an additional term for radiation
What terms can we neglect? Why do we say that at
early times curvature is almost zero, no matter
whether Omega1 or 0.3?
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Eras of Matter and Radiation domimation
Going back in time (z gtgt1), we go from a lambda
dominated Universe (just started) to a matter
dominated Universe (zgt1), to an radiation
dominated Universe. So this equation
Simplifies to
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The Hubble Radius in time
The Hubble constant varies in the matter
dominated phase
or
In the radiation dominated phase this is
or
The proper distance
The Hubble radius shrinks more rapidly than the
proper distance with redshift we see objects
now that were not visible in the past!
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The Horizon and Flatness problem
The Horizon problem The cosmic microwave
background is within our horizon, but the CMB
region in one direction is/was not within the
horizon of the region opposite to it.
How come the CMB appears homogeneous if different
were not in contact with each other?
What physical process could have made that in the
early Universe Otot - 1 0?
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Inflation and the Horizon Problem
Recall
For example n 2/3 in matter dominated phase n
1/2 in radiation dominated phase
Assume
We obtain
The horizons increases with t for nlt 1 and
shrinks for n gt 1!
So if we assume a phase in which n gt 1 we solve
the horizon problem! Such a phase is assumed to
have taken place, and the process is called
inflation.
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Our era a new era of inflation?
In one of the exercises we explored a Lambda
dominated phase (like we are entering now)
For a/a0 gt 1 (in the future). The solution is
A constant Hubble constant and clear a(t) grows
faster than t. Note that the Hubble radius is
therefore also a constant!
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A schematic view
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A philosophical remark
It looks now there were 2 periods in which the
Universe accelerated 1) in the very early
Universe 2) we just entered it This seems to
make it unlikely that Einsteins ? is a
constant, i.e. an extension to Einsteins
equation. The reason ? during inflation ? ? now.
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How much inflation is needed?
Recall
Use T as time coordinate
In the Planck era (T1019 GeV)we get
Recall
If we could blow a up by factor 1030 we could
reduce the importance of this term in the
Friedman equations. This is how inflation solve
the flatness problem.
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Some names associated withInflation theory
Andrei Linde
Alan Guth
Paul Steinhardt
Both wrote seminal papers in 1981
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What could cause inflation?
Quantum field processes associated with phase
transitions associated with symmetry breaking, or
the gradual decay of a scalar field.
Note that at the end of inflation, the Universe
needs to be reheated, probably by the creation of
relativistic particles created through the decay
of the scale field.
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A slide by Andrei Linde
A scalar field slowly rolls, thereby
providing energy for inflatory expansion. Potentia
l V
http//www-astro-theory.fnal.gov/Conferences/psw/t
alks/linde/
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Final remarks on inflation
Most cosmologists accept inflation theory.
However, in practice investigating the details
means by trial and error to deduce the right
behavior of the scalar field potential. It is
unclear what this scalar field actually is. On
the positive side The shape of the potential
does have an influence on the density initial
perturbrations, which can be tested.
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Summary

• We have just entered a phase in which the
  cosmological constant dominates. In future a ?
  exp(Ht), with Hconst
• In the recent past (10 lt z lt 1000) the Universe
  was matter dominated and a ? t2/3
• Even more in the past z gt 10000, the Universe
  energy density was radiation domianted a ? t1/2
• A rapid exponential expansion era in the past is
  assumed called inflation during which also a ?
  exp(Ht), with Hconst
• If a ? tn , with n lt 1 the particle horizon (the
  size of the Universe that can be observed)
  increases with time
• During the inflationary phase regions disappear
  out of sight (the horizon shrinks)