Transcript Accelerating Universe

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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
WMAP5 0803.0547
SDSS (BAO) 0705.3323v2
The Cosmological Constant (ρ=const) remains
consistent with all current data as a driving force of the acceleration and can
be generated by quantum fluctuations of the vacuum with a proper cutoff. A
signature in the Casimir effect would be expected in that case.
An Evolving Dark Energy Density (ρ=ρ(t)) is also allowed by the data
and a subset of the allowed evolving forms is inconsistent with most G. R. based models
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 CMB and large scale structure observations)
w z 
Cosmological Constant
Expansion History
z
w  1
3

a 2 8 G 
 a0 
H ( z)  2 
 0 m       a  
a
3 
a

2
Gmn - L gmn = k Tmn
a
w z 
1
1 z
Gmn = k Tmmn T’μν)
Dark Energy
z
Allowed Sector
p ( z)
w z  X

 X ( z)
a
 ~ e
3

1
da '
(1 w( a '))
a'
2
d ln H
1
1  z 
3
dz
2
3
 H0 
1 
 0 m 1  z 
 H 
w  1
Eq. of state evolution
Forbidden
(ghosts)
w z 
Modified
Gravity
G’mn = k Tmmn
z
w  1
Allowed Sector
2
d ln H
1
1  z 
dz
w z  3
2
3
 H0 
1 
  0 m 1  z 
 H 
Direct Probes of H(z):
Luminosity Distance (standard candles: SnIa,GRB):
SnIa
GRB
Obs
dz 
d L ( z )th  c 1  z  
0 H  z 
SnIa : z  (0,1.7]
z
L
l
4 d L2
dL  z 
GRB : z  [0.1,6]
flat
Significantly less accurate probes
S. Basilakos, LP, arXiv:0805.0875
Angular Diameter Distance (standard rulers: CMB sound horizon, clusters):
dA  z 


rs
dA  z 
rs

c z dz 
d A ( z )th 

1

z
  0 H  z
BAO : z  0.35
CMB Spectrum : z  1089
LCDM   w0 , w1    1,0
Parametrize H(z):
w  z   w0  w1
Minimize:
z
1 z
5log10  d L, A ( zi )obs   5log  d L, A ( zi ; w0 , w1 )th 
  min
 2  m , w0 , w1    
2
2
N
i 1
ESSENCE+SNLS+HST data
i
WMAP3+SDSS(2007) data
Standard Candles
(SnIa)
Lazkoz, Nesseris, LP
arxiv: 0712.1232
0 m  0.24
2σ tension between
standard candles and
standard rulers
Standard Rulers
(CMB+BAO)
Measure growth function of cosmological perturbations:
Evolution of δ :
f  m  a 
Parametrization:

LCDM : de  L  const
 
6
11
Fit to LSS data:
0 m  0.3
ΛCDM
ΛCDM provides an excellent fit
to the linear perturbations
growth data
best fit
S. Nesseris, LP,
Phys.Rev.D77:023504,2008
Quantum Vacuum is not empty!
Sea of virtual particles
e
e
e
e

e

e
e

e

e
e
Whose existence has been
detected (eg shift of atomic
levels in H) W. Lamb, Nobel Prize 1955
Quantum Vacuum is elastic (p=-ρ)
pvac vac
e
e
e
e
e
e
F
ΔV
dE   pdV
1st law
vac dV   pvac dV  vac   pvac
same as Λ
Quantum Vacuum is Repulsive (ρ+3p=-2ρ)
Quantum Vacuum is divergent!
Vacuum Energy of a
Scalar Field:
cutoff
Q: Can we probe a diverging zero point energy of the vacuum in the lab?
A: No! Non-gravitational experiments are only sensitive to changes
of the zero point energy.
But: This is not so in the presence of a physical finite cutoff !
Majajan, Sarkar, Padmanbhan,
Phys.Lett.B641:6-10,2006
Casimir Force Experiments can pick up the presence of a physical cutoff !!
Vacuum Energy gets modified in the presence
of the plates (boundary conditions)
  2
hc
240d 4
  2
hc

720d 3
FCas 
d2
ECas
k3
Attractive Force
k3
k2
k2
d
k1
k1
d
d
Density of Modes (relative to continuum)
decreases
Cutoff:
EM vacuum energy with cutoff (allow for
compact extra dimension):
k2
d  lc
k1
d
Required Cutoff:
c  103 eV  lc  0.1mm  V  L  1030 g  cm3
k2
k1
d
Density of Modes is Constant.
Energy of Each Mode Increases.
Force becomes repulsive!
With Cutoff
Compact Extra dim, No cutoff
LP, Phys. Rev. D 77, 107301 (2008)
No extra dim.
Poppenhaeger et. al.
hep-th/0309066 Phys.Lett.B582:1-5,2004
with compact extra dim
The cutoff predicts a Casimir force which
becomes repulsive for d<0.6mm
What is so special about today?
m   r
L
L  a  
L
m  a   r  a   L
m  a   r  a 
m  a    r  a  
m  a   r  a    L
Q1: What theories are consistent with range of observed H(z)?
•Minimally Couled Scalars (Quintessence)
•Barotropic fluids (eg Chaplygin Gas)
• k-Essence
• Topological Defect Network
•…
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?
Address Q2-Q3 for Quintessence
1 2
L    V  
2
Quintessence
 Quint   1
1 2

 V  
p 2
 0
w 

1
 1 2 V 
 
2
To cross the w=-1 line the kinetic energy term
must change sign
(impossible for a quintessence field)
Generalization for k-essence:
ESSENCE+SNLS+HST data
w  z   w0  w1
z
1 z
Q1: What theories are consistent with range of observed H(z)?
• Extended (Scalar–Tensor) Quintessence
• f(R) Modified Gravity
• Braneworld models (eg DGP)
•…
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?
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:
0
S. Nesseris, LP ,
Phys.Rev.D75:023517,2007
solar system
G n
Fn  gn 
G0 H 0n
Q.: What constraints do the consistency requirements imply for H(z), F(z)
at low z and are these constraints respected by observations?

  z 
2


   z  
Freezing
z 0
0
z 0
0
Thawing
2
U   z  0  U1  0
0m  0.24
G(t) close to maximum
0m  0.24
G(t) close to minimum
Solar System Constraints on g2:
Lower bound on g2:
G
  4  5 1015 yrs 2  g2  (4  5) 105 J. Mueller 2006
G
g2  (2  1) 105
E. Pitjeva 2007
Observational Probes of the
Accelerating Expansion
w(z) is close to -1
w(z) crossing the w=-1
w(z) =-1
The cosmological constant may be
generated by quantum fluctuations of the
vacuum with a cutoff. A change of sign of
the Casimir force is predicted in that case.
w(z) crossing the w=-1
Inconsistent with
Minimally Coupled Quintessence
and also with
Scalar Tensor Quintessence
if G(t) is increasing with time.
Consistency of
Scalar-Tensor Quintessence
with local gravity and
crossing of w=-1
G0
 104
G0 H 0
G0
 O(1)
G0 H 02
G r  F0

G0
F r 