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

Venice 2013

Maps of the World

Kosmas IV c. d.C.

SDSS XXI c. d.C.

1.6 billion yrs

Lighthouses in the dark

2

4

Ld

f

5log 25Lm M d Supernovae Ia

Venice 2013

Venice 2013Heidelberg 2010

Lighthouses in the dark

0.5m

2.0m

Venice 2013

Hubble diagram

1997

1998

2010

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

Cosmological constant

Venice 2013

Matter density

Lam

bda

dens

ity

Venice 2013

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

Galaxy power spectrum

δ =

P(k) =

Venice 2013

Peculiar velocities

.

r = cz/H0

Venice 2013

Observer

Dark matter halos

Background sources

Weak lensing

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

Combine lensing and galaxy clustering !

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

SensitivityHu, 1999

1998 2011

History repeats itself…

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

Venice 2013

CambridgeUniversityPress

Rio de Janeiro 2013

Standard rulers

θ

0 0

0 0

1( ) sinh( )

( )k

k

R dzD z H

H zH

R

Rio de Janeiro 2013

Standard rulers

( )dz

H zR

R

Rio de Janeiro 2013

BAO ruler

Charles L. Bennett

Nature 440, 1126-1131(27 April 2006)

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

Rio de Janeiro 2013

Theoretical behaviour

or

   

Matter conservation equation