Eternal Inflation in Stringy Landscapein Stringy …susy06.physics.uci.edu/talks/p/linde.pdfInflation and Cosmological Constant Three crucial steps in finding the anthropic solution

Eternal Inflationin Stringy Landscape

Eternal InflationEternal Inflationin Stringy in Stringy LandscapeLandscape

and A-wordaand And A--wordword

Andrei LindeAndrei Linde

Inflationary MultiverseInflationary MultiverseInflationary MultiverseFor 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.

Example: SUSY landscapeExample: SUSY landscapeExample: SUSY landscapeSupersymmetric SU(5)

V

SU(5) SU(4)xU(1) SU(3)xSU(2)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.

Landscape of eternal inflationLandscape of eternal inflation

Lesson of Inflation:Do not be afraid to consider such trivial factsas a large size, flatness and homogeneity of

the universe as observational data

Lesson of Inflation:Lesson of Inflation:Do not be afraid to consider such Do not be afraid to consider such trivial factstrivial factsas a large size, flatness and homogeneity of as a large size, flatness and homogeneity of

the universe as the universe as observational dataobservational data

Anthropic Principle:Do not be afraid to consider trivial facts of our

own life as observational data

Anthropic Principle:Anthropic Principle:Do not be afraid to consider Do not be afraid to consider trivial factstrivial facts of our of our

own life as own life as observational dataobservational data

Simple rules:Simple rules:Simple rules:If we find that neutrino have masses, study those theories that If we find that neutrino have masses, study those theories that allow it. With each new experiment we will know better which allow it. With each new experiment we will know better which theories should we use.theories should we use.If our universe is flat and contains perturbations with a flat If our universe is flat and contains perturbations with a flat spectrum, study those theories where this can happen.spectrum, study those theories where this can happen.

If we find that our life is carbonIf we find that our life is carbon--based, study only those based, study only those theories, or those parts of the universe, which allow carbontheories, or those parts of the universe, which allow carbon--based life. Not life in general, not atoms in general, not any kbased life. Not life in general, not atoms in general, not any kind ind of siliconof silicon--based life, but life as we see it.based life, but life as we see it.

We should not try to find all parameters that allow our life to We should not try to find all parameters that allow our life to exist. We should consider all our experimental results, exist. We should consider all our experimental results, including including the fact of our existencethe fact of our existence, and see whether their combination , and see whether their combination looks surprising. If so, we need a theory to explain it. If the looks surprising. If so, we need a theory to explain it. If the combination of the facts is not surprising, we do not need a combination of the facts is not surprising, we do not need a theory to explain them.theory to explain them.

Example: Why do we live in a 4D space?Example:Example: Why do we live in a 4D space?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.

We may still try to invent a theory which explains why our universe must be 4D. But the fact that our universe is 4D is not surprising, so we do not need to do it. It may be more productive to concentrate on many problems that do not have an anthropic solution.

For example, there is no anthropic replacement of inflation

For example, there is no For example, there is no anthropic replacement of inflationanthropic replacement of inflation

It was never easy to discuss anthropic principle, even with friends…

It was never easy to discuss anthropic It was never easy to discuss anthropic principle, even with friends…principle, even with friends…

But recently the concept of the string theory landscape came to the rescue

But recently the concept of the string theory But recently the concept of the string theory landscape came to the rescuelandscape came to the rescue

String Theory Landscape

String Theory String Theory LandscapeLandscape

Perhaps 10100 - 101000

different minima in string theory

Perhaps 10Perhaps 10100100 -- 101010001000

different minima in string different minima in string theorytheory

Inflation and Cosmological ConstantInflation and Cosmological ConstantInflation and Cosmological ConstantThree 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 us considered it obvious that we cannot live in the universe with

2) Derivation of the anthropic constraintWeinberg 1987, Martel, Shapiro, Weinberg 1997, Vilenkin, Garriga 1999…

Inflation and Cosmological ConstantInflation and Cosmological ConstantInflation and Cosmological Constant

3) String theory landscape

Multiplicity of (unstable) vacua:Lerche, Lust and Schellekens 1987: 101500 vacuum states

Bousso, Polchinski 2000; Feng, March-Russell, Sethi, Wilczek 2000

Vacuum stabilization:KKLT 2003, Susskind 2003, Douglas 2003,…

perhaps 101000 metastable dS vacuum states - still counting…

Probabilities in the LandscapeProbabilities in the LandscapeProbabilities in the Landscape

We must find all possible vacua (statistics), and We must find all possible vacua (statistics), and all possible continuous parameters (outall possible continuous parameters (out--ofof--equilibrium cosmological dynamics).equilibrium cosmological dynamics).

We must also find a way to compare the We must also find a way to compare the probability to live in each of these states.probability to live in each of these states.

Let 101000 flowers blossomLet 10Let 101000 1000 flowers flowers blossomblossom

Λ < 0Λ Λ < 0< 0

Λ = 0Λ Λ = 0= 0Λ > 0Λ Λ > 0> 0

Example: Two dS vacuaExample:Example: Two dS vacuaTwo dS vacua

is dS entropyis dS entropyPP00

PP11

PPii is the probability to find a is the probability to find a given point in the vacuum given point in the vacuum dSdSii

This isThis is the square of the Hartlethe square of the Hartle--Hawking wave functionHawking wave function, which tells , which tells that the fraction of the comoving volume of the universe with ththat the fraction of the comoving volume of the universe with the e cosmological constant Vcosmological constant Vi i == ΛΛ is proportional tois proportional to

In this context the HH wave function describes In this context the HH wave function describes the ground state of the the ground state of the universeuniverse, it has no relation to creation of the universe “from nothing”,, it has no relation to creation of the universe “from nothing”, and and it does not require any modifications recently discussed in the it does not require any modifications recently discussed in the literature.literature.

In this scenario we should live in the lowest of all dS spaces compatible with the existence of our life In this scenario we should live in the lowest of all In this scenario we should live in the lowest of all dS spaces compatible with the existence of our life dS spaces compatible with the existence of our life

However, this would also mean that instead of inflation we However, this would also mean that instead of inflation we would have eternal recycling of dead dS spaces. This would would have eternal recycling of dead dS spaces. This would disagree with observations.disagree with observations.

Dyson, Goheer, Kleban, Susskind 2002

Fortunately, this problem disappears in the KKLT scenario Fortunately, this problem disappears in the KKLT scenario because of metastability of dS vacua.because of metastability of dS vacua.

KKLT potential always has a Minkowski minimum KKLT potential always has a Minkowski minimum (Dine(Dine--Seiberg vacuum)Seiberg vacuum)

Probability of tunneling from Probability of tunneling from dS to Minkowski space dS to Minkowski space typically is somewhat greater typically is somewhat greater than than

ee--SS ~ e~ e--1/1/ΛΛ ~ e~ e--1010120120

After the tunneling, the field does After the tunneling, the field does not jump back not jump back -- no recycling.no recycling.

Now we will study decay from dS to the collapsing vacua Now we will study decay from dS to the collapsing vacua with negative vacuum energy.with negative vacuum energy.

Two dS vacua and AdS sinkTwo dS vacua and AdS sinkTwo dS vacua and AdS sink

PP00

PP11

Parts of dS space tunneling to space Parts of dS space tunneling to space with negative V rapidly collapse and with negative V rapidly collapse and drop out of equilibriumdrop out of equilibrium (one(one--way road way road to hell). to hell). Therefore instead of detailed Therefore instead of detailed balance equations, one has flow balance equations, one has flow equations:equations:

Ceresole, Dall’Agata, Giryavets, Kallosh, A.L., hep-th/0605266

Tunneling to the sinkTunneling to the sinkTunneling to the sinkIn the class of the KKLT models that we explored, the In the class of the KKLT models that we explored, the probability of the tunneling to the collapsing space with probability of the tunneling to the collapsing space with negative vacuum energy is related to SUSY breaking negative vacuum energy is related to SUSY breaking after the AdS uplifting, and is of the orderafter the AdS uplifting, and is of the order

In the simplest SUSY models, the rate of a decay to In the simplest SUSY models, the rate of a decay to a sink is ~ ea sink is ~ e1010120120 times greater than the probability to times greater than the probability to jump from our vacuum to a higher dS vacuum.jump from our vacuum to a higher dS vacuum.

That is why our part of the universe was produced by That is why our part of the universe was produced by inflation rather than by recycling of dead dS spaces: inflation rather than by recycling of dead dS spaces: Only ~ eOnly ~ e--1010120120 of all points produced by inflation are of all points produced by inflation are recycled; all others go to the sink.recycled; all others go to the sink.

Narrow sink Narrow sink Narrow sink

If the decay to the sink is slower than the decay of the upper If the decay to the sink is slower than the decay of the upper dS vacuum to the lower dS vacuum, then the probability dS vacuum to the lower dS vacuum, then the probability distribution is given by the Hartledistribution is given by the Hartle--Hawking expression, Hawking expression, despite the vacuum instability and the general probability despite the vacuum instability and the general probability flow down.flow down.

Generic probability leaksGeneric probability leaksGeneric probability leaks

In general, however, the probability In general, however, the probability leaks from dS to a collapsing leaks from dS to a collapsing space or to a Minkowski space space or to a Minkowski space may occur from may occur from allall dS vacua, and dS vacua, and the resulting probability distribution the resulting probability distribution may differ dramatically from the may differ dramatically from the HartleHartle--Hawking distributionHawking distribution..

In particular, if there is a strong probability leak from the In particular, if there is a strong probability leak from the upper dSupper dS vacua, then the probability to live there is vacua, then the probability to live there is exponentially small, and it does not depend on their exponentially small, and it does not depend on their vacuum energy. vacuum energy. In some other cases, the probability to In some other cases, the probability to live in the lower dS vacuum is exponentially live in the lower dS vacuum is exponentially smallersmaller than than in the upper ones (in the upper ones (inverted probability distributioninverted probability distribution).).

Conclusion:Conclusion:Conclusion:In the string landscape scenario In the string landscape scenario we do not study we do not study the ground state of the universethe ground state of the universe, as we did , as we did before. Instead of that, before. Instead of that, we study the universe with we study the universe with many holes in the groundmany holes in the ground..

Instead of studying static probabilities, like in a Instead of studying static probabilities, like in a pond with still water, we study probability currents, pond with still water, we study probability currents, like in a river dividing into many streams.like in a river dividing into many streams.

In other words, in addition to exploring In other words, in addition to exploring vacuum vacuum statisticsstatistics, we also explore , we also explore vacuum dynamicsvacuum dynamics..

The main conclusion:

IT IS SCIENCEIT IS SCIENCEIT IS SCIENCE

It is unusual, it is complicated, it has many unsolved problems, one may

like it or hate it, but we must learn how to live in a free world where many different possibilities are available

It is unusual, it is complicated, it has It is unusual, it is complicated, it has many unsolved problems, one may many unsolved problems, one may

like it or hate it, but we must learn how like it or hate it, but we must learn how to live in a free world where many to live in a free world where many different possibilities are availabledifferent possibilities are available

Two types of questions:Two types of questions:Two types of questions:

What is a What is a typical historytypical history of a given point in an of a given point in an eternally inflating universe? eternally inflating universe? (That is what we (That is what we studied so far.)studied so far.)

What is a What is a typical populationtypical population ? ? (Volume(Volume--weighted distributions)weighted distributions)

Example:Example:Example:

1) What is a typical age when any particular 1) What is a typical age when any particular scientist makes his best discoveries?scientist makes his best discoveries?

2) What is the average age of scientists making 2) What is the average age of scientists making greatest discoveries?greatest discoveries?

Both questions make sense, but the answers are significantly Both questions make sense, but the answers are significantly different because of the exponentially growing population of different because of the exponentially growing population of scientists.scientists.

Similarly, in the context of inflationary cosmology one Similarly, in the context of inflationary cosmology one may study a typical behavior at a given may study a typical behavior at a given pointpoint, or an , or an average behavior per unit average behavior per unit volumevolume..

PointilistsPointilists (like Seurat, Pissaro, and some of our friends) (like Seurat, Pissaro, and some of our friends) see no point in studying volume. Meanwhile inflation is see no point in studying volume. Meanwhile inflation is all about the exponential growth of volume. All all about the exponential growth of volume. All physically relevant physically relevant points, points, such as baryons, galaxies, such as baryons, galaxies, and observers, were created AFTER inflation, and their and observers, were created AFTER inflation, and their number was proportional to volume. number was proportional to volume.

Here I will illustrate the difference by studying the Here I will illustrate the difference by studying the simplest model of chaotic inflation.simplest model of chaotic inflation.

Naturalness (?) of chaotic inflationNaturalness (?) of chaotic inflationNaturalness (?) of chaotic inflation

Eternal InflationEternal Inflation

Chaotic inflation requires φ > Mp. This condition can be easily satisfied in the scalar field theory plus gravity, but it is difficult to construct inflationary models with φ > Mp in supergravity and string theory. It took almost 20 years to construct a natural version of chaotic inflation in SUGRA. In string theory we started doing it only 3 years ago, with limited success.

HOWEVER…HOWEVER…HOWEVER…Let us imagine that just one out of 101000 of string theory vacua allows existence of the field φ ~ 100, in units of Mp. The volume produced during chaotic inflation in this universe is proportional to eφ2 ~ 1010000 .

Therefore a part of the universe in such an improbable and “unnatural” state will have more volume (and contain more observers like us) than all other string theory vacua combined.

Latest anthropic constraints on Λ Latest anthropic constraints on Latest anthropic constraints on Λ Λ Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774

observed valueobserved value

Dark Energy (Cosmological Constant) is about 73% of the cosmic pieDark EnergyDark Energy (Cosmological Constant) (Cosmological Constant) is about 73% of the cosmic pieis about 73% of the cosmic pie

What’s about Dark Matter, another 23% of the pie? Why there is 5 times more dark matter than ordinary matter?

What’s about What’s about Dark MatterDark Matter, another 23% , another 23% of the pie? Why there is 5 times more of the pie? Why there is 5 times more dark matter than ordinary matter?dark matter than ordinary matter?

Example: Dark matter in the axion fieldExample:Example: Dark matter in the axion fieldDark matter in the axion field

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).Recently this possibility was analyzed by Aguirre, Rees, Tegmark, and Wilczek.

Latest anthropic constraints on Dark Matter Latest anthropic constraints on Dark MatterLatest anthropic constraints on Dark Matter Aguirre, Rees, Tegmark, and Wilczek, astro-ph/0511774

The situation with Dark Matter is similar to the situation with The situation with Dark Matter is similar to the situation with CC !CC !

observed valueobserved value

Split SupersymmetrySplit SupersymmetrySplit Supersymmetry

Arkani-Hamed, Dimopoulos, 2005

The amplitude of spontaneous symmetry breaking can be explained anthropically. This allows a new SUSY phenomenology, to be tested at LHC.

Exciting possibility: Testing anthropic principle on a collider…