L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina
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Open page. Accelerating Universe and Scalar-Tensor Theories. L. Perivolaropoulos http://leandros.physics.uoi.gr Department of Physics University of Ioannina. Main Points. Dark Energy Equation of State w(z)=p/ρ may be crossing the w=-1 line. Minimally Coupled Quintessence is - PowerPoint PPT Presentation
Transcript of L. Perivolaropoulos leandros.physics.uoi.gr Department of Physics University of Ioannina
L. Perivolaropouloshttp://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
Open page
2 8
3 m
GH a a a
DirectlyObservable
DirectlyObservable
Dark Energy(Inferred)
NoYes
2
2 8
3 m
a GH a a
a
Flat
Friedmann Equation 3~ taV
mm
Not Consistent
1
r czH z
Accelerating Universe: (rate of expansion) was smaller in the past. Thus H-1(t) was larger in the past.
1a t
pastt
0 01t a t
zt a t
aH t
a
Ld
emptyL
L
d
dlog5
emptyL
L
d
dlog5
z~0.5: Acceleration starts
1
( )1
1Ld za d
z H za c dz z
157 SnIa
4 43 3
3 3i i m Xi
a G Gp p
a
Equation of State: 41 3
3X
m
p a Gw w
a
Necessary condition for acceleration:
1 Negative Pressure
3w
4 43
3 3i i mi
a G Gp
a
3 3
3 1~X w
X
d a p d aa
p w
322 0
02
320 0
8( )
3
1
m
m X
aa GH z a
a a
H z z
~ =?a
00 0.2 0.3m
mcrit
(from large scale structure observations)
crit
1
'3 (1 ( '))
'~
ada
w aa
e
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
Gold datasetRiess -et. al. (2004)
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
SNLS datasetAstier -et. al. (2005)
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
Other data:CMB, BAO, LSS, Clusters
0 0.2m
Gold datasetRiess -et. al. (2004)
SNLS datasetAstier -et. al. (2005)
Other data:CMB, BAO, LSS, Clusters
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
0 0.25 0.5 0.75 1 1.25 1.5 1.75
1.5
1
0.5
0
0.5
1
1.5
S. Nesseris, L.P. in prep.
)(zw
z
)(zw Other data:CMB, BAO, LSS, Clusters
z
z z
z z
0 0.3m S. Nesseris, L.P. astro-ph/0511040Phys.Rev.D72:123519,2005
z
zwwzw
1)( 10
2
300
2 ln1 1( ) 3
( )1 1
DE
DEm
d Hzp z dzw z
z Hz
H
What theory produces crossing of the w=-1?
VL 2
2
1 +: Quintessence
-: Phantom
2
0
2
12 112
Vpw
V
To cross the w=-1 line the kinetic energy term must change sign
(impossible for single phantom or quintessence field)
Phant < 1
Quint 1
Generalization for k-essence:
Non-minimal Coupling
1
, U ΦF
1F
1
8 effG
p,
21
2 m mH p F HFF
2 21 13
3 2mH U HFF
Minimum: Generic feature
F(Φ)
ΦΦ
U(Φ)
L.P. astro-ph/0504582, JCAP 0510:001,2005, S. Nesseris, L.P. astro-ph/0602053, Phys.Rev.D73:103511,2006
JCAP 0511:010,2005
0
, 1
ma
a a D aa
Growth Factor:
Growth Factor Evolution (Linear-Fourier Space):
0,,
2
3,'
'3,'' 25
0
akDakf
aHaakD
aH
aH
aakD m
General Relativity: ( , ) 1 ( , ) ( )f k a D k a D a
DGP: 0
1 ( ) '( )( , ) 1 , 1 1
3 3 ( )rc
H a H a af k a
a H H a
Scalar Tensor: 0( , ) ( ) 1 1f k a G a G a
Modified Poisson: 2
1( , ) 1
1 s
f k akr
a
0 )( aaaD
Koyama and Maartens (2006)
Sealfon et. al. (2004)
Esposito-Farese and Polarski (2001)Uzan (2006)
0 0.2 0.4 0.6 0.8 1a
0.4
0.5
0.6
0.7
0.8
0.9
1
ga
ΛCDM (SnIa best fit, Ωm=0.26)
DGP SnIa best fit
+Flat Constraint
Scalar Tensor (α=-0.5, Ωm=0.26)
Flat Matter Only
11.051.0)(
)('15.01
1
aD
aaD
azg
S. Nesseris, L.P. in prep.
Verde et. al. MNRAS 2002Hawkins et. al. MNRAS 2003
'( )
( )
aD ag a
D a
• The Expansion of the Universe is currently accelerating.
• This acceleration can be modeled either by a Dark Energy or by Extended Gravity Theories.
• All recent data indicate that w(z) is close to -1. Thus w(z) may be crossing the w=-1 line.
• Minimally Coupled Scalar predicts no crossing of w=-1 line
• Scalar Tensor Theories are consistent with crossing of w=-1
• Extended Gravity Theories (DGP, Scalar Tensor etc) predict uniquesignatures in the growth rate of cosmological perturbations
dz
d'
positive energy of gravitons
G(z)~1/F(z) decreases at recent times thus boosting
accelerating expansion
Minimum: Generic feature
