Inflation%20and%20Stringy%20Landscape

1
Inflation and Stringy Landscape

• Andrei Linde

2
New Inflation
V
3
Chaotic Inflation
Eternal Inflation
4
Hybrid Inflation
5
Inflation in String Theory
The volume stabilization problem A potential
of the theory obtained by compactification in
string theory of type IIB
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
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.
Giddings, Kachru, Polchinski 2001
Dilaton stabilization
Volume stabilization KKLT construction
Kachru, Kallosh, A.L., Trivedi 2003
6
Basic steps of the KKLT scenario

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 a positive
   vacuum energy by adding a positive energy of an
   anti-D3 brane in warped Calabi-Yau space

AdS minimum
Metastable dS minimum
7
String Theory Landscape
Perhaps 101000 different minima
Lerche, Lust, Schellekens 1987
Bousso, Polchinski Susskind Douglas, Denef,
8
Two types of string inflation models

• Modular Inflation. The simplest class of models.
  They use only the fields that are already present
  in the KKLT model.
• Brane inflation. The inflaton field corresponds
  to the distance between branes in Calabi-Yau
  space. Historically, this was the first class of
  string inflation models.

9
Inflation in string theory
KKLMMT brane-anti-brane inflation
D3/D7 brane inflation
Racetrack modular inflation
DBI inflation (non-minimal kinetic terms)
10
More about inflation in string theory - in talks
by Bousso, Sarangi, Conlon, Kallosh, Tye, Shiu,
McAllister, Kofman and others
11
CMB and Inflation
Blue and black dots - experimental results (WMAP,
ACBAR) Brown line - predictions of inflationary
theory
12
Predictions of Inflation

• 1) The universe should be homogeneous, isotropic
  and flat,
• ? 1 O(10-4) ???????

• Observations it is homogeneous, isotropic and
  flat

• 2) Inflationary perturbations should be gaussian
  and adiabatic, with flat spectrum, ns 1
  O(10-1). Spectral index ns slightly differs from
  1. (This is an important prediction, similar to
  asymptotic freedom in QCD.)

Observations perturbations are gaussian and
adiabatic, with flat spectrum
13
Initial conditions for inflation
In the simplest chaotic inflation model, eternal
inflation begins at the Planck density under a
trivial condition the potential energy should be
greater than the kinetic and gradient energy in a
smallest possible domain of a Planckian size.
A.L. 1986
In the models where inflation is possible only at
a small energy density (new inflation, hybrid
inflation) the probability of inflation is not
suppressed if the universe is flat or open but
compact, e.g. like a torus.
Zeldovich and Starobinsky 1984 A.L. 2004
14
In the string landscape scenario, with many dS
vacua stabilized by KKLT mechanism, one either
directly rolls down to the state where life of
our type is impossible (AdS, 10D Minkowski
space), or enters the state of eternal inflation.
This essentially eliminates the problem of
initial conditions, replacing it by the problem
of the probability measure for eternal inflation.
If any other regime (ekpyrotic collapse, string
gas) is possible in string theory, it should be a
part of the string landscape context. The problem
of the probability measure is not a problem of
inflationary cosmology, it is a generic problem
of any regime which can exist in string theory.
One cannot avoid eternal inflation by proposing
its alternatives.
15
Do not ask for whom the bell tolls, it tolls for
thee.


Ernest Hemingway
The problem of measure in eternal inflation and
anthropic selection is NOT the problem of eternal
inflation. It is a problem for anybody who wants
to work in the context of string theory with
vacuum stabilization.
16
Alternatives Ekpyrotic/cyclic scenario
Fake it till you
make it
17
Whats in a name?
18
Singularity problem remains unsolved after many
years of attempts and optimistic announcements.
Recent developments New ekpyrotic scenario
based on the ghost condensate theory with the
curvaton heart.
Even the authors of the ghost condensate theory
dislike it violation of the null energy
condition, absence of the ultraviolet completion
(difficulty to embed it in string theory),
problems with black hole thermodynamics,
etc. Generation of density perturbations with
flat spectrum requires an additional field. At
the stage of collapse, classical inhomogeneities
of this field must be smaller that its quantum
fluctuations. Otherwise classical irregularities
will be amplified, and dominate density
perturbations. This is a severe homogeneity
problem.
Adams, Arkani-Hamed, Dubovsky, Nicolis and
Rattazzi, 2006 Arkani-Hamed, Dubovsky, Nicolis,
Trincherini and Villadoro, 2007
19
Even newer ekpyrotic scenario
Buchbinder, Khouri and Ovrut (tachyon
stabilization)
The authors admit that solving the homogeneity
problem in this scenario requires explaining
homogeneity on the scale of 1 meter, i.e. 35
orders of magnitude greater than the Planck
scale. The authors do not solve this problem, but
hope that it should be as easy as in chaotic
inflation, where initial homogeneity is required
only on the Planck scale.
It is claimed that this scenario solves flatness
problem, but it is not explained why the total
number of particles in our universe is greater
than 1088 and its mass is greater than 1055 g.
These are the entropy and mass problems, which
are equivalent to the flatness problem. These
problems are easily solved by inflation.
20
Other alternatives String gas cosmology

Brandenberger, Vafa, Nayeri, 4 papers in 2005-2006
Many loose ends and unproven assumptions (e.g.
stabilization of the dilaton and of extra
dimensions). Flatness/entropy problem is not
solved. This class of models differs from the
only known class of stringy models (KKLT-type
construction) where stabilization of all moduli
was achieved.
Even if one ignores all of these issues, the
perturbations generated in these models are very
non-flat Instead of ns 1 one
finds ns 5

Kaloper, Kofman, Linde, Mukhanov 2006,
hep-th/0608200 Brandenberger et al, 2006
21
To summarize, inflationary cosmology is quite
healthy. It agrees well with the existing
observations. In my opinion, no compelling
alternatives to inflation are available so far.
Now we will discuss inflationary multiverse
22
Inflationary Multiverse
For a long time, people believed in the
cosmological principle, which asserted that the
universe is everywhere the same.
This principle is no longer required.
Inflationary universe may consist of many parts
with different properties depending on the local
values of the scalar fields, compactifications,
etc.
23
Example SUSY landscape
Supersymmetric SU(5)
V
SU(5)
SU(3)xSU(2)xU(1)
SU(4)xU(1)
Weinberg 1982 Supersymmetry forbids tunneling
from SU(5) to SU(3)xSU(2)XU(1). This implied that
we cannot break SU(5) symmetry.
A.L. 1983 Inflation solves this problem.
Inflationary fluctuations bring us to each of the
three minima. Inflation make each of the parts of
the universe exponentially big. We can live only
in the SU(3)xSU(2)xU(1) minimum.
24
Landscape of eternal inflation
25
String Theory Multiverse
and eternal old inflation
??gt 0
?? 0
??lt 0
26
Discrete and continuous parameters
Properties of our world (local part of the
universe) depend on 101000 discrete parameters
(topological numbers, quantized fluxes, etc.),
which describe our vacuum state.
Beyond the landscape Our world may
depend on a continuous set of parameters, which
took different values during the cosmological
evolution far away from the vacuum state.

• EXAMPLES
• Axion field could take different values during
  inflation, which should affect the local value of
  the density of dark matter.
• Affleck-Dine fields could take different values
  in different parts of the universe, thus
  affecting the local value of the baryon asymmetry
  of the universe.

27
Inflation and Cosmological Constant
4 steps in finding the anthropic solution of the
CC problem

• Anthropic solutions of the CC problem using
  inflation and fluxes of antisymmetric tensor
  fields (A.L. 1984), multiplicity of KK vacua
  (Sakharov 1984), and slowly evolving scalar field
  (Banks 1984, A.L. 1986). We considered it obvious
  that we cannot live in the universe with
• but the proof was needed for positive .

2) Derivation of the anthropic constraint
Weinberg 1987 Martel, Shapiro, Weinberg 1997,
28
Inflation and Cosmological Constant
3) String theory landscape
Multiplicity of (unstable) vacua Lerche, Lust
and Schellekens 1987 101500 vacuum
states Duff, 1986, 1987 Bousso, Polchinski
2000
Vacuum stabilization and
statistics KKLT 2003, Susskind 2003, Douglas
2003, perhaps 101000 metastable
dS vacuum states - still counting
4) Counting probabilities in an eternally
inflating universe (more about it later)
29
Anthropic constraints on ??
Aguirre, Rees, Tegmark, and Wilczek,
astro-ph/0511774
observed value
30
Dark Energy (Cosmological Constant) is about 74
of the cosmic pie
Dark Matter constitutes another 22 of the pie.
Why there is 5 times more dark matter than
ordinary matter?
31
Example Dark matter in the axion field
Old lore If the axion mass is smaller than
10-5 eV, the amount of dark matter in the axion
field contradicts observations, for a typical
initial value of the axion field.
Can we give a scientific definition of typical
?
Anthropic argument Inflationary fluctuations
make the amount of the axion dark matter a
CONTINUOUS RANDOM PARAMETER. We can live only in
those parts of the universe where the initial
value of the axion field was sufficiently small
(A.L. 1988).
Recently this possibility was analyzed by
Aguirre, Rees, Tegmark, and Wilczek.
32
Anthropic Constraints on Axion Dark Matter?
Aguirre, Rees, Tegmark, and Wilczek,
astro-ph/0511774
observed value
The situation with Dark Matter is even better
than with the CC !
33
What is so special about our world?
Problem Eternal inflation creates infinitely
many different parts of the universe, so we must
compare infinities
34
Two different approaches
1. Study events at a given point, ignoring
growth of volume Starobinsky 1986,
Garriga, Vilenkin 1998, Bousso 2006, A.L. 2006
No problems with infinities, but the results
depend on initial conditions. It is not clear
whether these methods are appropriate for
description of eternal inflation, where the
exponential growth of volume is crucial.
Recent developments were described in the talk by
Bousso
2. Take into account growth of volume
A.L. 1986 A.L., D.Linde, Mezhlumian,
Garcia-Bellido 1994
Garriga, Schwarz-Perlov, Vilenkin, Winitzki
2005 A.L. 2007
No dependence on initial conditions, but we are
still learning how to do it properly. I will
review some recent progress.
35
V
Boltzmann Brains are coming!!!
BB1
BB3
Fortunately, normal brains are created even
faster, due to eternal inflation
36
Problems with probabilities
V
3
4
2
1
5
37
Time can be measured in the number of
oscillations ( ) or in the number of
e-foldings of inflation ( ). The
universe expands as
is the growth of volume during
inflation
Unfortunately, the result depends on the time
parametrization.
38
t21
t45
t 0
We should compare the trees of bubbles not at
the time when the trees were seeded, but at the
time when the bubbles appear
39
A possible solution of this problem
If we want to compare apples to apples, instead
of the trunks of the trees, we need to reset the
time to the moment when the stationary regime of
exponential growth begins. In this case we obtain
the gauge-invariant result
As expected, the probability is proportional to
the rate of tunneling and to the growth of volume
during inflation.
A.L., arXiv0705.1160
40
This result agrees with the expectation that the
probability to be born in a part of the universe
which experienced inflation can be very large,
because of the exponential growth of volume
during inflation.
41
Applications Probabilities and the solution of
the CC problem in the BP landscape
Clifton, Shenker,
Sivanandam, arXiv07063201
The main source of volume of new bubbles is the
tunneling from the fastest growing dS vacua with
large vacuum energy towards the anthropic sphere
with .
If the tunneling occurs sequentially, between the
nearby vacua, the process typically moves us to a
minor fraction of the anthropic sphere with
one of the fluxes being much greater than all
others. This allows sharp predictions. One of the
predictions - vacuum decay few billion years from
now.
However, if the tunneling with large jumps is
possible due to nucleation of large stacks of
branes (which seems plausible during the
tunneling from the high energy dS vacua), then
the probability distribution on the anthropic
sphere becomes rather uniform, no doomsday.
42
The cosmological constant problem is solved in
this scenario in either case (small or large
jumps) the probability distribution for the CC
is flat and smooth near the anthropic sphere. It
seems that the solution of the CC problem can be
achieved with many different probability
measures.
Predictions of other features of our world,
including stability/instability of our vacuum,
depend on the properties of the landscape, on the
possibility of the nucleation of large stacks of
branes, on the proper choice of the probability
measure, and on the duration of the slow-roll
stage of inflation.
Hopefully we will learn many new interesting
things before the next summer