andrei linde - lectures munich 3

7/25/2019 Andrei Linde - Lectures Munich 3

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Inflation,Inflation, StringStringyy LandscapeLandscape

and Anthropic Principleand Anthropic Principle


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Inflation in String TheoryInflation in String TheoryThe volume stabilization problem:

A potential of the theory obtained by compactification instring theory of type IIB:

The potential with respect to X and Y is very steep, these fields rapidly run

down, and the potential energy Vvanishes. We must stabilize these fields.

Volume stabilization: KKLT construction

Kachru, Kallosh, A.L., Trivedi 2003

Xand Yare canonically normalized field corresponding to the dilaton fieldand to the volume of the compactified space; !is the field driving inflation

Dilaton stabilization: Giddings, Kachru, Polchinski 2001


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Basic steps of the KKLT scenario:

Basic steps of the KKLT scenario:

AdS minimumAdS minimum Metastable dS minimumMetastable dS minimum

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

100 150 200 250 300 350 400s

-2

-1.5

-1

-0.5

0.5

V

100 150 200 250 300 350 400s

0.2

0.4

0.6

0.8

1

1.2

V


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It was never easy to discuss anthropicIt was never easy to discuss anthropic

principle, even with friendsprinciple, even with friends

But recently the concept of the string theoryBut recently the concept of the string theory

landscape came to the rescuelandscape came to the rescue


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String Theory LandscapeString Theory Landscape

Perhaps 10Perhaps 1010001000

different minimadifferent minima

Bousso, Polchinski; Susskind; Douglas, Denef,Bousso, Polchinski; Susskind; Douglas, Denef,Bousso, Polchinski; Susskind; Douglas, Denef,

LercheLerche, Lust, Schellekens 1987, Lust, Schellekens 1987


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Two types of string inflation models:Two types of string inflation models:

Modular Inflation.Modular Inflation.The simplest class of models.

They use only the fields that are already present

in the KKLT model.

Brane inflation.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.


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Inflation in string theoryInflation in string theory

KKLMMT brane-anti-brane inflation

Racetrack modular inflation

D3/D7 brane inflation

DBI inflation (non-minimal kinetic terms)


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CMB and InflationCMB and InflationBlue and black dots- experimental results (WMAP, ACBAR)

Brown line- predictions of inflationary theory


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Predictions of Inflation:Predictions of Inflation:

1) The universe should be homogeneous, isotropic and flat,"= 1 + O(10-4) ["=#/#0]

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:

Observations: it is homogeneous, isotropic and flat:


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Tensor modes:Tensor modes:

Kallosh, A.L. 2007

It does make sense to look for tensor modes even if

none are found at the level r ~ 0.1 (Planck)


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The height of the KKLT barrier is smaller than |VAdS| =m2

3/2. The

inflationary potential Vinflcannot be much higher than the height of thebarrier. Inflationary Hubble constant is given by H2= Vinfl/3 < m

23/2.

Constraint on Hand rin this class of models:

H < m3/2

V

VAdS

Modification ofVat large H

STRING COSMOLOGY AND GRAVITINO MASSSTRING COSMOLOGY AND GRAVITINO MASS

Kallosh, A.L. 2004


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Tensor Modes and GRAVITINO

Superheavy

gravitino

A discovery or non-discovery of tensor modesA discovery or non-discovery of tensor modes

would be a crucial test for string theorywould be a crucial test for string theory


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Inflationary MultiverseInflationary 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.


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Example: SUSY landscapeExample: SUSY landscape

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 toeach 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.

Supersymmetric SU(5)


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Landscape of eternal inflationLandscape of eternal inflation


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String Theory MultiverseString Theory Multiverse

$$< 0< 0

$$= 0= 0$$> 0> 0

and eternal old inflationand eternal old inflation


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Discrete and continuous parametersDiscrete and continuous parameters

Properties of ourworld (local part of the universe) dependon 101000 discreteparameters(topological numbers,quantized fluxes, etc.), which describe our vacuum state.

Beyond the landscape: Our world may depend on

a continuousset of parameters,which took differentvalues during the cosmological evolution far away fromthe vacuum state.

EXAMPLES:

a) Axion field could take different values during inflation, which shouldaffect the local value of the density of dark matter.

b) Affleck-Dine fields could take different values in different parts of the

universe, thus affecting the local value of the baryon asymmetryof the

universe.


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Inflation and Cosmological ConstantInflation and Cosmological Constant

1) Anthropic solutions of the CC problemusing inflation andfluxesof 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 obviousthat 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,

4 stepsin finding the anthropic solution of the CC problem:


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Inflation and Cosmological ConstantInflation and Cosmological Constant

3)String theory landscape

Multiplicity of (unstable) vacua:

Lerche, Lust and Schellekens 1987: 101500vacuum states

Duff, 1986, 1987; Bousso, Polchinski 2000

Vacuum stabilization and statistics:

KKLT 2003, Susskind 2003, Douglas 2003,

perhaps 10

1000

metastable dS vacuum states - still counting

4)Counting probabilities in an eternallyinflating universe (more about it later)


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Anthropic constraints onAnthropic constraints on $$Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774

observed valueobserved value


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Dark EnergyDark Energy(Cosmological Constant)(Cosmological Constant)

is about 74% of the cosmic pieis about 74% of the cosmic pie

Dark MatterDark Matterconstitutes another 22% ofconstitutes another 22% of

the pie.the pie. Why there is 5 times more darkWhy there is 5 times more dark

matter than ordinary matter?matter than ordinary matter?


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Example:Example: Dark matter in the axion fieldDark 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.

Anthropic argument: Inflationary fluctuations make theamount 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.

Can we give a scientific definition ofCan we give a scientific definition of typicaltypical??


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Anthropic Constraints on Axion Dark MatterAnthropic Constraints on Axion Dark Matter

Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774

The situation with Dark Matter is even better than with the CC !The situation with Dark Matter is even better than with the CC !

observed valueobserved value


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Problem:Problem: Eternal inflation creates infinitely many differentEternal inflation creates infinitely many differentparts of the universe, so we must compare infinitiesparts of the universe, so we must compare infinities

What is so special about our world?What is so special about our world?


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1.1. Study events at a given point, ignoring growth of volumeStudy events at a given point, ignoring growth of volume

Starobinsky 1986, Garriga, Vilenkin 1998, Bousso 2006, A.L. 2006Starobinsky 1986, Garriga, Vilenkin 1998, Bousso 2006, A.L. 2006

Two different approaches:Two different approaches:

2.2. Take into account growth of volumeTake into account growth of volume

A.L. 1986; A.L., D.Linde, Mezhlumian, Garcia-Bellido 1994;A.L. 1986; A.L., D.Linde, Mezhlumian, Garcia-Bellido 1994;

Garriga, Schwarz-Perlov, Vilenkin, Winitzki 2005;Garriga, Schwarz-Perlov, Vilenkin, Winitzki 2005; A.L. 2007A.L. 2007

No problems with infinities, but the results depend on initial conditions.No problems with infinities, but the results depend on initial conditions.

It is not clear whether these methods are appropriate for description ofIt is not clear whether these methods are appropriate for description of

eternal inflation, where the exponential growth of volume is crucial.eternal inflation, where the exponential growth of volume is crucial.

No dependence on initial conditions, but we are still learning how to doNo dependence on initial conditions, but we are still learning how to do

it properly. I will review some recent progress.it properly. I will review some recent progress.


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V

BB1BB3

Boltzmann Brains are coming

oltzmann Brains are coming

Fortunately

ortunately

normal brains

ormal brains

are created even faster

re created even faster

due

due

to eternal inflation

o eternal inflation


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V

3

4 2 15

Problems with probabilitiesProblems with probabilities


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Time can be measured in the

number of oscillations ( )

or in the number of e-foldings ofinflation ( ). The universe

expands as

Unfortunately, the result depends on the time parametrization.

is the

growth of volume

during inflation


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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


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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., arXiv:0705.1160

A possible solution of this problem:A possible solution of this problem:


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This result agrees with the expectation that theprobability to be born in a part of the universe

which experienced inflation can be very large,because of the exponential growth of volumeduring inflation.


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Applications: Probabilities and the solution of theApplications: Probabilities and the solution of the

CC problem in the BP landscapeCC problem in the BP landscape

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 spherewith 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 nucleationof 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.

Clifton, Shenker, Sivanandam, arXiv:0706:3201


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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 beachieved with many different probability measures.

Predictions of other features of our world, includingstability/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 theprobability measure, and on the duration of the slow-roll

stage of inflation.

Hopefully we will learn many new interesting

things before the next Biermann lectures

andrei linde - lectures munich 3

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