The Universe: a sphere, a donut, or a fractal? Andrei Linde Andrei Linde.

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Transcript of The Universe: a sphere, a donut, or a fractal? Andrei Linde Andrei Linde.
The Universe:The Universe: a sphere, a donut, or a a sphere, a donut, or a
fractal?fractal?
The Universe:The Universe: a sphere, a donut, or a a sphere, a donut, or a
fractal?fractal?
Andrei Linde
Andrei Linde
Contents:Contents: Contents:Contents:
From the Big Bang theory to Inflationary Cosmology and the theory of Dark Energy
Inflation as a theory of a harmonic oscillator Inflation in string theory Initial conditions for inflation Does our universe looks like a sphere or like a bagel? Eternal inflation and string theory landscape: From a
bagel to a fractal
From the Big Bang theory to Inflationary Cosmology and the theory of Dark Energy
Inflation as a theory of a harmonic oscillator Inflation in string theory Initial conditions for inflation Does our universe looks like a sphere or like a bagel? Eternal inflation and string theory landscape: From a
bagel to a fractal
Two major cosmological discoveries:Two major cosmological discoveries: Two major cosmological discoveries:Two major cosmological discoveries:
The newborn universe experienced rapid acceleration (inflation)
A new (slow) stage of acceleration started 5 billion years ago (dark energy)
How did it start, and how it is going to end?How did it start, and how it is going to end? How did it start, and how it is going to end?How did it start, and how it is going to end?
Closed, open or flat universeClosed, open or flat universe Closed, open or flat universeClosed, open or flat universe
Big Bang TheoryBig Bang Theory Big Bang TheoryBig Bang Theory
Inflationary UniverseInflationary Universe Inflationary UniverseInflationary Universe
Why do we need inflation?Why do we need inflation? Why do we need inflation?Why do we need inflation?
What was before the Big Bang?
Why is our universe so homogeneoushomogeneous (better than 1 part in 10000) ?
Why is it isotropicisotropic (the same in all directions)?
Why all of its parts started expanding simultaneously?
Why it is flatflat? Why parallel lines do not intersect? Why it contains so many particles? Why there are so many people in this auditorium?
What was before the Big Bang?
Why is our universe so homogeneoushomogeneous (better than 1 part in 10000) ?
Why is it isotropicisotropic (the same in all directions)?
Why all of its parts started expanding simultaneously?
Why it is flatflat? Why parallel lines do not intersect? Why it contains so many particles? Why there are so many people in this auditorium?
Problems of the standard Big Bang theory:Problems of the standard Big Bang theory:Problems of the standard Big Bang theory:Problems of the standard Big Bang theory:
Inflation as a theory of a harmonic oscillatorInflation as a theory of a harmonic oscillator Inflation as a theory of a harmonic oscillatorInflation as a theory of a harmonic oscillator
Eternal InflationEternal Inflation
Einstein:
KleinGordon:
Einstein:
KleinGordon:
Equations of motion:Equations of motion:Equations of motion:Equations of motion:
Compare with equation for the harmonic oscillator with friction:
Logic of Inflation:Logic of Inflation: Logic of Inflation:Logic of Inflation:
Large φLarge φ large H large H large friction large friction
field φ moves very slowly, so that its potential energy for a long time remains nearly constantfield φ moves very slowly, so that its potential energy for a long time remains nearly constant
No need for false vacuum, supercooling, phase transitions, etc.No need for false vacuum, supercooling, phase transitions, etc.
Inflation makes the universe flat, Inflation makes the universe flat, homogeneous and isotropichomogeneous and isotropic
Inflation makes the universe flat, Inflation makes the universe flat, homogeneous and isotropichomogeneous and isotropic
In this simple model the universe typically grows 101000000000000 times during inflation.
Now we can see just a tiny part of the universe of size ct = 1010 light yrs. That is why the universe looks homogeneous, isotropic, and flat.
Generation of Quantum FluctuationsGeneration of Quantum Fluctuations Generation of Quantum FluctuationsGeneration of Quantum Fluctuations
QuickTime™ and a decompressor
are needed to see this picture.
WMAP and the temperature of the skyWMAP and the temperature of the sky WMAP and the temperature of the skyWMAP and the temperature of the sky
Name RecognitionName RecognitionName RecognitionName Recognition
Stephen Hawking
A photographic A photographic image of quantum image of quantum
fluctuations blown up fluctuations blown up to the size of the to the size of the
universeuniverse
A photographic A photographic image of quantum image of quantum
fluctuations blown up fluctuations blown up to the size of the to the size of the
universeuniverse
WMAPWMAP
and spectrum of the cosmic microwave background anisotropy
WMAPWMAP
and spectrum of the cosmic microwave background anisotropy
Add a constant to the inflationary potential
 obtain inflation and acceleration
Add a constant to the inflationary potential
 obtain inflation and acceleration
inflation
acceleration
Predictions of Inflation:Predictions of Inflation:Predictions of Inflation:Predictions of Inflation:
1) The universe should be homogeneous, isotropic and flat, = 1 + O(104) [
Observations: the universe is homogeneous, isotropic
and flat, = 1 + O(102)
• Inflationary perturbations should be gaussian and adiabatic, with flat spectrum, ns = 1+ O(101)
Observations: perturbations are gaussian and adiabatic,
with flat spectrum, ns = 1 + O(102)
Chaotic inflation in supergravityChaotic inflation in supergravity Chaotic inflation in supergravityChaotic inflation in supergravity
Main problem:
Canonical Kahler potential is
Therefore the potential blows up at large φ, and slowroll inflation is impossible:
Too steep, no inflation…
A solution:A solution: shift symmetryshift symmetry A solution:A solution: shift symmetryshift symmetryKawasaki, Yamaguchi, Yanagida 2000
Equally good Kahler potential
and superpotential
The potential is very curved with respect to X and Re φ, so these fields vanish.
But Kahler potential does not depend on
The potential of this field has the simplest form, without any exponential terms:
Inflation in String TheoryInflation in String Theory Inflation in String TheoryInflation in String TheoryThe volume stabilization problem:
A potential of the theory obtained by compactification in string theory of type IIB:
The volume stabilization problem:
A potential of the theory obtained by compactification in string theory of type IIB:
The potential with respect to X and Y is very steep, these fields rapidly run down, and the potential energy V vanishes. We must stabilize these fields.
Volume stabilization: KKLT construction Kachru, Kallosh, A.L., Trivedi 2003Kachru, Kallosh, A.L., Trivedi 2003Burgess, Kallosh, Quevedo, 2003Burgess, Kallosh, Quevedo, 2003
Maloney, Silverstein, Strominger, in noncritical string theory
X and Y are canonically normalized field corresponding to the dilaton field and to the volume of the compactified space; is the field driving inflation
Dilaton stabilization: Giddings, Kachru, Polchinski 2001Giddings, Kachru, Polchinski 2001
Volume stabilizationVolume stabilization Volume stabilizationVolume stabilization
Basic steps of the KKLT scenario:Basic steps of the KKLT scenario:Basic steps of the KKLT scenario:Basic steps of the KKLT scenario:
AdS minimumAdS minimum Metastable dS minimumMetastable dS minimum
Kachru, Kallosh, A.L., Trivedi 2003Kachru, Kallosh, A.L., Trivedi 2003
1) Start with a theory with runaway potential discussed above
2) Bend this potential down due to (nonperturbative) quantum effects
3) Uplift the minimum to the state with positive vacuum energy by adding a positive energy of an antiD3 brane in warped CalabiYau space
The results:The results:The results:The results:
It seems possible to stabilize internal dimensions, and to obtain an accelerating universe. Eventually, our part of the universe will decay and become tendimensional, but it will only happen in 1010120 years
Apparently, vacuum stabilization can be achieved in 10100  101000 different ways. This means that the potential energy V of string theory may have 10100  101000 minima where we (or somebody else) can enjoy life
String Theory LandscapeString Theory Landscape String Theory LandscapeString Theory Landscape
Perhaps 10Perhaps 10100100  10  1010001000 different minimadifferent minima
Perhaps 10Perhaps 10100100  10  1010001000 different minimadifferent minima
Bousso, Polchinski; Susskind; Douglas, Denef,…Bousso, Polchinski; Susskind; Douglas, Denef,…Bousso, Polchinski; Susskind; Douglas, Denef,…Bousso, Polchinski; Susskind; Douglas, Denef,…
Lerche, Lust, Schellekens 1987Lerche, Lust, Schellekens 1987 Lerche, Lust, Schellekens 1987Lerche, Lust, Schellekens 1987
Inflation in string theoryInflation in string theory Inflation in string theoryInflation in string theory
KKLMMT braneantibrane inflation
Racetrack modular inflation
D3/D7 brane inflation
DBI inflation
Example: Racetrack InflationExample: Racetrack Inflation Example: Racetrack InflationExample: Racetrack Inflation
waterfall from the saddle point
waterfall from the saddle point
Many versions of stringy inflation (KKLMMT, D3/D7) are similar to hybrid inflation. In such models inflation ends with a “waterfall,” which may result in production of cosmic strings. Gravitational waves produced by such strings may serve as a unique source of information about string theory
Tye et al 2002, KKLMMT 2003, Polchinski et al 2004
The height of the KKLT barrier is smaller than VAdS =m23/2. The
inflationary potential Vinfl cannot be much higher than the height of the barrier. Inflationary Hubble constant is given by H2 = Vinfl/3 < m2
3/2.
Constraint on the Hubble constant in this class of models:
H < m3/2 H < m3/2
V
VAdS
Modification of V at large H
STRING COSMOLOGY AND GRAVITINO MASSSTRING COSMOLOGY AND GRAVITINO MASSSTRING COSMOLOGY AND GRAVITINO MASSSTRING COSMOLOGY AND GRAVITINO MASS
In the AdS minimum in the KKLT construction
Therefore
A new class of KKLT modelsA new class of KKLT models A new class of KKLT modelsA new class of KKLT modelsKallosh, A.L. hepth/0411011
Small mass of gravitino, no correlation with the height of the barrier Small mass of gravitino, no correlation with the height of the barrier and with the Hubble constant during inflationand with the Hubble constant during inflation
Inflation in the new class of KKLT models can occur at H >> m
3/2
One can obtain a supersymmetric Minkowski vacuum without any uplifting of the potential
One of the problem with string inflation is that inflation in such models starts relatively late. A typical closed universe will collapse before inflation begins. Open or flat universes would not collapse, but they are infinite, it is hard to make them...
Can we create a finite flat universe?
Take a box (a part of a flat universe) and glue its opposite sides to each other. What we obtain is a
torus, which is a topologically nontrivial flat universe.
Yes we can!Yes we can!Yes we can!Yes we can!
The size of the torus (our universe) grows as t1/2, whereas the mean free path of a relativistic particle grows much faster, as t
Therefore until the beginning of inflation the universe remains smaller that the size of the horizon t
If the universe initially had a Planckian size (the smallest possible size), then within the cosmological time t >> 1 (in Planck units) particles run around the torus many times and appear in all parts of the universe with equal probability, which makes the universe homogeneous and keeps it homogeneous until the beginning of inflation
Zeldovich, Starobinsky 1984; Cornish, Starkman, Spergel 1996; A.L. hepth/0408164
Closed versus compact flat universe Closed versus compact flat universe
in quantum cosmologyin quantum cosmologyClosed versus compact flat universe Closed versus compact flat universe
in quantum cosmologyin quantum cosmology
Closed universe
Wave function is exponentially
suppressed at large scale factor a
Compact flat universe
Wave function is not exponentially suppressed
tunneling
Creation of a closed inflationary universe, and of
an infinite flat or open universe is exponentially less probable than creation of a compact topologically nontrivial flat or open universe
Spheres are expensive, bagels are freeSpheres are expensive, bagels are freeSpheres are expensive, bagels are freeSpheres are expensive, bagels are free
This generalizes the standard KaluzaKlein idea that some spatial dimensions are compactified. Now it seems likely that all spatial dimensions are compactified. Some of them remain small (KKLT mechanism), whereas some other dimensions become large due to inflation
This does not necessarily mean that our This does not necessarily mean that our universe looks like a torus.universe looks like a torus. Inflation in string theory is always eternal, due to large number of metastable dS vacua (string theory landscape).
The newborn universe typically looks like a bagel, but the grownup universe looks like an eternally growing fractal.
Selfreproducing Inflationary UniverseSelfreproducing Inflationary Universe Selfreproducing Inflationary UniverseSelfreproducing Inflationary Universe
Populating the LandscapePopulating the Landscape Populating the LandscapePopulating the Landscape
QuickTime™ and a decompressor
are needed to see this picture.
Landscape of eternal inflation Landscape of eternal inflation