Transcript PowerPoint Presentation - Inflation, String Theory,

Inflation and String
Cosmology
Andrei Linde
The Simplest Inflationary Model
Eternal Inflation
Predictions of Inflation:
1) The universe should be homogeneous, isotropic
and flat,  = 1 + O(10-4)
[
Observations: the universe is homogeneous, isotropic
and flat,  = 1 + O(10-2)
2) Inflationary perturbations should be gaussian
and adiabatic, with flat spectrum, ns = 1+ O(10-1)
Observations: perturbations are gaussian and adiabatic,
with flat spectrum, ns = 1 + O(10-2)
Any problems of principle?
1) We must introduce a small parameter to explain
a small amplitude of density perturbations .
To explain  one should have m =  Is it a
real problem?
2) Transplanckian physics?
These effects are not expected to affect basic features of
inflationary scenario. In the worst case, one may expect
minor corrections to the spectrum of perturbations. These
effects vanish for low-scale inflation.
3) Singularity problem
This is NOT a problem of inflation. Moreover, inflationary
predictions practically do not depend on the existence of
the singularity.
4) Cosmological constant problem
This is NOT a problem of inflation. Moreover, the only
presently known solution of this problem requires inflation,
in combination with anthropic principle and string theory
landscape.
5) Inflation requires initial homogeneity on scale
greater than horizon
In simplest models of chaotic inflation homogeneity is
requires on the smallest possible scale, Planck length,
which is not a problem.
In low-scale inflation, such as new or hybrid inflation, this
was a real problem. However, this problem was solved by
considering inflation in compact topologically nontrivial flat
or open universes: In this case homogeneity is required on
Planck scale, as in chaotic inflation.
A.L. hep-th/0408164
Are there any real problems of inflation?
The main problem is to construct realistic models
of inflation in the situation when the final theory
of all fundamental interactions is still absent.
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.
Dilaton stabilization:
Giddings, Kachru, Polchinski 2001
Volume stabilization: KKLT construction
Kachru, Kallosh, A.L., Trivedi 2003
Burgess, Kallosh, Quevedo, 2003
Volume stabilization
Kachru, Kallosh, A.L., Trivedi 2003
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 positive vacuum energy by adding
a positive energy of an anti-D3 brane in warped Calabi-Yau space
V
V
0.5
100
150
200
250
300
350
s
400
1.2
1
-0.5
0.8
-1
0.6
0.4
-1.5
-2
AdS minimum
0.2
100
150
200
250
300
Metastable dS minimum
350
400
s
Main conclusions after 2 years of
investigation:

It is possible to stabilize internal dimensions,
and obtain an accelerating universe. Eventually,
our part of the universe will decay and become
10120
ten-dimensional, but it will only happen in 10
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…
Related ideas existed long before
the stringy landscape
Example: Supersymmetric SU(5)
V
SU(5)
SU(4)xU(1)
SU(3)xSU(2)xU(1)
Weinberg 1982: No way to tunnel from SU(5) to SU(3)xSU(2)XU(1)
A.L 1983: Inflationary fluctuations bring us there
Self-reproducing Inflationary Universe
String Theory Landscape
Perhaps 10100 - 101000
different minima
Lerche, Lust, Schellekens 1987
Bousso, Polchinski; Susskind; Douglas, Denef,…
Stringy landscape provides us with a DISCRETE
set of parameters corresponding to 101000 vacua
of string theory.
In addition, we may have many CONTINUOUS
parameters, such as the amplitude of density
perturbations, the ratio of dark matter to baryons,
etc., which depend on cosmological dynamics.
The simplest curvaton model
A.L., Mukhanov, astro-ph/9610212
Consider a light field  during inflation with Hubble
constant H. Bunch-Davies distribution of fluctuations:
The main contribution to these fluctuations is given by
exponentially large wavelengths
The main contribution to these fluctuations is given by
exponentially large wavelengths
Interpretation:
Because of the fluctuations, curvaton typically takes values of the order +
H2/m or - H2/m in domains separated by walls where it vanishes (shown
as a shoreline in the figure below). A typical size of these domains is
Amplitude of the curvaton perturbations
A.L., Mukhanov, astro-ph/0511736
The constant C shows the energy density of the curvaton
particles produced during reheating. As far as we know, this
contribution previously was ignored, but it can be very large.
The amplitude of density perturbations depends on our
position in the curvaton landscape. In the interior of the
exponentially large islands the perturbations are (locally)
gaussian. On a larger scale including many domains the
perturbations are nongaussian.
Curvaton Web
Usually we assume that the amplitude of inflationary perturbations is constant,
 ~ 10-5 everywhere. However, in the curvaton scenario the value of  is
different in different exponentially large parts of the universe.
A.L., Mukhanov, astro-ph/0511736
Curvaton-Inflaton Transmutations
Bartolo, Liddle 2003, A.L., Mukhanov 2005
Consider inflaton and curvaton with masses M >> m
Even if initially  >> , then during eternal inflation the fluctuations of the
field  are generated, and it becomes much greater than  almost
everywhere in the universe. Then the field  rolls down (its potential is
more steep) and the curvaton  drives inflation, i.e. it becomes the
inflaton.
 is a curvaton only near the walls everywhere else it is an
inflatonThe amplitude of perturbations is
almost everywherebut it
grows near the walls, forming the curvaton web.
Dark Energy (Cosmological Constant)
is about 73% of the cosmic pie. Why?
What’s about Dark Matter, another 23%
of the pie? Why there is 5 times more
dark matter than ordinary matter?
Inflation and Cosmological Constant
Three crucial steps in finding the anthropic solution of the CC problem:
1) 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).
All of these authors took for granted that we cannot live in the universe with
2) Derivation of the anthropic constraint
(Weinberg 1987, Martel, Shapiro, Weinberg 1997)
3) String landscape
(Bousso-Polchinski 2000, KKLT 2003, Susskind 2003, Douglas 2003,…)
Latest anthropic constraints on 
Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774
observed value
Dark matter: the axion scenario
Standard 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.
Anthropic argument: Due to inflationary fluctuations, the
amount of the axion dark matter is 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).
Latest anthropic constraints on Dark Matter
Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774
observed value
Anthropic predictions for Dark Matter are even better
than the predictions for the cosmological constant !
Why do we live in a 4D space?
Ehrenfest, 1917: Stable planetary and atomic systems are
possible only in 4D space. Indeed, for D > 4 planetary system
are unstable, whereas for D < 4 there is NO gravity forces
between stars and planets.
If one wants to suggest an alternative solution to a problem that
is solved by anthropic principle, one is free to try. But it may be
more productive to concentrate on many problems that do not
have an anthropic solution.
For example, there is no anthropic
replacement for inflation
Two types of string inflation models:

Moduli Inflation.

Brane inflation.
The simplest class of
models. They use only the fields that are
already present in the KKLT model.
The inflaton field
corresponds to the distance between branes in
Calabi-Yau space. Historically, this was the first
class of string inflation models.
Inflation in string theory
KKLMMT brane-anti-brane inflation
Racetrack modular inflation
D3/D7 brane inflation
Kahler modular inflation
D3/D7 inflation
Herdeiro, Hirano, Kallosh, Dasgupta 2001, 2002
Unlike in the brane-antibrane scenario, inflation
in D3/D7 model does not require fine-tuning
because of the shift symmetry
Let 10
500
flowers blossom
> 0
< 0
= 0
In the beginning one has eternal inflation when the fields
jumped from one de Sitter minimum to another. However,
at some point the fields must stop jumping, as in old
inflation, and start rolling, as in new or chaotic inflation:
the last stage of inflation must be of the slow-roll
type. Otherwise we would live in an empty open universe
with << 1.
How can we create initial conditions for a
slow-roll inflation after the tunneling?
Initial Conditions for D3/D7 Inflation
In D3/D7 scenario flatness of the inflaton direction does not depend on fluxes
V
Eternal inflation
in a valley with
different fluxes
H >>> m
Slow roll inflation
H >> m
s
The field drifts in the upper valley due to quantum fluctuations and
then tunneling occurs due to change of fluxes inside a bubble
The resulting scenario:
1) The universe eternally jumps from one dS vacuum to
another due to formation of bubbles. Each bubble contains a
new dS vacuum. The bubbles contain no particles unless this
process ends by a stage of a slow-roll inflation. Here is how:
2) At some stage the universe appears in dS state with a large
potential but with a flat inflaton direction, as in D3/D7 model.
Quantum fluctuations during eternal inflation in this state push
the inflaton field S in all directions along the inflaton valley.
3) Eventually this state decays, and bubbles are produced.
Each of these bubbles may contain any possible value of the
inflaton field S, prepared by the previous stage. A slow-roll
inflation begins and makes the universe flat. It produces
particles, galaxies, and the participants of this conference:)