accelerating expansion from inhomogeneities ?
DESCRIPTION
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 PresentationTRANSCRIPT
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)
Acceleration Expansion
Based on FRW Cosmology
(homogeneous & isotropic)
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 ?
Einstein equations
abmnab GTgG 8
abmnabmnab TGgGgG 8
, abmn Tg
abmn Tg ,
satisfy Einstein equations
BUT in general
DO NOT.
Supernova data ? Cosmic Acceleration
Cosmic Acceleration requires Dark Energy ?
Questions
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
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.
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)
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.
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
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)
Line (Radial) Acceleration
( qL < 0 )
Radial : Inhomogeneity AccelerationAngular : No Inhomogeneity No Acceleration
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
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
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
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.
Examples of Line (Radial) Acceleration : qL < 0
)( 0660.
Acceleration
Inhomogeneity
Examples of Line (Radial) Acceleration : qL < 0
)( 0660.
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
Examples of Line (Radial) Acceleration : qL < 0
nk kh rk 0 rL t
20 1 0.7 1 1 (1)
Lq
t
Deceleration
Acceleration
Domain Acceleration
( qD < 0 )
sphericaldomain r = 0
r = rD
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)
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)
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
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 .
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
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
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
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
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
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
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
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)
Summary and Discussions
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)
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?
source
earth LTB
LTB
LTB
LTBLTB
LTB
LTB
(Each circle represents a LTB region.) over-density
under-density
Can Inhomogeneities explain SN Ia Data ?
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, …)
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.
Summary and Discussions
GR is still not fully understood
after 90 years !!