accelerating expansion from inhomogeneities ?

41
Accelerating Expansion from Inhomogeneities ? Je-An Gu ( 顧顧顧 ) National Taiwan University IoPAS 2006/03/17 Collaborators: Chia-Hsun Chuang ( 莊莊莊 ) W-Y. P. Hwang ( 莊莊莊 ) astro-ph/0512651)

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Accelerating Expansion from Inhomogeneities ?. Je-An Gu ( 顧哲安 ) National Taiwan University. Collaborators: Chia-Hsun Chuang ( 莊家勛 ) W-Y. P. Hwang ( 黃偉彥 ). (astro-ph/0512651). IoPAS 2006/03/17. Acceleration Expansion. Based on FRW Cosmology. - PowerPoint PPT Presentation

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Page 1: Accelerating  Expansion  from  Inhomogeneities ?

Accelerating Expansion

from

Inhomogeneities ?

Je-An Gu ( 顧哲安 )National Taiwan University

IoPAS 2006/03/17

Collaborators: Chia-Hsun Chuang (莊家勛 ) W-Y. P. Hwang (黃偉彥 )

(astro-ph/0512651)

Page 2: Accelerating  Expansion  from  Inhomogeneities ?

Acceleration Expansion

Based on FRW Cosmology

(homogeneous & isotropic)

Page 3: Accelerating  Expansion  from  Inhomogeneities ?

Based on FRW Cosmology

(homogeneous & isotropic)

Supernova data ? Cosmic Acceleration

However, apparently,

our universe is NOT homogeneous & isotropic.

At large scales, after averaging,the universe IS homogeneous & isotropic.

But, averaging !?

Is it legal ? Does it make sense ?

Page 4: Accelerating  Expansion  from  Inhomogeneities ?

Einstein equations

abmnab GTgG 8

abmnabmnab TGgGgG 8

, abmn Tg

abmn Tg ,

satisfy Einstein equations

BUT in general

DO NOT.

Page 5: Accelerating  Expansion  from  Inhomogeneities ?

Supernova data ? Cosmic Acceleration

Cosmic Acceleration requires Dark Energy ?

Questions

Page 6: Accelerating  Expansion  from  Inhomogeneities ?

Cosmic Acceleration requires Dark Energy ?

Normal matter attractive gravity

slow down the expansion

Need something abnormal :

e.g. cosmological constant, dark energy

-- providing anti-gravity (repulsive gravity)

Is This True ?

CommonIntuition /

Consensus

Page 7: Accelerating  Expansion  from  Inhomogeneities ?

Is This True ? Intuitively, YES ! (of course !!)

Normal matter attractive gravity slow down the expansion

Common Intuition / Consensus

** Kolb, Matarrese, and Riotto (astro-ph/0506534) :

Inhomogeneities of the universe might induce acceleration.

Mission Impossible ? or Mission Difficult ?

Two directions: 1. Prove NO-GO theorem.2. Find counter-examples. This is what we did.

We found counter-examples for a dust universe of spherical symmetry,described by the Lemaitre-Tolman-Bondi (LTB) solution.

Page 8: Accelerating  Expansion  from  Inhomogeneities ?

What is Accelerating Expansion ?

(I) Line Acceleration

What is Accelerating Expansion ?

(II) Domain Acceleration

Lemaitre-Tolman-Bondi (LTB) Solution(exact solution in GR) (spherically symmetric dust fluid)

Page 9: Accelerating  Expansion  from  Inhomogeneities ?

What is Accelerating Expansion ? (I)

Line Acceleration

L

00

00

LL

LL

:ration Accele; :onDecelerati

:Collapse ; :Expansion

22

:parameter onDecelerati

:rate Expansion

L

LL

H

LLq

LLH

LL

L

homogeneous & isotropic universe: RW metric:

22

2

222

2222 2

1 11

aaaLLLqaaLLH

rk

drtaLdr

rk

drtadtds

LL

r

r

;

: distance proper ;

)(

)(

We found examples of qL < 0 (acceleration)in a dust universe described by the LTB solution.

Page 10: Accelerating  Expansion  from  Inhomogeneities ?

What is Accelerating Expansion ? (II)

Volume VD

a large domain D (e.g. size ~ H01)

2

31

DDDD

DDD

DD

aaaq

aaH

Va

NO-GO qD 0 > 0 (deceleration) in a dust universe(see, e.g., Giovannini, hep-th/0505222)

We found examples of qD < 0 (acceleration)in a dust universe described by the LTB solution.

[Nambu and Tanimoto (gr-qc/0507057) : incorrect example.]

Domain Acceleration

Page 11: Accelerating  Expansion  from  Inhomogeneities ?

Lemaitre-Tolman-Bondi (LTB) Solution(exact solution in GR)

(unit: c = 8G = 1) Dust Fluid + Spherical Symmetry

k(r) = const., 0(r) = const., a(t,r) = a(t) FRW cosmology

arra

rrt

a

r

a

rk

a

a

drrrk

dr

a

artadtds

r

r

22

30

30

2

2

222

22222

6, :density energy

3 : equation Einstein

11 ,

/

Solution (parametric form with the help of ) adt

rtrkrkrk

rrt

rkrk

rra

b

sin1

6,

cos16

,arbitrary functions of r :

k(r) , 0(r) , tb(r)

Page 12: Accelerating  Expansion  from  Inhomogeneities ?

Line (Radial) Acceleration

( qL < 0 )

Radial : Inhomogeneity AccelerationAngular : No Inhomogeneity No Acceleration

Page 13: Accelerating  Expansion  from  Inhomogeneities ?

Line (Radial) Acceleration : qL < 0

Inhomogeneity the less smoother, the better

arbitrary functions of r : k(r) , 0(r) , tb(r)

0

1

11

00

rt

r

rr

rrkrk

b

nk

nkh

k

k

; const.

;

dr

rrk

rta

a

adrgL

LL r

r

rr

r rr

0 2

22

0 11

:distance Radial

,

parameters : (nk , kh , rk) , 0 , rL , t

1

kh

rk

k(r)

r0

Page 14: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Line (Radial) Acceleration : qL < 0

arbitrary functions of r : k(r) , 0(r) , tb(r)

0

1

11

00

rt

r

rr

rrkrk

b

nk

nkh

k

k

const.

parameters : (nk , kh , rk) , 0 , rL , t

1

kh

rk

k(r)

r0

nk kh rk 0 rL t qL qD

20 1 0.7 1 1 1 0.9

Observations q ~ 1 (based on FRW cosmology)

Acceleration

Page 15: Accelerating  Expansion  from  Inhomogeneities ?

0.2 0.4 0.6 0.8 1

50

100

150

200

250

300

350

Examples of Line (Radial) Acceleration : qL < 0

nk kh rk 0 rL t qL qD

20 1 0.7 1 1 1 0.9

1, tr

r

k(r) = 0 at rk = 0.7

Over-density Under-density

Page 16: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Line (Radial) Acceleration : qL < 0

rrt g2

r

Deceleration Deceleration

Acceleration

nk kh rk 0 rL t qL qD

20 1 0.7 1 1 1 0.9 k(r) = 0 at rk = 0.7

)( 0660.

Page 17: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Line (Radial) Acceleration : qL < 0

)( 0660.

Page 18: Accelerating  Expansion  from  Inhomogeneities ?

Acceleration

Inhomogeneity

Examples of Line (Radial) Acceleration : qL < 0

)( 0660.

Page 19: Accelerating  Expansion  from  Inhomogeneities ?

10 20 30 40nk

-1.25

-1

-0.75

-0.5

-0.25

qr

Examples of Line (Radial) Acceleration : qL < 0

Lq

kn

nk kh rk 0 rL t

(20) 1 0.7 1 1 1

Deceleration

Acceleration larger nk

larger inhomogeneity

k

k

nk

nkh

rr

rrkrk

1

11

1

kh

rK

k(r)

r0

Easy to generate

nk=3

Page 20: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Line (Radial) Acceleration : qL < 0

nk kh rk 0 rL t

20 1 0.7 1 1 (1)

Lq

t

Deceleration

Acceleration

Page 21: Accelerating  Expansion  from  Inhomogeneities ?

Domain Acceleration

( qD < 0 )

sphericaldomain r = 0

r = rD

Page 22: Accelerating  Expansion  from  Inhomogeneities ?

Domain Acceleration : qD < 0

) ; ; ( 231DDDDDDDDD aaaqaaHVa

tb(r) = 0 : NO acceleration

t

t

k

k

nt

ntbh

b

nk

nkh

rr

rrtrt

r

rr

rrkrk

1

1

11

00

; const.

;

k(r)

parameters : (nk , kh , rk), (nt , tbh , rt), 0 , rD , t

[Nambu and Tanimoto: incorrect example.]

arbitrary functions of r : k(r) , 0(r) , tb(r)

tb(r)

Page 23: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

) ; ; ( 231DDDDDDDDD aaaqaaHVa

t

t

k

k

nt

ntbh

b

nk

nkh

rr

rrtrt

r

rr

rrkrk

1

1

11

00

const.

parameters : (nk , kh , rk), (nt , tbh , rt), 0 , rD , t

arbitrary functions of r : k(r) , 0(r) , tb(r)

nk kh rk nt tbh rt 0 rD t qD

40 40 0.9 40 10 0.9 105 1.1 0.1 1Acceleration

tb(r)

k(r)

Page 24: Accelerating  Expansion  from  Inhomogeneities ?

0.2 0.4 0.6 0.8 1

10

20

30

40

50

60

Examples of Domain Acceleration : qD < 0

nk kh rk nt tbh rt 0 rD t qD

40 40 0.9 40 10 0.9 105 1.1 0.1 1

1.0, tr

r

k(r) = 0 at r = 0.82

Over-density Under-density

Page 25: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

0.2 0.4 0.6 0.8 1

500

1000

1500

2000

2500

rrt g2

r

Deceleration Deceleration

Acceleration

nk kh rk nt tbh rt 0 rD t qD

40 40 0.9 40 10 0.9 105 1.1 0.1 1

k(r) = 0 at r = 0.82

)( 51094 .

Page 26: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

nk kh rk nt tbh rt 0 rD t

(40) 40 0.9 40 10 0.9 105 1.1 0.1

Acceleration

Page 27: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

nk kh rk nt tbh rt 0 rD t

40 (40) 0.9 40 10 0.9 105 1.1 0.1

Deceleration

Acceleration

Page 28: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

nk kh rk nt tbh rt 0 rD t

40 40 (0.9) 40 10 (0.9) 105 1.1 0.1

Deceleration

Acceleration

Page 29: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

Deceleration

Accelerationlarger nt

larger inhomogeneity

tb(r)

t

t

nt

ntbh

brr

rrtrt

1

nk kh rk nt tbh rt 0 rD t

40 40 0.9 (40) 10 0.9 105 1.1 0.1

Page 30: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

Acceleration

nk kh rk nt tbh rt 0 rD t

40 40 0.9 40 (10) 0.9 105 1.1 0.1

Deceleration

Page 31: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

Acceleration

nk kh rk nt tbh rt 0 rD t

40 40 0.9 40 10 0.9 (105) 1.1 0.1

Page 32: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration

nk kh rk nt tbh rt 0 rD t

40 40 0.9 40 10 0.9 105(1.1) 0.1

Page 33: Accelerating  Expansion  from  Inhomogeneities ?

Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration

nk kh rk nt tbh rt 0 rD t

40 40 0.9 40 10 0.9 105 1.1 (0.1)

Page 34: Accelerating  Expansion  from  Inhomogeneities ?

Summary and Discussions

Page 35: Accelerating  Expansion  from  Inhomogeneities ?

Summary and Discussions

Against the common intuition and consensus : normal matter attractive gravity deceleration,

Counter-examples for both the Line and the Domain Acceleration are found.

These examples support :

Inhomogeneity Acceleration

These examples raise two issues : (next slide)

Page 36: Accelerating  Expansion  from  Inhomogeneities ?

How to understand the examples ?

(GR issue)

Can Inhomog. explain “Cosmic Acceleration”?

(Cosmology issue)

Page 37: Accelerating  Expansion  from  Inhomogeneities ?

IF YES

Can Inhomog. explain “Cosmic Acceleration”?

SN Ia Data Cosmic Acceleration

Inhomogeneities

?

?Mathematically, possible. In Reality ???

Can Inhomogeneities explain SN Ia Data?

Do these Inhomog. Indicate Cosmic Acceleration?

Page 38: Accelerating  Expansion  from  Inhomogeneities ?

source

earth LTB

LTB

LTB

LTBLTB

LTB

LTB

(Each circle represents a LTB region.) over-density

under-density

Can Inhomogeneities explain SN Ia Data ?

Page 39: Accelerating  Expansion  from  Inhomogeneities ?

energy density (x)

x

light

Can Inhomogeneities explain SN Ia Data ?

The effects of inhomogeneities on the cosmic evolution should be restudied.

(No matter whether inhomogeneities can solely explain SN Ia data, …)

Page 40: Accelerating  Expansion  from  Inhomogeneities ?

How to understand the examples ?

Normal matter attractive gravity

slow down the expansion

CommonIntuition /

Consensus

Intuition for GR ? NO !?

(x)

(valid only for … ?)

)( )(

xgx 00 Newton? NO. GR? YES.

Intuition from Newtonian gravity, not from GR.

Page 41: Accelerating  Expansion  from  Inhomogeneities ?

Summary and Discussions

GR is still not fully understood

after 90 years !!