Transcript Crossing the Phantom Divide

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S. Nesseris, LP, astro-ph/0610092, astro-ph/0611238
L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
Observational Probes of the
Accelerating Expansion
w(z) crossing the w=-1
Marginal Consistency of
Scalar-Tensor Quintessence with
Observed Accelerating Expansion
Maximal Agreement of
Scalar-Tensor Quintessence
with the Full Parameter Range of
Observed Acelerating Expansion
w(z) is close to -1
w(z) crossing the w=-1
Inconsistent with
Minimally Coupled Quintessence
and also with
Scalar Tensor Quintessence
if G(t) is increasing with time.
Close to Extremum
(Solar System)
G(t) can not increase
rapidly with t
(not ‘sharp’ Maximum)
G0
 5 104
G0 H 0
SNLS
Close to Extremum
(Solar System)
G(t) decreases with t
(close to a Minimum)
G0
 1.91
G0 H 02
G0
 5 104
G0 H 0
SNLS
G0
 1.97
G0 H 02
1.5
1
w( z )
0.5
0
0.5
1
1.5
z
0
0.25
0.5
0.75
1
1.25
1.5
1.75
z
Physical Model  H  z; a1 , a2 ,..., an 
 dz
0
ansatz 


z
 dz
Data: d Lobs  zi 
th
0

 d L  z; a1 , a2 ,..., an  

 2  2
min
 H  z; a1 , a2 ,..., an 

d L  z; a1 , a2 ,..., an 
Data: d Lobs  zi 

  a1 , a2 ,..., an   
2
 2   min
 w  z; a1 , a2 ,..., an 
2
  min
 a1 , a2 ,..., an 

• All best fit parameterizations cross the phantom divide at z~0.25
• The parametrization with the best χ2 is oscillating
m  0.3
CP  L
2
2
 CDM   177.1
min
OA  171.7 min
Lazkoz, Nesseris, LP 2005
w( z )  w0  w1
z
1 z
SNLS (115 points z<1)
m  0.24
Trunc. Gold (140 points, z<1)
Full Gold (157 points, z<1.7)
SNLS data show no trend for crossing the phantom divide w=-1!
S. Nesseris, L.P.
Phys. Rev. D72:123519, 2005
astro-ph/0511040
2
d ln H
1 z 
1

pDE ( z )
3
dz
w z 

2
 DE ( z )
3
 H0 
1 
 0 m 1  z 
 H 
1.5
1.5
1.5
Gold dataset
Riess -et. al. (2004)
1
w(z )
SNLS dataset
Astier -et. al. (2005)
1
0.5
0.5
0.5
0
0
0
0.5
0.5
0.5
1
1
1.5
1.5
0m  0.2
1
w( z )  w0  w1
z
1 z
1.5
Other data:
Other BAO,
data: LSS, Clusters
CMB,
CMB, BAO, LSS, Clusters
1
S. Nesseris, L.P.
0
0.25
0.5
0.75
1
1.25
1.5
1.75
0
z
0.25
0.5
0.75
1
1.25
1.5
0
1.75
1.5
Gold dataset
Riess -et. al. (2004)
w(z )
SNLS dataset
Astier -et. al. (2005)
0
 R 

0.5
0.5
m , w1 , w2   1.70 
0.032
1
Wang, Mukherjee 2006
0.5
0.75
0.5
2
2
2
 CMB
 m , w1 , w2   0BAO
 m , w1 , w2    cl2  w1 , w2    LSS
 w1 , w2  0
0m  0.3
Minimize:
0 m  0.2
0.25
1
Other data:
CMB, BAO, LSS, Clusters
1
0.5
0
1.25
1.5
1.75
astro-ph/0610092
0.75
1.5
1
0.5
1.5
0.5
z
1.5
1
0.25
z
1
1.25
z
1.5
1.75
2
 A

1
m , w1 , w2   0.469 
2
0.017 2
26

i 1
1.5
f
 zi ; w1 , w2   f gas i 
SCDM0.5
gas
0.5
0.75
1
1.25
z
1.5
1.75
2
0.112
1

 aD' (a)
g  z   1  0.15 
 0.51 0.11
a

 D( a )
Eisenstein et. al. 2005
0.25
 g  z  0.15; w , w   0.51

1
2
 gas
i
1
1.5
0
2
0
0.25
0.5
Allen et. al. 2004
0.75
1
z
1.25
1.5
2dF:Verde
et. al.
1.75
MNRAS 2002
2
CMB  BAO  Clusters  LSS m  0.2
0m  0.2
CMB  BAO  Clusters  LSS m  0.3
0m  0.3
Riess et. al. astro-ph/0611572
Old Gold
Filtered Gold+New HST
Filtered Gold+New HST+Best of SNLS
S. Nesseris, LP in prep.
Old Gold
Filtered Gold+New HST
Filtered Gold+New HST+Best of SNLS
Q1: What theories are consistent with range of observed H(z)?
• Cosmological Constant
• Quintessence
• Extended (Scalar–Tensor) Quintessence
• Braneworld models (eg DGP)
• Barotropic fluids (eg Chaplygin Gas)
Q2: What forms of H(z) are inconsistent with each theory?
(forbidden sectors)
Q3: What is the overlap of the observationally allowed range of H(z)
with the forbidden sector of each theory?
Goal: Address Q2-Q3 for Extended Quintessence
8 G 
1 2



 U 
m

3 
2

dU
  3H   
d
H2 
V(Φ)
Thawing
Thaw
Accelerate
Φ
V(Φ)
Caldwel, Linder 2005
Freezing
Decelerate
Freeze
Plausibility Arguments
+
Numerical Simulations
Φ
 , p
1 
1 2

H 
  m    U  3HF 
3F 
2

1
2
H 



p


 F  HF 

m
m
2F
2
'
d
dz
Consistency Requirements:
Express Fi in terms of G(t) current time derivatives:
Gannouji, Polarski, Ranquet, Starobinsky
astro-ph/0606287
Ignored g1 :
(Solar System Tests, Pitjeva 2005)
   z  
0
Freezing
z 0
   z  
z 0
0
Thawing
2
2
U   z  0  U1  0

  z 
2


   z  
Freezing
z 0
0
z 0
0
Thawing
2
U   z  0  U1  0
Chevallier-Polarski-Linder
Lower bound on g2:
Chevallier-Polarski-Linder
Lower bound on g2:
Upcoming Solar System Constraints on g2:
9 105  g2  105
J. Mueller 2006
Why does g2  0 shrink the forbidden sector beyond the w=-1 limit?
g2  0 implies decreasing G which helps
boost accleration beyond the w=-1 barrier
SnIa Absolute Luminosity:
Steps of Analysis:
1. Assume G(z) parametrization consistent with Solar System + Nucleosynthesis bounds
2. Consider modified magnitude-redshift relation
3. Minimize χ2
The shift of the contours is not significant
compared to the area of the contours.
Observational Probes of the
Accelerating Expansion
w(z) crossing the w=-1
Consistency of
Scalar-Tensor Quintessence
Observed Accelerating Expansion
Maximal Agreement of
Scalar-Tensor Quintessence
with the full range of observed
Acelerating Expansion
w(z) is close to -1
w(z) crossing the w=-1
Inconsistent with
Minimally Coupled Quintessence
and also with
Scalar Tensor Quintessence
if G(t) is increasing with time.
Close to Extremum
(Solar System)
G0
 104
G0 H 0
G(t) can not increase
rapidly with t
(not ‘sharp’ Maximum)
G0
 1.91
G0 H 02
Close to Extremum
(Solar System)
G0
 104
G0 H 0
G(t) decreases with t
(close to a Minimum)
G0
 1.97
G0 H 02