1 cosmic inflation and the arrow of time a. albrecht ucd p262 spring 2006

1

Cosmic Inflation and the Arrow of

Time

A. Albrecht

UCD

P262

Spring 2006

2

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

3



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



4

Inflation:

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

• Flatness

• Homogeneity

• Monopole

• Horizon


5

a

1

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

At GeVT 1610

or

28

0

10a

a

The “GUT scale”

Require c to 55 decimal places to get

c today

22

2

8

3

a kH

a a

c

23

8c

H

Dominates with time

43 , aa


i

6

Gravitational instability: The Jeans Length


i

1/ 22

Jeans J s

cR c

G

Sound speedAverage energy density

• Overdense regions of size

collapse under their own weight.

If the size is they just oscillate

JeansR

JeansR

7

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

i


8

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:

3

4 "

( )( )

( )(

"

)

M i

M i

Normal i

Normal

i iM

Norma

i

l T

i

TT T

TT

TT

T

TT

Monopole dominated Universe

9

t=0

Here & Now

SBB Horizon

1080 causally disconnected regions at the GUT epoch

i


0

'( ) '

( ')

t

H

dtd a t dt

a t

Hd

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”

11

The Basic Tools of Inflation:

Consider a scalar field with:1

( ) ( )2

V L

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

Then( ) 0 0 0

0 ( ) 0 0

0 0 ( ) 0

0 0 0 ( )

V

VT

V

V

Which implies p 0d

da

~ Hta e Inflation

w=-1

i


12

A period of early inflation gives:

Flatness:2

22

8

3

a kH

a a

a

1

Dominates over & during inflation

33

'H

H

Hconst

V

Homogeneity

At horizon crossing:

510HA suitably adjusted potential will

give :

i


1c

Evaluate when k=H during inflation

.const

r m

13

A period of early inflation gives:

Monopoles:

a

1

Dominates over & during inflation (and )

i


1

1

1

3

1

3

( )( )

( ) (0

)

M

M HtM

a

aa

a Const a

aa

e

M

Monopoles are erased

~ Hta e

22

2

8

3

a kH

a a

1c

r m

14

Inflation Horizon:

Here & Now

Inflation starts

Inflation ends

i


15



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



16



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

18

• total=1

Bennett et al Feb 11 ‘03

WMAP

I.1 Successes

19

• total=1


WMAP

I.1 Successes

Tegmark et al

astro-ph/0310723

WMAP Only

WMAP + SDSS

20

• Characteristic oscillations in the CMB power

Adapted from


WMAP

“Active” models

Inflation

I.1 Successes

Tem

pera

ture

Pow

er

Angular scale

21

•Nearly scale invariant perturbation spectrum


WMAP

I.1 Successes

1 sn

H k

k Ak

22

•Characteristic Gravity wave, CMB Polarization etc


WMAP

“Active” models

Inflation

TxE polarization power

I.1 Successes

23



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications


24



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications


25

• Emerging prospects for high precisions tests

|nS’ |

ns

n

|nS’ |B. Gold & AA ‘03

I.2 Future tests

Future Ly-alpha

Generic slow roll inflation

WMAP

1 sn

H k

k Ak

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

/ lnS Sn dn d k

26



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



27



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

29


Great accomplishments and exiting future prospects

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

30



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



31



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?

33

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

34

• 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

35



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



36



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



37

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”

38

Jeansl l , gravity unimportant)(Taking

Dynamical trends or “attractors”

Special initial conditions

Choice of coarse graining

An Example:


39

• Recording/Learning

• Harnessing energy (actually “low entropy”)

Key roles of the arrow of time:


40

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

• Quantum Measurement

Everett same old “thermodynamic” arrow of time


41

- 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”


42

Time 1 Time 2 Time 3


43

Jeansl l : gravity very importantNow consider

A completely different trend/attractor:

Gravitational Collapse


44

: 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

45

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

46

The everyday link to gravitational collapse


47

The everyday link to gravitational collapse


48



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



49



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:

-Flat

-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?

51

Warm up 1: Big Bang Nucleosynthesis Prediction of abundances.

Time

Mass

Fra

ctio

n

Species

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

Figure: Burles, Nollett, &Turner


52

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

Time

Mass

Fra

ctio

n

Eq. Time

Time to species freeze-out

Coarse Graining:

Just ask about mass fractions


53

Warm up 2: Gas in ice

Ice

Insulator

Ice

Time 1

Insulator


54

Ice

Insulator

Ice

Time 2

Insulator



55

Ice

Insulator

Ice

Time 3

Insulator

Frozen



56

Internal eqm time << freezing time

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



57

End warm up… now the real thing:


58

Key ingredient:

8G T

Cosmological constant => different gravitational at attractor:

de Sitter space

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

state

3dSS

Gibbons & Hawking, See also Bousso

Equivalent to “perfect” potential dominated state


59

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.

eff


60

The Inflaton:

Consider a scalar field with:

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

2x x x V x

L

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

Htea ~

Inflation

0a

8 ( )GV

V

Quantum fluctuations


61

Comparisons:

System Initial Conditions

•Nucleosynthesis

•Slow Freeze

•Inflation

V

Created by early time attractor (eqm)




62

Comparisons:

System Initial Conditions

•Nucleosynthesis

•Slow Freeze

•Inflation

V

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

63



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



64



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



65

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

66

LABLA

BLABLA

BLABLA

B

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

Total knowledge about the universe

Input Theory Output

II.4 Implications

67

LABLA

BLABLA

BLAB

LAB

Comment on the “A” word:


Input Theory Output

II.4 Implications

68

LABLA

BLABLA

BLAB

LAB



Input Theory Output

II.4 Implications

69

LABLA

BLABLA

BLAB

LAB



Input Theory Output

II.4 Implications

70

LABLA

BLABLA

BLAB

LAB



Input Theory Output

LABPR

ED

II.4 Implications

71

LABLA

BLABLA

BLAB

LAB

Input Theory Output

LABPR

ED

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

II.4 Implications

72

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

73

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)

74

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

V


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


94



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



95



I.1 Successes

I.2 Future tests


III) Conclusions


II.1 Introduction



II.4 Implications



96

Dark energy and Equilibrium

97

Supernova

Preferred by modern data

Amount of gravitating matter

A

mount

of

“anti

gra

vit

y”

matt

er

(Dark

En

erg

y)

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?

98

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”)


99

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”


100

2 1S A H

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

Horizon

Quantum effects: Hawking Temperature

8

3 DE

GT H


101

Rare Fluctuation

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


102

Rare Fluctuation

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


The only really physics way to discuss “initial” conditions

103

Concept:

Realization:

“de Sitter Space”


104

Rare Fluctuation


105

Big question:

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

-Normal Big Bang?

-Inflating Region?


106

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:

fluct

fluct

SS Sfluct

fluct SR

t eP e

t e

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

The basic picture:


107

fluct

fluct

SS Sfluct

fluct SR

t eP e

t e

fluctt

Rt1S

fluctP

= Recurrence time for a particular fluctuation

= Recurrence time for whole system

= Total microstates of system

= Probability of fluctuation


108

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


109

Picture from A. Guth

qP

cP


110

• The stat mech piece for

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

BHA A A A

Gibbons & Hawking

cP


111

• The stat mech piece for

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

BHA A A A

Gibbons & Hawking

So

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

infP

I dSI

mS S

m

where

cP

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


112

• Box of gas analogy

Rare fluctuation in a box of gas:

(1 ),V f T

, 'gfV T

fV

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


113

The Answer:

C BHS S S S

C

BH

SS S

C S

eP e

e


114

The Answer:

C BHS S S S

and

C

BH

SS S

C S

eP e

e

4P

I

m

mQP e

4

inf

PBH

I

mS S

mC QP P P e


115

The Answer:

C BHS S S S

and

C

BH

SS S

C S

eP e

e

4P

I

m

mQP e

4

inf

PBH

I BH

mS S

m S SC QP P P e e

Dominated by “entropy lost by environment”


116

Compare with “regular big bang”

8510BBS

fluct

BB

SS S

BB S

eP e

e


117

Compare with “regular big bang”

8510BBS

so

fluct

BB

SS S

BB S

eP e

e

inf 1BH BH

BB BB

SS S S

S S SBB

P e e

P e e

85 510 10BB BHS S Inflation highly favored


118

inf 1BH BH

BB BB

SS S S

S S SBB

P e e

P e e

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.


119

BUT

120


iii. Horizons, Entropy and Causal Patch Physics



121



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”?)


122

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.


123

• 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.

4

2inf

PI I I

I

mS A H S

m


124

• 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.

4

2inf

PI I I

I

mS A H S

m

BHS S Se

125

• Causal patch principles replace

inf 1BH

BB

SS

SBB

P e

P e

with

4

inf 1

P

II

BB BB

m

mS

S S S S S SBB

P e e

P e e

Inflation highly

disfavored

Inflation highly favored


126

• Causal patch principles replace

inf 1BH

BB

SS

SBB

P e

P e

Inflation highly favored

with

4

inf 1

P

II

BB BB

m

mS

S S S S S SBB

P e e

P e e

Low entropy of inflating region converted from benefit to liability

Inflation highly

disfavored

Counting of exterior makes inflation cheap


127

v. Discussion & Conclusions

Topics

• Transcending the specifics of de Sitter eqm

• Boltzmann’s Brain

• Conclusions


128

• Transcending the specifics of de Sitter eqm

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

4

inf 1

P

II

BB BB

m

mS

S S S S S SBB

P e e

P e e


129

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

Time 1Time 2


130

And this is even more rare!

Time 1Time 2


131

1010S

Surely this is rare too

landscape


132

1010S

and this!

Eternal inflation


133

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

For example for large spaces, consider the

limit

0

( )S

This looks like a

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

4

inf 1

P

II

BB BB

m

mS

S S S S S SBB

P e e

P e e


134

• 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

135

•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


136

END

137

Burning question:

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

-Normal Big Bang?

-Inflating Region?

138

Additional material

139

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

140

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?

141

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

142

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

143

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

no

no

yes yes

yes (w/inflation)

yes “Yes”no

Version 1Version 2

no Xyes yes

no X

no

144III Conclusions


I.1 Successes

I.2 Future tests


Exciting future

145


• 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

146


• 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

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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

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• Fun combination of physics ideas

III Conclusions


1 cosmic inflation and the arrow of time a. albrecht ucd p262 spring 2006

Documents

cosmic inflation

inflation horizon

inflation homogeneity

inflation w

period of early inflation

basic tools of inflation

universe slide

arrow of time slide