1 Cosmic Inflation and the Arrow of Time A. Albrecht UCD P262 Spring 2006

Cosmic Inflation and the Arrow of

A. Albrecht

Spring 2006

I) Inflation in the era of WMAP

I.0 What is Cosmic Inflation?

I.1 Successes

I.2 Future tests

I.3 Theoretical advances

III) Conclusions

II) Inflation and the arrow of time

II.1 Introduction

II.2 Arrow of time basics

II.3 Inflation and the arrow of time

II.4 Implications

II.5 Can the Universe Afford Inflation?

Cosmic Inflation and the Arrow of Time

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

Inflation:

Try and solve the following puzzles/features of the Standard Big Bang (SBB) universe:

• Flatness

• Homogeneity

• Monopole

• Horizon

In the SBB, flatness is an “unstable fixed point”:

At GeVT 1610

The “GUT scale”

Require c to 55 decimal places to get

c today

Dominates with time

43 , aa

Gravitational instability: The Jeans Length

Jeans J s

Sound speedAverage energy density

• Overdense regions of size

collapse under their own weight.

If the size is they just oscillate

JeansR

SBB Homogeneity:

On very large scales the Universe is highly homogeneous, despite the fact that gravity will

clump matter on scales greater than RJeans

At the GUT epoch the observed Universe consisted of 1079 RJeans sized regions.

The Universe was very smooth to start with.NB: Flatness & Homogeneity SBB Universe starts in highly unstable state.

35 35 210 10 4Univ bh Max UnivS S M

SBB Monopolesi

• A GUT phase transition (or any other process) that injects stable non-relativistic matter into the universe at early times (deep in radiation era, ie Ti =1016 GeV) will *ruin* cosmology:

( )( )

Normal i

Normal

Monopole dominated Universe

Here & Now

SBB Horizon

1080 causally disconnected regions at the GUT epoch

'( ) '

dtd a t dt

Horizon: The distance light has traveled since the big bang:

10I.0 What is Cosmic Inflation?

The flatness, homogeneity & horizon features become “problems” if one feels one must explain initial conditions.

Basically, the SBB says the universe must start in a highly balanced (or “fine tuned”) state, like a pencil on its point.

Must/can one explain this?

Inflation says “yes”

The Basic Tools of Inflation:

Consider a scalar field with:1

( ) ( )2

If ( )V all space and time derivative (squared) terms

Then( ) 0 0 0

0 ( ) 0 0

0 0 ( ) 0

0 0 0 ( )

Which implies p 0d

~ Hta e Inflation

A period of early inflation gives:

Flatness:2

Dominates over & during inflation

Hconst

Homogeneity

At horizon crossing:

510HA suitably adjusted potential will

give :

Evaluate when k=H during inflation

.const

A period of early inflation gives:

Monopoles:

Dominates over & during inflation (and )

( )( )

( ) (0

a Const a

Monopoles are erased

~ Hta e

Inflation Horizon:

Here & Now

Inflation starts

Inflation ends

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

17I.1 Successes

Inflation:

• An early period of nearly exponential (“superluminal”) expansion set up the “initial” conditions for the standard big bang

Predictions:

• total=1 (to one part in 100,000 as measured)

• Characteristic oscillations in the CMB power

• Nearly scale invariant perturbation spectrum

• Characteristic Gravity wave, CMB Polarization etc

• etc

• total=1

Bennett et al Feb 11 ‘03

I.1 Successes

• total=1

I.1 Successes

Tegmark et al

astro-ph/0310723

WMAP Only

WMAP + SDSS

• Characteristic oscillations in the CMB power

Adapted from

“Active” models

Inflation

I.1 Successes

Angular scale

•Nearly scale invariant perturbation spectrum

I.1 Successes

•Characteristic Gravity wave, CMB Polarization etc

“Active” models

Inflation

TxE polarization power

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

• Emerging prospects for high precisions tests

|nS’ |

|nS’ |B. Gold & AA ‘03

I.2 Future tests

Future Ly-alpha

Generic slow roll inflation

( ) n ...lS S Sn k n n k

/ lnS Sn dn d k

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

28I.3 Theoretical advances

A.A, Davis Meeting on Cosmic Inflation ‘03

Great accomplishments and exiting future prospects

For an “snapshot” view the slides at:inflation03.ucdavis.edu

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

32II.1 Introduction

1) The physical (“thermodynamic”) arrow of time

2) Cosmic Inflation

Explained by initial conditions

Explains the initial conditions of the cosmos

Davies ’83 & ’84, Page ’83 (Nature)

Q: How are these two related?

Why wonder about arrow of time inflation?

•Understand what we are really trying to accomplish with inflation more solid foundations

•Fun combination of physics ideas

•Evaluate “alternatives to inflation”

II.1 Introduction

•Window on current hot topics

• Initial conditions in ”normal Physics”:

- Pose physical question

- Chose initial conditions which best describe “apparatus”

- Calculate and compare with experimental results

• Cosmic Inflation: Explain cosmic initial conditions using physics

Initial conditions play supporting role

Laws of physics play supporting role

Examples:

- Arrow of time

- Choice of vacuum in quantum field theory

II.1 Introduction

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

See H.D. Zeh The physical basis of the direction of time

- Macroscopic (or thermodynamic) arrow of time emerges from a combination of:

• Dynamical trends or “attractors”

• Special initial conditions

• Choice of coarse graining

- Despite a completely reversible microscopic world

NB: Not about “T symmetry”

Jeansl l , gravity unimportant)(Taking

Dynamical trends or “attractors”

Special initial conditions

Choice of coarse graining

An Example:

• Recording/Learning

• Harnessing energy (actually “low entropy”)

Key roles of the arrow of time:

Key roles of the arrow of time (cont.):

• Quantum Measurement

Everett same old “thermodynamic” arrow of time

- Macroscopic (or thermodynamic) arrow of time emerges from a combination of:

• Dynamical trends or “attractors”

• Special initial conditions

• Choice of coarse graining

Most Fundamental

Entropy, laws of thermodynamics, counting number of states etc:

-Ways to quantify the above

- “Icing on the cake”

Time 1 Time 2 Time 3

Jeansl l : gravity very importantNow consider

A completely different trend/attractor:

Gravitational Collapse

: gravity very important

Equilibrium under gravitational collapse:

Black Hole

(the state of ultimate collapse)

24bhS M

(Sbh not as well developed as ordinary entropy, but good enough for our purposes as a way to quantify a dynamical trend.)

Jeansl l

The Punch Line:

The thermodynamic arrow of time originates with the very special initial conditions of the cosmos:

The early universe is very homogeneous on scales very far from Eqm. (= black hole)

35 35 210 10 4Univ bh Max UnivS S M

Cosmic Microwave Background uniform to one part in 105

Penrose

Jeansl l

The everyday link to gravitational collapse

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

50II.3 Inflation and the arrow of time

Standard inflation spiel begins:

Cosmological problems of standard big bang:

Universe starts far from dynamical trend:

-Homogeneous

-Horizons prevent dynamical explanation

Q: How can this fact be explained?But isn’t starting far from the dynamical trend exactly what is required to explain the arrow of time? And when do we ever explain initial conditions anyway?

Warm up 1: Big Bang Nucleosynthesis Prediction of abundances.

Species

But doesn’t the answer just depend on the initial state?

Figure: Burles, Nollett, &Turner

Warm up 1: Big Bang Nucleosynthesis: Nuclear Statistical (“chemical”) equilibrium (attractor) erases initial conditions dependence.

Eq. Time

Time to species freeze-out

Coarse Graining:

Just ask about mass fractions

Warm up 2: Gas in ice

Insulator

Time 1

Insulator

Time 2

Insulator

Time 3

Insulator

Frozen

Internal eqm time << freezing time

Internal eqm. set initial conditions for condensation & final frozen state.

End warm up… now the real thing:

Key ingredient:

Cosmological constant => different gravitational at attractor:

de Sitter space

- Perfectly flat, homogeneous, exponentially expandingProperties of Big Bang initial

Gibbons & Hawking, See also Bousso

Equivalent to “perfect” potential dominated state

Can be mimicked by a scalar field in a special “potential dominated state”

Inflaton field can turn on and off eff

Inflation: Let the inflaton field turn on and leave it on for *many* de Sitter equilibration times, then decay into ordinary matter.

A standard “big bang” (arrow of time and all) is created.

The Inflaton:

Consider a scalar field with:

1( ( )) ( ) ( ) ( ( ))

2x x x V x

If )(V all space and time derivative (squared) terms

Htea ~

Inflation

8 ( )GV

Quantum fluctuations

Comparisons:

System Initial Conditions

•Nucleosynthesis

•Slow Freeze

•Inflation

Created by early time attractor (eqm)

Comparisons:

System Initial Conditions

•Nucleosynthesis

•Slow Freeze

•Inflation

Created by early time attractor (eqm) in subspace

But driven by non-eqm degree of freedom

Background Spacetime

Out of eqm ice

Special Inflaton field configurationIssues with very small scales!II.3 Inflation and the arrow of time

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

Does inflation

-Predict the arrow of time? (Sets up IC’s for Big Bang)

-Depend on the arrow of time? (Requires special initial state of inflaton etc.)

II.4 Implications

BLABLA

Comment on how we use knowledge (“A” word!)

Total knowledge about the universe

Input Theory Output

II.4 Implications

BLABLA

Comment on the “A” word:

Input Theory Output

II.4 Implications

BLABLA

Input Theory Output

II.4 Implications

BLABLA

Input Theory Output

II.4 Implications

BLABLA

Input Theory Output

II.4 Implications

BLABLA

Input Theory Output

The best science will use up less here and produce more here

II.4 Implications

Q: To what extent should our arrow of time (smooth initial state of Big Bang) best used as INPUT, rather than OUTPUT?

A: The arrow of time (smooth initial state of Big Bang) can NOT be 100% output.

The very nature of the arrow of time requires initial conditions that are not completely generic

II.4 Implications

What Role What role inflation?

-Gives package deal: Universe very large, flat, and with particular perturbations (falsifiable!). -Answers Boltzmann’s concerns about typical regions with arrow of time being much smaller and “shorter” then we experience. (inflation as amplifier). [Also modern cosmological version.]

- Answers “How did our Universe come about?”

II.4 Implications

NB: In the spirit of Linde’s “chaotic inflation”

-“Dominant channel” into Big Bang (Uses attractor behavior and exponential volume factors to maximize impact)

Rare Fluctuation

II.4 Implications

75II.4 Implications

Boltzmann's “cosmology”:

76II.4 Implications

77II.4 Implications

78II.4 Implications

79II.4 Implications

80II.4 Implications

81II.4 Implications

82II.4 Implications

83II.4 Implications

Boltzmann's “cosmology” appeared to make very strange predictions:

84II.4 Implications

85II.4 Implications

86II.4 Implications

(Boltzmann's brain)

87II.4 Implications

88II.4 Implications

89II.4 Implications

90II.4 Implications

Inflation (**schematic**):

91II.4 Implications

92II.4 Implications

)(V all space and time derivative (squared) terms

The “rare fluctuation” is in the inflaton field

93II.4 Implications

Inflation exponentially expands the volume

Reheated regions give big bang

Special package of features predicted by inflation

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

I.1 Successes

I.2 Future tests

III) Conclusions

II.1 Introduction

II.4 Implications

Dark energy and Equilibrium

Supernova

Preferred by modern data

Amount of gravitating matter

“anti

Red line: No anti-gravity matter

Mass-Energy of the a Universe made only out of standard model matter

Surprise factor

II.5 Can the Universe afford Inflation?

An interesting property of some types of dark energy (including a w=-1 cosmological constant): Formation of an event horizon:

Black Hole Event Horizon (schematic):

Outside observer sees in-falling object take infinite time to reach the horizon (“never reaches the horizon”)

An interesting property of some types of dark energy (including the cosmological constant): Formation of an event horizon:

Dark Energy Event Horizon (schematic):

INSIDE observer sees OUT-flying object take infinite time to reach the horizon (“never reaches the horizon”)

2 1S A H

t1t2t3t4……

“de Sitter Space”

2 1S A H

“De Sitter Space: The ultimate equilibrium for the universe?

Horizon

Quantum effects: Hawking Temperature

Rare Fluctuation

A cosmological constant can help realize the “rare fluctuation” cosmology.

Rare Fluctuation

A cosmological constant can help realize the “rare fluctuation” cosmology.

The only really physics way to discuss “initial” conditions

Concept:

Realization:

“de Sitter Space”

Rare Fluctuation

Big question:

What is the most likely fluctuation to “give what we see:?:

-Normal Big Bang?

-Inflating Region?

The universe spends most of its time in “equilibrium”

The equilibrium state is given by an observer’s “causal patch” in de Sitter space with a very small Λ.

Cosmology given by the appearance of rare fluctuations away from this eqm. state.

Recurrence times/probabilities given by stat mech:

SS Sfluct

fluct SR

t eP e

Dyson, Kleban & Susskind (hep-th/0208013)AND AA & Sorbo hep-th/0405270

The basic picture:

SS Sfluct

fluct SR

t eP e

fluctt

fluctP

= Recurrence time for a particular fluctuation

= Recurrence time for whole system

= Total microstates of system

= Probability of fluctuation

A&S: How to calculate the inflationary fluctuation the

Darwinian cosmology with Λ :1) Use standard work on tunneling into inflation (“free lunch”, “universe in a garage”)

Farhi Guth & Gueven; Blau Gundelman & Guth; Fischler Morgan & Polchinski

2) Use stat mech to determine Pc for the classical solutions in 1)

inf c qP P P

quantum tunneling

Probability to form “incoming” classical solution

AA & Sorbo hep-th/0405270

Picture from A. Guth

• The stat mech piece for

de Sitter space with a small perturbation looks Schwarzschild far from the perturbation:

BHA A A A

Gibbons & Hawking

• The stat mech piece for

de Sitter space with a small perturbation looks Schwarzschild far from the perturbation:

BHA A A A

Gibbons & Hawking

C BH I BHS S S S S S S S 4

Dominated by reduction in entropy of full system (not SI)

• Box of gas analogy

Rare fluctuation in a box of gas:

(1 ),V f T

, 'gfV T

f fraction of V affected

g size of fluctuation as a fraction of fV

Assuming entropy density (s) obeys3s T

1/ 41fluct eqm eqmS S f S fg

and using conservation of energy

Entropy of remaining “normal” region

Entropy of “weird” region

4E Vol T

fluct eqmS S

fluctP e

1/ 4(1 )eqm eqmS f g S fe e The dominant effect is that a volume fV has been deprived of eqm entropy

The Answer:

C BHS S S S

The Answer:

C BHS S S S

mC QP P P e

The Answer:

C BHS S S S

m S SC QP P P e e

Dominated by “entropy lost by environment”

Compare with “regular big bang”

8510BBS

Compare with “regular big bang”

8510BBS

inf 1BH BH

SS S S

S S SBB

85 510 10BB BHS S Inflation highly favored

inf 1BH BH

SS S S

S S SBB

8510BB BHS S Inflation highly favored

This is a quantification of the standard intuition:

• Inflation starts with a “cheap” fluctuation vs Standard Big Bang

• This makes a inflation “more likely” start for our observed universe.

iii. Horizons, Entropy and Causal Patch Physics

Principles of Causal Patch Physics:

• To the outside observer there is no “inside of Black Hole”

• Infalling observer reuses the same degrees of freedom to describe the interior* (outside observer absent)

• Could resolve BH info paradox

iii. Horizons, Entropy and Causal Patch Physics

*Requires highly non-local transformation between frames (“stringy magic”?)

Implications of causal patch physics for our calculations:

• Basis for De Sitter space as finite closed system & application of stat mech

• During inflation (quasi-De Sitter) a horizon forms: Possibly dramatic implications.

• Dyson Kleban & Susskind: There is no “outside the De Sitter horizon” during inflation. All degrees of freedom are inside.

• Principles of causal patch physics change everything:

DKS: A horizon forms for the inflating region and holographic magic is evoked:

de Sitter + small fluctuation (mass M)

( )dS BH MA A A

“Magic”

Inflation: approximate de Sitter

degrees of freedom re-organize to only describe inside the horizon.

Most degrees of freedom must “condense out” to manifest the very low inflationary entropy.

PI I I

mS A H S

• Principles of causal patch physics change everything:

DKS: A horizon forms for the inflating region and holographic magic is evoked:

de Sitter + small fluctuation (mass M)

( )dS BH MA A A

“Magic”

Inflation: approximate de Sitter

degrees of freedom re-organize to only describe inside the horizon.

Most degrees of freedom must “condense out” to manifest the very low inflationary entropy.

PI I I

mS A H S

BHS S Se

• Causal patch principles replace

inf 1BH

S S S S S SBB

Inflation highly

disfavored

Inflation highly favored

• Causal patch principles replace

inf 1BH

Inflation highly favored

S S S S S SBB

Low entropy of inflating region converted from benefit to liability

Inflation highly

disfavored

Counting of exterior makes inflation cheap

v. Discussion & Conclusions

Topics

• Transcending the specifics of de Sitter eqm

• Boltzmann’s Brain

• Conclusions

• Transcending the specifics of de Sitter eqm

This looks like a problem no matter how confused you are about what to put here

S S S S S SBB

This is rare no matter how poorly you understand the entropy at Time 1

Time 1Time 2

And this is even more rare!

Time 1Time 2

Surely this is rare too

landscape

and this!

Eternal inflation

Landscapes and eternal inflation etc do not obviously get you off the hook.

For example for large spaces, consider the

This looks like a

problem no matter how confused you are about what to put here

S S S S S SBB

• Boltzmann’s Brain paradox:

The most likely fluctuation consistent with everything you know is your brain fluctuating out of chaos and immediately re-equilibrating. (Also works for planets) [Related to in DKS]

Only inflation has an answer to this paradox. With inflation, most probable way to create one brain (or planet) comes packaged with a huge flat universe (+body, fellow creatures etc)

This is as least as important as the other successes of inflation!

BB XBBP P

•Conclusions

Darwinian cosmology is better

DKS /AS/Λ offer an attractive scheme for Darwinian cosmology. Can bring discussions of inflation/etc to next level.

Cosmology appears to place causal patch physics in conflict with inflation (even when not using Λ eqm.).

Fundamental issue: Is there really more universe outside the horizon during inflation? (yes inflation OK)

Resolving this conflict between will teach us something very interesting about at least one of these:

-inflation

-causal patch physics

-quantum gravity

Burning question:

What is the most likely fluctuation to “give what we see:?:

-Normal Big Bang?

-Inflating Region?

Additional material

Where to go from here:

• How to fit all this into a “big picture”

- Can inflation be “eternal”? (Brode, Vilenkin, Guth, Aguirre & Gratton)

- Connection with quantum gravity, quantum measurement… (Banks, Banks & Fischler, Dyson et al, AA Kaloper & Song)

- Quantify “dominant channel” claim

- etc.

• Evaluate competing ideas:

- Ekpyrotic (no “attractor”, no volume factors. How can this channel compete?... a super-rare fluctuation)

- Cyclic (“a perpetual motion machine of the 2nd kind”?)

- Holographic (built in arrow of time)

II.4 Implications

More thoughts

Q: Can the thermodynamic arrow of time be sufficiently tightly linked with emergence of classicality to reduce waste of data as input?

(Do classical “regions” automatically have a “low S end”?)

Related to standard “wavefunction of the universe” work

II.4 Implications

Does gravity radically transform the nature of the arrow of time?

More thoughts:

-Sort our measures! (Usually we can handle this.)

- How can we contemplate the “general chaotic state of all possibilities”?

vs eternal inflation,

vs causal patch physics

II.4 Implications

Evaluate alternatives

• Attractor behavior vs “statement of state” (i.e ekpyrotic)

• Special initial conditions must be somewhere (vs. early statements about the “new” cyclic universe)

II.4 Implications

Idea“Creates” IC’s(attractor behavior)

Volume

Factors

Standard Big Bang no

Holographic Cosmology (Banks & Fischler)**

Inflation (Chaotic = ++)Wavefunction of Univ.

VSL Cosmology

Ekpyrotic Universe no

Eternal (Aguirre & Gratton)

New Cyclic

II.4 Implications

yes yes

yes (w/inflation)

yes “Yes”no

Version 1Version 2

no Xyes yes

144III Conclusions

I.1 Successes

I.2 Future tests

Exciting future

• Understand what we are really trying to accomplish with inflation a more solid foundation

Inflation:

1) Can not take all possible initial conditions into SBB

2) Can give “dominant channel” to Standard Big Bang.. (Still have predictive power, successful so far)

3) Solves the “Boltzmann’s Brain” problem

III Conclusions

-Initial attractor

-Volume factor

Special inflaton initial state (arrow of time) Required of all theories

• Evaluate “alternatives to inflation”

1) Attractor behavior is not the same as “statement of state”

2) Arrow of time all theories of initial conditions require something “special” (not completely generic)

3) (No Perpetual Motion!)

III Conclusions

“Statement of state” much less ambitious

III Conclusions

•Window on current hot topics

1) Singularities in quantum gravity

2) “Equilibrium” states in quantum gravity

3) Entropy and gravity (“Holography”) (AA, NK, Y-SS)

4) “Before” inflation

5) Arrow of time in quantum gravity

• Fun combination of physics ideas

III Conclusions

1 Cosmic Inflation and the Arrow of Time A. Albrecht UCD P262 Spring 2006

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