Transcript The Accelerating Universe

Open page
L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
New High Quality Cosmological Data
have confirmed and mapped in detail
the accelerating expansion
SNLS astro-ph/0510447
Gold06-HST astro-ph/0611572
Essence astro-ph/0701041
The Cosmological Constant (w=-1) remains
consistent with all current data as a driving force of the acceleration.
An Evolving Dark Energy Density (w=w(t)) is also allowed by the data
and a subset of the allowed evolving forms is inconsistent with General Relativity.
Scalar Tensor extensions of General Relativity are consistent with
the full range of allowed expansion histories.
Demanding consistency of Scalar-Tensor theories
with solar system tests and full range of allowed expansion
histories implies constraints on Newton’s constant evolution G(t)
m 
Friedmann Equation
Flat
8aG
8 G
H
H aa   m  a   maa
3
3a 
2
22
Directly
Observable
No
Yes
m
3
~ a t 
V
Not
Consistent
Directly Dark Energy
Observable (Inferred)
m( z )  M 46
5log  d L  z  / Mpc   25
44
42
40
38
36
34
0
0.25
0.5
0.75
1
1.25
1.5
1.75
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
w
Friedman eqn I:
pX


a
4 G

m    1  3w 



a
3
w 
1
3
 Negative
a
d

3
a
   pX d

p X  w 
 ~ e
 a 

 
3

1
da '
(1 w ( a '))
a'
3




Pressure 
~ a
31 w 
Friedman eqn II:
2
H ( z)
 H
0 m 
2
0
2
a

a2

0m
3

8 G
 a0 



0m 
  

3 
 a 
1  z 
0 m
 0.2  0.3
crit
3
 X
 z 

 
 
 crit 



a


(from large scale structure observations)
0m    k  1

2
a
3
2
2
2
H ( z )  2  H 0 0 m 1  z     k 1  z 
a

 L 
d L ( z )obs
2.5 log10 
  m( z )  M  25  5 log10
Mpc
 l ( z) 
d L ( z )th 
c 1  z 
m  
H0
N
 2  m ,     
i 1

sin 
1


m  

H 0 dz 
 1
0 H  z ;  m ,  
z

5 log10  d L ( zi )obs   5 log  d L ( zi ; m ,  )th  

 i2





2
 min
SNLS (115 SNeIa):
Astier et. al. 2005
Gold Dataset (157 SNeIa):
Riess et. al. 2004
SNLS
Truncated
Gold
Full
Gold
S. Nesseris, L.P. astro-ph/0511040
Phys.Rev.D72:123519,2005
Q.: Can we get better fits to the data?
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
m  0.3
CP  L
Lazkoz, Nesseris, LP 2005
1 2
L     V  
2
+: Quintessence
-: Phantom
 Quint   1
1 2
   V  
p
 0
w  2

1
  1  2  V   Phant  < 1
 
2
To cross the w=-1 line the kinetic energy term
must change sign
(impossible for single phantom or quintessence field)
Generalization for k-essence:
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
dA

rs

dA  H  
1.5
Gold dataset
Riess -et. al. (2004)
w(z )
SNLS dataset
Astier -et. al. (2005)
1
0.5
0.5
0
0
0
0.5
0.5
0.5
1
1
1.5
1.5
1
w( z )  w0  w1
z
1 z
1.5
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
Gold dataset
Riess -et. al. (2004)
SNLS dataset
Astier -et. al. (2005)
0
 R 

0.5
0.032
Wang, Mukherjee 2006
0.75
1.25
1.5
1.75
0.5
0.5
m , w0 , w1   1.70 
1
0.5
1
2
2
2
 CMB
 m , w0 , w1   0BAO
 m , w0 , w1    cl2  w0 , w1    LSS
 w0 , w1  0
0m  0.3
Minimize:
0 m  0.2
0.25
0.75
Other data:
CMB, BAO, LSS, Clusters
1
0.5
0
0.5
1.5
1
0.5
1.5
0.25
z
1.5
w(z )
S. Nesseris, L.P. , astro-ph/0610092, JCAP 0701:018,2007
z
1.5
1
Other data:
Other BAO,
data: LSS, Clusters
CMB,
CMB, BAO, LSS, Clusters
1
0.5
0m  0.2

1.5
1.5
1
rs
1
1.25
z
1.5
1.75
2
 A

1
m , w0 , w1   0.469 
2
0.017 2
26

i 1
1.5
f
 zi ; w0 , w1   f gas i 
SCDM0.5
gas
2
0
2
 gas
i
1
 g  z  0.15; w , w   0.51

1
0.112
1.5
Eisenstein et. al. 2005
0
0.25
0.5
0.75
1
1.25
z
1.5
1.75
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
Q : What is the origin of the mild (2σ) tension between Gold and SNLS?
Subsets of Gold06182:
S. Nesseris, LP astro-ph/0612653
JCAP 0702:025,2007
Compare Random Data Subtraction with
Subset Data Subtraction
Wood-Vasey et. al astro-ph/0701041
Q1: What theories are consistent with range of observed H(z)?
• Cosmological Constant
• Quintessence
• Extended (Scalar–Tensor) Quintessence
• f(R) Modified Gravity
• 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
 , p
1 
1 2

H 
  m    U  3HF 
3F 
2

1
2
H 



p


 F  HF 

m
m
2F
2
'
d
dz
Consistency Requirements:
S. Nesseris, LP , astro-ph/0611238
Phys.Rev.D75:023517,2007
Q.: What constraints do the consistency requirements imply for H(z), F(z)
at low z and are these constraints respected by observations?
Express Fi in terms of G(t) current time derivatives:
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
0m  0.24
Lower bound on g2:
Upcoming Solar System Constraints on g2:
g2  (4  5) 105
J. Mueller 2006
g2  (2 1) 105
E. Pitjeva 2007
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.
S. Nesseris, LP , astro-ph/0611238
Phys.Rev.D75:023517,2007
Observational Probes of the
Accelerating Expansion
w(z) crossing the w=-1
Consistency of
Scalar-Tensor Quintessence
with local gravity and
crossing of w=-1
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.
G0
 104
G0 H 0
G0
 O(1)
G0 H 02
Growth Factor:
Growth Factor Evolution
(Linear-Fourier Space):
 a 
 a
m
a, D a 

  a0  1
 3 H ' a  
3 0 m
 D' k , a  
D' ' k , a    
f k , a Dk , a   0
2
5


a
H
a
2
a H a 


D(a)  a
General Relativity:
a0
f (k , a)  1  D(k , a)  D(a)
Koyama and Maartens (2006)
DGP:
Scalar Tensor:
Modified Poisson:
f (k , a)  1 
1
3  a 
  1
,
f (k, a)  G(a)  G0 1   1  a 
f (k , a )  1  
H (a)  H '(a)a 
1 

H 0rc 
3H (a) 
Esposito-Farese and Polarski (2001)
Uzan (2006)
1
kr
1   s 
 a
2
Sealfon et. al. (2004)
1
Flat Matter Only
0.9
0.8
ga
g a 
S. Nesseris, L.P.
astro-ph/0610092
ΛCDM (SnIa best fit, Ωm=0.26)
JCAP 0701:018,2007
aD '(a)
D(a )
Scalar Tensor (α=-0.5, Ωm=0.26)
0.7
DGP
SnIa best fit
+
Flat Constraint
0.6
1

 aD' (a)
g  z   1  0.15 
 0.51 0.11
a

 D( a )
Verde et. al.
MNRAS 2002
Hawkins et. al.
MNRAS 2003
0.5
0.4
0
0.2
0.6
0.4
a
0.8
1
Observational Probes of the
Accelerating Expansion
w(z) crossing the w=-1
Consistency of
Scalar-Tensor Quintessence
with crossing of w=-1
 a
H a
f  k, a
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.
G0
 104
G0 H 0
G0
 O(1)
G0 H 02
 1 (General Re lativity)
 1 ( Modified Gravity)
Observational Probes of the
Accelerating Expansion
w(z) crossing the w=-1
Consistency of
Scalar-Tensor Quintessence
crossing of w=-1
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
Wood-Vasey et. al astro-ph/0701041
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
l
Obs
SnIa
L
4 d L2
dL
Know L
Measure l(z)

d
dz
L
 H ( z )
 d L ( z ) 
l ( z)
 dz
l
Obs
SnIa
L
4 d L2
dL
l
L
4 a(t0 ) 2 x 2 ( z ) 1  z 
2
a ( t0 ) 1

 d L ( z )  x( z )(1  z )
l
L
4 a(t0 ) x ( z ) 1  z 
2
2
Flat
ds2  0
1
2
a ( t0 ) 1

 d L ( z )  x( z )(1  z )
cdt  a( z )dx( z )
2
a
1  d  dL ( z) 
2   z   H  z    

a
c  dz  1  z  
Know L
Measure l(z)

1
1
d
dz
L
 H ( z )
 d L ( z ) 
l ( z)
 dz
 L
m

M

2.5log
10 
Distance Modulus:

 l 
d L2
Growth Factor:
Growth Factor Evolution
(Linear-Fourier Space):
 a 
 a
m
a, D a 

  a0  1
 3 H ' a  
3 0 m
 D' k , a  
D' ' k , a    
f k , a Dk , a   0
2
5


a
H
a
2
a H a 


D(a)  a
General Relativity:
a0
f (k , a)  1  D(k , a)  D(a)
Koyama and Maartens (2006)
DGP:
Scalar Tensor:
Modified Poisson:
f (k , a)  1 
1
3  a 
  1
,
f (k, a)  G(a)  G0 1   1  a 
f (k , a )  1  
H (a)  H '(a)a 
1 

H 0rc 
3H (a) 
Esposito-Farese and Polarski (2001)
Uzan (2006)
1
kr
1   s 
 a
2
Sealfon et. al. (2004)
1
Flat Matter Only
0.9
ΛCDM (SnIa best fit, Ωm=0.26)
S. Nesseris, L.P.
astro-ph/0610092
0.8
ga
g a 
aD '(a)
D(a )
Scalar Tensor (α=-0.5, Ωm=0.26)
0.7
DGP
SnIa best fit
+
Flat Constraint
0.6
1

 aD' (a)
g  z   1  0.15 
 0.51 0.11
a

 D( a )
Verde et. al.
MNRAS 2002
Hawkins et. al.
MNRAS 2003
0.5
0.4
0
0.2
0.6
0.4
a
0.8
1
8 G 
1 2



 U 
m

3 
2

dU
  3H   
d
H2 
V(Φ)
Thawing
Thaw
Accelerate
Q.: Can the observed equation of state w(z)
distinguish between the two classes of models?
Φ
V(Φ)
Freezing
Decelerate
Freeze
Φ
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
Chevallier-Polarski-Linder
Lower bound on g2: