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Venice 2013
– Luca Amendola
– University of Heidelberg
The next ten years of dark energy research
Rap
hael
, The
Sch
ool o
f Ath
ens,
Rom
e
Venice 2013
Bug or feature?
Evolution in time: standard candles
Conclusion: SNIa are dimmer than expected in a matter universe !
BUT:
- Dependence on progenitors?
- Contamination?- Environment?- Host galaxy?- Dust?- Lensing?- Unknowns?
Ordinary matter
Venice 2013
Cosmological explanation
Evolution in time: standard candles
There is however a simple cosmological solution
)(
)(zH
dzzr
0
)(H
zzr
If H(z) in the past is smaller (i.e. acceleration), then r(z) is larger:larger distances (for a fixed redshift) make dimmer supernovae
a(t)
time
Local Hubblelaw
Global Hubble
law
now
Venice 2013
Cosmological constant
acceleration, in GR, can only occur if pressure is large and negative )3(
3
4p
G
a
a
Properties:dominantdark,weakly clusteredwith large negative pressure
Einstein 1917
p
Venice 2013
Cosmological explanation
Evolution in time: standard candles
There is however a simple cosmological solution
)(
)(zH
dzzr
0
)(H
zzr
Local Hubblelaw
Global Hubble
law
3 2 1/20( ) [ (1 ) (1 )(1 ) ]m mH z H z z
Time view
We know so little about the evolution of the universe!We assumed for many years that there were just matter and radiation
Venice 2013
matter
DE
radiation
Shall we repeat our mistake and think that there is just a Λ ?
BBN
CMB
Venice 2013
L = crossover scale:
• 5D gravity dominates at low energy/late times/large scales• 4D gravity recovered at high energy/early times/small scales
5D Minkowski bulk:
infinite volume extra dimension
gravity leakage
2
1
1
rVLr
rVLr
brane
An example of Modified Gravity: DGP
RgxdLRgxdS 4)5()5(5
(Dvali, Gabadadze, Porrati 2000)
3
82 G
L
HH
Venice 2013
Space-time geometry
The most general (linear, scalar) metric at first-order
Full metric reconstruction at first order requires 3 functions
2 2 2 2 2 2[(1 2 ) (1 2 )( )]ds a dt dx dy dz
( ) ( , ) ( , )H z k z k z
background
perturbations
Venice 2013
Two free functions
At linear order we can write:
2 24 m mGa Poisson equation
zero anisotropic stress
)])(21()21[( 222222 dzdydxdtads
1
Venice 2013
Two free functions
2 2 ( ,4 ) m mQ aa kG modified Poisson equation
non-zero anisotropic stress
)])(21()21[( 222222 dzdydxdtads
( , )k a
At linear order we can write:
Venice 2013
Modified Gravity at the linear level
scalar-tensor models
2
2
2
2
0,
*
'
')(
'32
)'(2)(
FF
Fa
FF
FF
FG
GaQ
cav
( , ) 1
( , ) 1
Q k a
k a
standard gravity
DGP
13
2)(
21;3
11)(
a
wHraQ DEc
f(R)
Rak
m
Rak
ma
Rak
m
Rak
m
FG
GaQ
cav2
2
2
2
2
2
2
2
0,
*
21)(,
31
41)(
Lue et al. 2004; Koyama et al. 2006
Bean et al. 2006Hu et al. 2006Tsujikawa 2007
coupled Gauss-Bonnet see L. A., C. Charmousis, S. Davis 2006...)(
...)(
a
aQ
Boisseau et al. 2000Acquaviva et al. 2004Schimd et al. 2004L.A., Kunz &Sapone 2007
Venice 2013
Classifying the unknown1. Cosmological constant2. Dark energy w=const3. Dark energy w=w(z)4. quintessence5. scalar-tensor models6. coupled quintessence7. mass varying neutrinos8. k-essence9. Chaplygin gas10. Cardassian11. quartessence12. quiessence13. phantoms14. f(R)15. Gauss-Bonnet16. anisotropic dark energy17. brane dark energy18. backreaction19. void models20. degravitation21. TeVeS22. oops....did I forget your model?
Venice 2013
The past ten years of dark energy models
4 ,,
1( )
2 matterdx g R V L
4 ,,
1( ) ( )
2 matterdx g f R V L
4 ,,
1( ) ( ) ( )
2 matterdx g f R K V L
4 , , , ,, ,
1 1( , ) ( ) ( )
2 2 matterdx g f R G K V L
First found by Horndeski in 1975 rediscovered by Deffayet et al. in 2011 no ghosts, no classical instabilities it modifies gravity! it includes f(R), Brans-Dicke, k-essence, Galileons, etc etc etc
4i matter
i
dx g L + L
The most general 4D scalar field theory with second order equation of motion
A quintessential scalar field
Saõ Paulo 2013
Venice 2013
The next ten years of DE research
Combine observations of background, linear and non-linear perturbations to reconstruct
as much as possible the Horndeski model
… or, even better, rule it out!
Venice 2013
Modified Gravity at the linear level
Every Horndeski model is characterized at linear scales by the two observable functions
2
42 2
5
25
1 23
1( , )
1
1( , )
1
k hk a h
k h
k hQ k a h
k h
De Felice et al. 2011; L.A. et al.,arXiv:1210.0439, 2012
k = wavenumber
= time-dependent functions
Modified Gravity at the linear level
De Felice et al. 2011; L.A. et al.,arXiv:1210.0439, 2012
Saõ Paulo 2013
Generality of the Yukawa correction
Every Horndeski model induces atlinear level, on sub-Hubble scales, a Newton-Yukawa potential
/( ) (1 )rGMr e
r
where both α and λ depend on space and time
Every consistent modification of gravitybased on a scalar field must generate
this gravitational potential
Venice 2013
Dark Force
Schlamminger et al 2008
/
2 2
(1 )
''( )
( )
rGM GMe
r r
m V
r
Limits on Yukawa coupling are strong but local!
Venice 2013
Venice 2013
Reconstruction of the metric
v Hv
dzperp )(
massive particles respond to Ψ
massless particles respond to Φ-Ψ
2 2 2 2 2 2[(1 2 ) (1 2 )( )]ds a dt dx dy dz
Venice 2013
All you can ever get out of Cosmology
Expansion rateAmplitude of the power spectrum
Redshift distortion of the power spectrumLensing
How to combine them to test the theory?
as function of redshift and scale!
Venice 2013
Model-independent ratios
Redshift distortion/Amplitude
Lensing/Redshift distortion
1
redshift distortion
amplitudeP
2
lensing
redshift distP
Redshift distortion rate 3 rate of variation redshift distP
expansion rateE Expansion rate
Venice 2013
Testing the entire Horndeski Lagrangian
A unique combination of model independent observables
L.A. et al. 1210.0439
Observables
Theory
Venice 2013
Horndeski Lagrangian: not too big to fail
L.A. et al. 1210.0439
2, , ,2 3( ) 0k kkk kkg g g
2
2
( ) '( , )
REag z k
LEa
If this relation is falsified, the Horndeski theory is rejected
Venice 2013
Euclid Surveys– Simultaneous (i) visible imaging (ii) NIR photometry (iii) NIR spectroscopy
– 15,000 square degrees
– 100 million redshifts, 2 billion images
– Median redshift z = 1
– PSF FWHM ~0.18’’
– >900 peoples, >10 countries
Euclid in a nutshell
Euclid satellite
SELECTED!
arXiv Red Book 1110.3193
Venice 2013
Euclid’s challenge
Growth of matter fluctuations
C. Di Porto & L.A. 2010
Euclid error forecast
Present error
log
log
ds
d a
IPMU Dark Energy Conference
Euclid - Primary Science Goals
Issue Our Targets
Dark Energy
Measure the DE equation of state parameters w0 and wa to a precision of 2% and 10%, respectively, using both expansion history and structure growth.
Test of General Relativity
Distinguish General Relativity from the simplest modified-gravity theories, by measuring the growth factor exponent γ with a precision of 2%
Dark Matter
Test the Cold Dark Matter paradigm for structure formation, and measure the sum of the neutrino masses to a precision better than 0.04eV when combined with Planck.
The seeds of cosmic structures
Improve by a factor of 20 the determination of the initial condition parameters compared to Planck alone.
Summary: Euclid’s challenge
Rio de Janeiro 2013
Deconstructing the galaxy power spectrum
Redshift distortion
Galaxyclustering
Present mass power
spectrum
Galaxy bias
Growth function
Line of sightangle
Rio de Janeiro 2013
Three linear observables: A, R, L
μ=0Amplitude
A
μ=1Redshift distortion
R
LensingL
clustering
lensing
(1 )Y
8 ,0( , ,0) ( )gal tk z Gb k
8 ,0( , ,1) ( )gal tk z G f k
2 28 ,0
3( ) ( )
2lens m tk k G k
Rio de Janeiro 2013
The only model-independent ratios
Redshift distortion/Amplitude
Lensing/Redshift distortion
1
R fP
A b
02
mLP
R f
Redshift distortion rate 3
' 'R fP f
R f
How to combine them to test the theory?
0
HE
HExpansion rate