Transcript Accelerating Universe

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L. Perivolaropoulos
http://leandros.physics.uoi.gr
Department of Physics
University of Ioannina
1
Introduction - Key Questions - Latest Data
Geometric Constraints: Standard Rulers vs Standard Candles
Gamma Ray Bursts as Standard Candles
Current Dynamical Constraints: Growth Rate from Redshift Distortion
Weak Lensing
Potential Constraints from Laboratory Experiments:
Signatures of a cutoff in the Casimir Effect
Conclusions
2
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
2
d ln H
1
1  z 
dz
w z  3
2
3
 H0 
1 
  0 m 1  z 
 H 
w  1
Allowed Sector
3
Is General Relativity the correct theory on cosmological scales?
What is the most probable form of w(z) and what forms of w(z)
can be excluded?
Is ΛCDM (GR + Λ) consistent with all cosmological
observations?
What is the recent progress?
4


Latest data (307 SnIa)
Kowalski et. al.
arXiv:0804.4142
Recent data
Wood Vasey et. al.
astro-ph/0701041
w  z   w0  w ' z
4 years ago
Riess et. al. astro-ph/0402512
Astrophys.J.607:665-687,2004
m  0.27  0.03
w  z   w0  wa
z
1 z
Chevallier-Polarski, Linder
5
4 years ago
Riess et. al. astro-ph/0402512
Astrophys.J.607:665-687,2004
Latest data (307 SnIa)
Kowalski et. al. arXiv:0804.4142
1.2
1.2
0.7
0.7
6
Is ΛCDM (GR + Λ) consistent with all cosmological
observations?
Yes! Flat, ΛCDM remains at 1σ distance from the best fit since 2004.
The 1σ parameter contour areas remain about the same since 2004
despite of the double size of the SnIa sample and ΛCDM remains at
the lower right part of the (w0,wa) contour!
Q: Which Dark Energy Probe has the weakest
consistency with ΛCDM?
7
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, z  0.2
CMB Spectrum : z  1089
8
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
0 m  0.24
JCAP 0807:012,2008.
arxiv: 0712.1232
2σ tension between
standard candles and
standard rulers
Standard Rulers
(CMB+BAO)
9
Gamma-ray bursts (GRBs): The most luminus
electromagnetic events (1052 ergs~mass of Sun)
occurring in the universe since the Big Bang
Collimated emissions (0.1-100 seconds long)
caused either by the collapse of the core of a
rapidly rotating, high-mass star into a black holes
or from merging binary systems (short bursts).
GRBs are extragalactic events, observable to the limits of the visible universe; a typical GRB
has a z > 1.0 while the most distant known (GRB080913) has z=6.7
Swift Satellite (2004)
Shells of energy and matter ejected by the newly-formed hole collide
and merge ("internal shocks"). The shell sweeps up more and more
material it slows down and releases energy (afterglow).
10
GRBs are not standard candles but may be calibrated using empirical correlation
relations between energy output and lightcurve measurable observables.
Epeak : Peak Energy of spectrum
Example of Correlation:
apeak , Bpeak : Parameters to fit
Steps for cosmological fitting (Schaefer astro-ph/0612285,
Hong Li et. al. Phys.Lett.B658:95-100, 2008) :
1. Assume
log Li  log B  a log Epeak
Schaefer astro-ph/0612285
or
and fit for a, b using a specific
cosmological model to find Li
2. Use the fitted a, b to find the
‘correct’ Li from the observed Epeak i
L obtained from
3. Use the new Li , along with li, zi to fit
cosmological parameters
Circularirty problem: A cosmological model has been
used to calibrate a, b !!
11
S. Basilakos, LP, arXiv:0805.0875,
accepted in MNRAS (to appear)
Fit a, b along with the cosmological parameters (eg Ωm):
log Li  log  4 d L2  zi , m  Pbolo ,i 
log Li  b  a log Epeak ,i
xi
log Epeak ,i
xi
log E peak ,i 
log Li  b
a
Minimize χ2 wrt a, b, Ωm:
12
m  0.28  0.05
Current GRB data are not competitive with other geometric probes.
13
The calibration has too much scatter and there are additional parameters to be
fit.
The power spectrum at a given redshift is affected by systematic differences between
redshift space and real space measurements due to the peculiar velocities of galaxies.
 
Ps k :
Pg  k  :
Galaxy power spectrum in redshift space
Galaxy power spectrum in real space space
μ=cosθ and θ is the angle
between k and the line of sight.

Measure β
f
b
14
Find
f
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
15
L. Fu et al.: Very weak lensing in the CFHTLS Wide, arxiv. 0712.0884
Use weak lensing to observe the projected dark matter power spectrum (cosmic
shear spectrum) and compare with ΛCDM predictions using maximum likelihood.
16
Flat models 1, 2, 3 have
identical shift parameter R
and Ωm but different H(z).
The growth function D(a) in
the context of G.R. is mainly
determined by the shift
parameter R and Ωm . This
may be used as a test of G.R.
S. Nesseris, LP, JCAP 0701:018,2007
S. Basilakos, S. Nesseris, LP,
17
Mon.Not.Roy.Astron.Soc.387:1126-1130,2008.
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:
18
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)
19
decreases
Cutoff:
EM vacuum energy with cutoff (allow for
compact extra dimension):
k2
d  lc
k1
k1
d
Required Cutoff:
c  103 eV  lc  0.1mm  V  L  1030 g  cm3
k2
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
20
After the ‘Golden Age’ 1998-2005 of new dark energy observational
constraints, the improvement of these constraints has slowed down.
The most probable probe that may lead to disfavor of ΛCDM in the next
few years appears to be observations of Baryon Acoustic Oscillations
Laboratory Experiments related to Casimir effect have the potential to reveal
useful signatures of a physical cutoff associated with vacuum energy .
‘dark energy’
300
250
200
‘cmb’
150
100
No. of papers with words ‘dark energy’ and ‘CMB’ in
title per year (from spires database
http://www-spires.dur.ac.uk/spires/hep/
21
50
0
2000
2002
2004
2006
2008