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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.

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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

(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 ?

Based on FRW Cosmology

(homogeneous & isotropic)


Einstein equations

satisfy Einstein equations

BUT in general

DONOT.


Questions

Supernova data ? Cosmic Acceleration

Cosmic Acceleration requires Dark Energy?


Cosmic Acceleration requires Dark Energy?

Common

Intuition /

Consensus

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?


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

Mission Impossible ? orMission Difficult ?

This is what we did.

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.

  • Two directions:

  • Prove NO-GO theorem.

  • Find counter-examples.

We found counter-examples for a dust universe of spherical symmetry,

described by the Lemaitre-Tolman-Bondi (LTB) solution.


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)


What is Accelerating Expansion ? (I)

homogeneous & isotropic universe: RW metric:

Line Acceleration

L

We found examples of qL < 0 (acceleration)

in a dust universe described by the LTB solution.


What is Accelerating Expansion ? (II)

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

a large domain D

(e.g. size ~ H01)

Volume VD

NO-GOqD 0 > 0 (deceleration) in a dust universe

(see, e.g., Giovannini, hep-th/0505222)


Lemaitre-Tolman-Bondi (LTB) Solution

(exact solution in GR)

(unit: c = 8G = 1)

Dust Fluid + Spherical Symmetry

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

Solution (parametric form with the help of )

arbitrary functions of r :

k(r) , 0(r) , tb(r)


Line (Radial) Acceleration

( qL < 0 )

Radial: Inhomogeneity  Acceleration

Angular : No Inhomogeneity  No Acceleration


Line (Radial) Acceleration : qL < 0

k(r)

1

rk

0

r

kh

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

Inhomogeneity  the less smoother, the better

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


Examples of Line (Radial) Acceleration : qL < 0

1

k(r)

r

rk

0

kh

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

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

Acceleration

Observations  q ~ 1 (based on FRW cosmology)


Examples of Line (Radial) Acceleration : qL < 0

k(r) = 0 at rk = 0.7

Over-density

Under-density


Examples of Line (Radial) Acceleration : qL < 0

k(r) = 0 at rk = 0.7

Acceleration

Deceleration

Deceleration


Examples of Line (Radial) Acceleration : qL < 0


Examples of Line (Radial) Acceleration : qL < 0

Inhomogeneity

Acceleration


Examples of Line (Radial) Acceleration : qL < 0

1

k(r)

r

rK

0

nk=3

kh

Easy to generate

larger nk

larger inhomogeneity

Deceleration

Acceleration


Examples of Line (Radial) Acceleration : qL < 0

Deceleration

Acceleration


r = rD

spherical

domain

r = 0

Domain Acceleration

( qD < 0 )


Domain Acceleration : qD < 0

k(r)

tb(r)

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

 tb(r) = 0 :NOacceleration

[Nambu and Tanimoto: incorrect example.]

 parameters :

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


Examples of Domain Acceleration : qD < 0

k(r)

tb(r)

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

parameters :

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

Acceleration


Examples of Domain Acceleration : qD < 0

k(r) = 0 at r = 0.82

Over-density

Under-density


Examples of Domain Acceleration : qD < 0

k(r) = 0 at r = 0.82

Acceleration

Deceleration

Deceleration



Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration


Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration


Examples of Domain Acceleration : qD < 0

larger nt

larger inhomogeneity

tb(r)

Deceleration

Acceleration


Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration



Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration


Examples of Domain Acceleration : qD < 0

Deceleration

Acceleration



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)


How to understand the examples ?

(GR issue)

Can Inhomog. explain “Cosmic Acceleration”?

(Cosmology issue)


Can Inhomog. explain “Cosmic Acceleration”?

?

SN Ia Data

Cosmic Acceleration

Mathematically, possible.

In Reality??

?

?

Inhomogeneities

Can Inhomogeneities explain SN Ia Data?

IF YES

Do these Inhomog. Indicate Cosmic Acceleration?


Can Inhomogeneities explain SN Ia Data ?

under-density

over-density

LTB

LTB

LTB

LTB

source

LTB

LTB

LTB

earth

(Each circle represents a LTB region.)


Can Inhomogeneities explain SN Ia Data ?

light

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

The effects of inhomogeneities on the cosmic evolution

should be restudied.

energy density (x)

x


How to understand the examples ?

Intuition from Newtonian gravity, not from GR.

(valid only for … ?)

(x)

Newton?NO.

GR?YES.

Common

Intuition /

Consensus

Normal matter  attractive gravity

 slow down the expansion

Intuition for GR ?NO !?


Summary and Discussions

GR is still not fully understood

after 90 years !!


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