Inflation, infinity, equilibrium and the observable Universe Andreas Albrecht UC Davis UCD Colloquium October 3, 2011 1A. Albrecht @ UCD 10/3/11

A. Albrecht @ UCD 10/3/11 1

Inflation, infinity, equilibrium and the observable Universe

Andreas AlbrechtUC Davis

UCD ColloquiumOctober 3, 2011

E


Cosmic Inflation:

Great phenomenology, but

Original goal of explaining why the cosmos is *likely* to take the form we observe has proven very difficult to realize.


Cosmic Inflation:



This Talk


Cosmic Inflation:



OR: Just be happy we have equations to solve?


OUTLINE

1. Big Bang & inflation basics

2. Eternal inflation

3. de Sitter Equilibrium cosmology

4. Cosmic curvature from de Sitter Equilibrium cosmology


OUTLINE






Friedmann Eqn.

2

2 8

3 k r m DE

aH G

a


Friedmann Eqn.

2

2 8

3 k r m DE

aH G

a

Curvature

2a


Friedmann Eqn.

2

2 8

3 k r m DE

aH G

a

CurvatureRelativistic Matter

2a4a


Friedmann Eqn.

2

2 8

3 k r m DE

aH G

a


Non-relativistic Matter

2a

3a

4a


Friedmann Eqn.

2

2 8

3 k r m DE

aH G

a



Dark Energy

2a

3a

4a 0a


-30 -20 -10 0 10-20

0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m


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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m


-5 -4 -3 -2 -1 0 1 2

-10

-5

0

5

10

15

log(a/a0)

log( / c0 )

r

m


-30 -20 -10 0 10-20

0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m

k

The curvature feature/“problem”


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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m

k

!



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0

20

40

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80

100

120

log(a/a0)

log( / c0 )

r

m

k

!



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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m

k

!



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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m

k



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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

r

m

k

!



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0

20

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log(a/a0)

log( / c0 )

r

mMono

The monopole “problem”


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0

20

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60

80

100

120

log(a/a0)

log( / c0 )

r

mMono

!

The monopole “problem”


Friedmann Eqn.

2

2 8

3 k r m DE

aH G

a



Dark Energy

2a

3a

4a 0a


Friedmann Eqn.

2

2 8

3 I k r m DE

aH G

a



Dark Energy

2a

3a

4a 0a

Now add cosmic inflation

0a

Inflaton


Friedmann Eqn.

2

2 8

3 I k r m DE

aH G

a



Dark Energy

Now add cosmic inflation

0a

Inflaton


The inflaton:~Homogeneous scalar field obeying

3H V

2 01.

2I V V const a

All potentials have a “low roll” (overdamped) regime where

Cosmic damping Coupling to ordinary matter

V


The inflaton:~Homogeneous scalar field obeying

3H V

2 01.

2I V V const a

All potentials have a “low roll” (overdamped) regime where

Cosmic damping Coupling to ordinary matter

V


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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

I

r

m

Add a period of Inflation:


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0

20

40

60

80

100

120

log(a/a0)

log( / c0 )

I

r

m

k

With inflation, initially large curvature is OK:


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40

60

80

100

120

log(a/a0)

log( / c0 )

I

r

m

Mono

With inflation, early production of large amounts of non-relativistic matter (monopoles) is ok :


Inflation detail:

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0

0.5

log(a/a0)

/M

P

-28.8 -28.6 -28.4 -28.2 -28 -27.8 -27.6100

105

110lo

g( / c0 )

KE

V

r


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0

0.5

log(a/a0)

/M

P

-28.8 -28.6 -28.4 -28.2 -28 -27.8 -27.6100

105

110lo

g( / c0 )

KE

V

r

Inflation detail:

-2 0 20

1

2

3

/MP

V/M

GU

T4

2 21

2V m


2

2 8 8

3 3I k r m DE Tot

aH G G

a

Hubble Length

1/2

1H

Tot

cR

H


2

2 8 8

3 3I k r m DE Tot

aH G G

a

Hubble Length

1/2

1H

Tot

cR

H

(aka )c


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0

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100

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log(a/a0)

log( / c0 )

I

r

m

Tot


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100

120

log(a/a0)

log( / c0 )

Tot


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0

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100

log(a/a0)

log( / c0 )

Tot


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0

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100

log(a/a0)

log( / c0 )

Tot


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0

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100

log(a/a0)

log( / c0 )

Tot

1/21

HTot

cR

H


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-50

0

50

100

log(a/a0)

log(

(RH

/RH0

)2 )

RH2

1/21

HTot

cR

H


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-50

0

50

100

log(a/a0)

log(

RH

/RH0

)

RH

1/21

HTot

cR

H


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0

10

log(a/a0)

log(

RH

/RH0

)

RH

1/21

HTot

cR

H


1/21i

Hi i

cR

H

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0

10

log(a/a0)

log(

RH

/RH0

)

RHI

RHr

RHm

RH


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0

10

log(a/a0)

log(

RH

/RH0

)

RHI

RHr

RHm

RH

RHTot

1/21i

Hi i

cR

H


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0

10

log(a/a0)

log(

RH

/RH0

)

RH

1/21

HTot

cR

H


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10

log(a/a0)

log[

(RH/R

H0)-1

]

End of inflation


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log(a/a0)

log[

(RH/R

H0)-1

]

End of reheating


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log[

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]

Weak Scale


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log[

(RH/R

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]

BBN


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10

log(a/a0)

log[

(RH/R

H0)-1

]

Radiation-Matter equality


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10

log(a/a0)

log[

(RH/R

H0)-1

]

Today


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log(

RH/R

H0)

Perturbations from inflation

comoving


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10

log(a/a0)

log(

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Here


comoving


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10

log(a/a0)

log(

RH/R

H0)

Here

Here


comoving

2

2

H


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10

log(a/a0)

log(

RH/R

H0)

Here

Here

comoving

2

2

H


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10

log(a/a0)

log(

RH/R

H0)

Here

Here

comoving

2

2

H


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0

0.5

log(a/a0)

/M

P

-28.8 -28.6 -28.4 -28.2 -28 -27.8 -27.6100

105

110lo

g( / c0 )

KE

V

r

Inflation detail:

-2 0 20

1

2

3

/MP

V/M

GU

T4

2 21

2V m


-28.8 -28.6 -28.4 -28.2 -28 -27.8 -27.6-0.5

0

0.5

log(a/a0)

/M

P

-28.8 -28.6 -28.4 -28.2 -28 -27.8 -27.6100

105

110lo

g( / c0 )

KE

V

r

Inflation detail:

-2 0 20

1

2

3

/MP

V/M

GU

T4

2 21

2V m

128 10m GeV

to give

510


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10

log(a/a0)

log(

RH/R

H0)

Here

Here

comoving

2

2

H


Brown et al.Astrophys.J.705:978-999,2009


Brown et al.Astrophys.J.705:978-999,2009


Keiser et al. 2011


Keiser et al. 2011


OUTLINE






OUTLINE






Does inflation make the SBB natural?

How easy is it to get inflation to start?

What happened before inflation?


HR

Quantum fluctuations during slow roll:

A region of one field coherence length ( ) gets a new quantum contribution to the field value from an uncorrelated commoving mode of size in a time leading to a (random) quantum rate of change:

Thus

measures the importance of quantum fluctuations in the field evolution

HR

H 1t H

2Q H

2Q H

t


HR



Thus


HR

H 1t H

2Q H

( )

510

2Q H

t


HR



Thus


HR

H 1t H

2Q H

t

2Q H

( )

510

For realistic perturbations the evolution is very classical


-2 -1 0 1 20

0.5

1

1.5

2

2.5

/MP

V/M

GU

T4

If this region “produced our observable universe”…


-2 -1 0 1 20

0.5

1

1.5

2

2.5

/MP

V/M

GU

T4

It seems reasonable to assume the field was rolling up here beforehand (classical extrapolation)


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log[

(RH/R

H0)]


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0

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100

150

log(a/a0)

log[

(RH/R

H0)]

410


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0

200

400

600

log(a/a0)

log[

(RH/R

H0)]

410


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-1000

-500

0

500

1000

1500

2000

log(a/a0)

log[

(RH/R

H0)]

410

310


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-6000

-4000

-2000

0

2000

4000

6000

log(a/a0)

log[

(RH/R

H0)]

310


-15000 -10000 -5000 0-2

-1.5

-1

-0.5

0

0.5

1

1.5

2x 10

4

log(a/a0)

log[

(RH/R

H0)]

310

210


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x 104

-6

-4

-2

0

2

4

6

x 104

log(a/a0)

log[

(RH/R

H0)]

210


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x 104

-1

-0.5

0

0.5

1

x 105

log(a/a0)

log[

(RH/R

H0)]

210

110


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x 105

-6

-4

-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

1

110


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x 105

-6

-4

-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

1 Q

110


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x 105

-6

-4

-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

1 Q

110

Not at all classical!


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x 105

-6

-4

-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

110

Self-reproduction regime

Substantial probability of fluctuating up the potential and continuing the inflationary expansion “Eternal Inflation”

1 Q

Linde 1986 and (then) many others


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x 105

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-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

110



1 Q


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x 105

-6

-4

-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

110



1 Q

Observable Universe


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x 105

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-4

-2

0

2

4

6

x 105

log(a/a0)

log[

(RH/R

H0)]

1Q

110

4.410 310 Pl


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10 Pl


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x 105

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0

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6

x 105

log(a/a0)

log[

(RH/R

H0)]

110



1 Q


-200 -100 0 100 2000

0.5

1

1.5

2

2.5x 10

4

/MP

V/M

GU

T4

In self-reproduction regime, quantum fluctuations compete with classical rolling

Q


Self-reproduction is a generic feature of any inflaton potential:

3H V During inflation

3H V

3

V

H

2 3 3/2

Q H H V

V V


Self-reproduction is a generic feature of any inflaton potential:

3H V During inflation

3H V

3

V

H

2 3 3/2

Q H H V

V V

1 for self- reproduction


-200 -100 0 100 2000

0.5

1

1.5

2

2.5x 10

4

/MP

V/M

GU

T4

In self-reproduction regime, quantum fluctuations compete with classical rolling

Q

Linde & Linde


5 SHd R

t0t

Classically Rolling



2 5 SHd e R

2 /SHt R c

New pocket (elsewhere)

t

Classically Rolling

Classically Rolling



3 5 SHd e R

3 /SHt R c


t

Classically Rolling



500 5 SHd e R

500 /SHt R c


t

502r e d

Classically Rolling



1000 5 SHd e R

1000 /SHt R c


1002r e d

t

Classically Rolling



1400 5 SHd e R

1400 /SHt R c


1402r e d

t



1395 5 SHd e R

1400 /SHt R c


1393r e d

t

Classically Rolling



1991 5 SHd e R

2000 /SHt R c


1989r e d

t

Classically Rolling



534395 5 S IendH Hd e R R

602,785 /SHt R c


534393r e d

t

Classically Rolling





534393r e d

2 /IendHt R c

t

Reheating





534393r e d

3.2 /IendHt R c

t

Radiation Era



Eternal inflation features

• Most of the Universe is always inflating



• Most of the Universe is always inflating• Leads to infinite Universe, infinitely many pocket universes. The

self-reproduction phase lasts forever.




self-reproduction phase lasts forever (globally).




self-reproduction phase lasts forever.• Inflation “takes over the Universe”, seems like a good theory of

initial conditions.





initial conditions.• Need to regulate ’s to make predictions, typically use a cutoff.





initial conditions.• Need to regulate ’s to make predictions, typically use a cutoff.• For a specific time cutoff, the most recently produced pocket

universes are exponentially favored (produced in an exponentially larger region).






universes are exponentially favored (produced in an exponentially larger region). Young universe problem

End of time problemMeasure problems








State of the art: Instead of making predictions, the experts are using the data to infer the “correct measure”

















“True infinity” needed here










Multiply by 10500 to get landscape story!










Multiple (∞) copies of “you” in the wavefunction Page’s “Born Rule Crisis”











A problem has been detected and your calculation has been shut down to prevent damage

RELATIVE_PROBABILITY_OVERFLOW

If this is the first time you have seen this stop error screen,restart your calculation. If this screen appears again, follow these steps:

Check to make sure all extrapolations are justified and equations are valid. If you are new to this calculation consult your theory manufacturer for any measure updates you might need.

If the problems continue, disable or remove features of the theory that cause the overflow error. Disable BS options such as self-reproduction or infinite time. If you need to use safe mode to remove or disable components, restart your computation and utilize to select holographic options.

S










Or, just be happy we have equations to solve?


OUTLINE






OUTLINE






de Sitter Equilibrium (dSE) cosmology

• Take ideas from Holography, to construct a finite cosmology







• Build on initial motivation re the appeal of an equilibrium system (no “initial conditions”)





• Seek the “Bohr Atom” of cosmology





• Seek the “Bohr Atom” of cosmology• A counterpoint to the infinities of eternal inflation





• Seek the “Bohr Atom” of cosmology• A counterpoint to the infinities of eternal inflation• Unabashedly exploit uncertainties about the

fundamental physics (i.e. when continuum field theory is good, and when it breaks down) to construct a realistic cosmology





• Seek the “Bohr Atom” of cosmology• A counterpoint to the infinities of eternal inflation• Unabashedly exploit uncertainties about the

fundamental physics (i.e. when continuum field theory is good, and when it breaks down) to construct a realistic cosmology

AA: arXiv:1104.3315AA: arXiv:0906.1047AA & Sorbo: hep-th/0405270


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log[

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H0)]


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0

1

2

3

log(a/a0)

log[

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H0)]


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-4

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-1

0

1

2

3

log(a/a0)

log[

(RH/R

H0)]

domination


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-5

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0

1

2

3

log(a/a0)

log[

(RH/R

H0)]

domination

Asymptotic behavior de Sitter Space


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-1

0

1

2

3

log(a/a0)

log[

(RH/R

H0)]

The de Sitter horizon

Past horizon of observation event at this time

Past Horizon: Physical distance from (comoving) observer of a photon that will reach the observer at the time of the observation.


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Past horizon of observation event at this time



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log[

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Past horizon of any observation event deep in the de Sitter era



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0

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log(a/a0)

log[

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H0)]

Past horizon of any observation event deep in the de Sitter era

Future horizon of event at reheating (distance photon has traveled, in SBB).Hd



Implications of the de Sitter horizon

• Maximum entropy

• Gibbons-Hawking Temperature

12

3S A H

8

3GH

GT H

Gibbons & Hawking 1977


2 1S A H

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

Horizon

8

3GH

GT H


Banks & Fischler & Dyson et al.


• Maximum entropy


• Only a finite volume ever observed

• If is truly constant: Cosmology as fluctuating Eqm.

• Maximum entropy finite Hilbert space of dimension

12

3S A H

8

3GH

GT H

SN e




• Maximum entropy


• Only a finite volume ever observed

• If is truly constant: Cosmology as fluctuating Eqm.?

• Maximum entropy finite Hilbert space of dimension

12

3S A H

8

3GH

GT H

?SN e

dSE

cosm

olog

y


Equilibrium Cosmology


Rare Fluctuation


Rare Fluctuation


Concept:

Realization:

“de Sitter Space”


Rare Fluctuation


Fluctuating from dSE to inflation:

• The process of an inflaton fluctuating from late time de Sittter to an inflating state is dominated by the “Guth-Farhi process”

• A “seed” is formed from the Gibbons-Hawking radiation that can then tunnel via the Guth-Farhi instanton.

• Rate is well approximated by the rate of seed formation:

• Seed mass:

s s

GH

m m

T He e

1/2416

3110

0.0013s I II

GeVm cH kg






• Seed mass:

s s

GH

m m

T He e

1/2416

3110

0.0013s I II

GeVm cH kg

Small seed can produce an entire universe Evade “Boltzmann Brain” problem






• Seed mass:

s s

GH

m m

T He e

1/2416

3110

0.0013s I II

GeVm cH kg

See important new work on G-F process by Andrew Ulvestad & AA


degrees of freedom temporarily break off to form baby universe:

time

Eqm.

Seed Fluctuation

Tunneling

Evolution

Evolution

Evolution

Inflation

Radiation

Matter

de Sitter

IS SN e e

Recombination


SN e Implications of finite Hilbert space

• Recurrences

• Eqm.

• Breakdown of continuum field theory



• Recurrences

• Eqm.




• Recurrences

• Eqm.



-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

I

r

m

This much inflation fills one de Sitter horizon


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

I

r

m

This much inflation fills more than one de Sitter horizon, generating total entropyand affecting regions beyond the horizon of the observer

MaxS S


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

I

r

m

• In dSE cosmology this region is unphysical.

• Breakdown of continuum field theory prevents inflation from filling more than one de Sitter horizon


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

I

r

m

• In dSE cosmology this region is unphysical.

• Breakdown of continuum field theory prevents inflation from filling more than one de Sitter horizon

Equivalent to Banks-Fischler holographic constraint on number of e-foldings of inflation (D Phillips 2011)





• Rate is well approximated by the rate of seed formation

• Seed mass:

s s

GH

m m

T He e

1/2416

3110

0.0013s I II

GeVm cH kg

Large exponentially favored saturation of dSE bound

I


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

dSE bound on inflation given by past horizon


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

dSE bound on inflation given by past horizon

A variety of inflation models, all saturating the dSE bound


OUTLINE






OUTLINE






dSE Cosmology and cosmic curvature

• The Guth-Farhi process starts inflation with an initial curvature set by the curvature of the Guth-Farhi Bubble

• Inflation dilutes the curvature, but dSE cosmology has a minimal amount of inflation

Bk


Friedmann Eqn.

2

2 8

3 I k r m DE

aH G

a

2a


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]


Evolution of curvature radius 1

k

ca

H


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]

Curvature radius set by initial curvature

Bk



k

ca

H


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]



Bk


k

ca

H


-70 -60 -50 -40 -30 -20 -10 0 10-70

-60

-50

-40

-30

-20

-10

0

10

log(a/a0)

log[

L/(c

H0-1

)]



Bk

is given by this gap0

22

0

Hk kk

c k

RH

H R


k

ca

H


-1.5 -1 -0.5 0 0.5 1-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

log(a/a0)

log[

L/(c

H0-1

)]

AA: arXiv:1104.3315


dSE Cosmology and cosmic curvature

• The Guth-Farhi process starts inflation with an initial curvature set by the curvature of the Guth-Farhi bubble

• Inflation dilutes the curvature, but dSE cosmology has a minimal amount of inflation

Bk


Image bySurhud More

Predicted from dSE cosmology is:• Independent of almost

all details of the cosmology

• Just consistent with current observations

• Will easily be detected by future observations

k

k

0 /m


Image bySurhud More

Predicted from dSE cosmology is:• Independent of almost

all details of the cosmology

• Just consistent with current observations

• Will easily be detected by future observations

k

k

0 /m

Work in progress on expected values of (Andrew Ulvestad & AA)

Bk

0.5Bk

0.25Bk

0.1Bk


Conclusions• The search for a “big picture” of the Universe that explains

why the region we observe should take this form has proven challenging, but has generated exciting ideas.

• We know we can do science with the Universe

• It appears that there is something right about cosmic inflation

• dSE cosmology offers a finite alternative to the extravagant (and problematic) infinities of eternal inflation

• Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test


Conclusions• The search for a “big picture” of the Universe that explains

why the region we observe should take this form has proven challenging, but has generated exciting ideas.

• We know we can do science with the Universe

• It appears that there is something right about cosmic inflation

• dSE cosmology offers a finite alternative to the extravagant (and problematic) infinities of eternal inflation

• Predictions of observable levels of cosmic curvature from dSE cosmology will give an important future test

Documents

Inflation, infinity, equilibrium and the observable Universe Andreas Albrecht UC Davis UCD Colloquium October 3, 2011 1A. Albrecht @ UCD 10/3/11