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9,000,000,000 Years of Gravity at
Work in the Cosmic Factory
Christian Marinoni
Centre de Physique Théorique
Université de Provence
Nice 25-27 Jan 2005
Outline
• Galaxy bias
- Biasing from a theoretical & observational
perspective
• The
survey of the LSS at high z
- Results : biasing properties up to z=1.5
• Cosmological implication of our results
- Test of the Gravitational Instability Paradigm (GIP)
Marinoni et al. 2005 A&A in press (astro-ph/0506561)
Theoretical Background:
Dynamics of matter fluctuations


t
So what’s the problem?
Formation and evolution of luminous matter
Dynamics of galaxy fluctuations


g
• Where and when
did galaxies form?
• How do they
evolve?
• Formal problem:
g  g ( )
Biasing scheme
From an observational point of view....
• Biasing must exist on both small and large cosmological scales!
- Halo and galaxy profiles
- Galaxies of different types cluster differently
- Void phenomenon

From an observational point of view....
• Biasing must exist on both small and large cosmological scales!
- Halo and galaxy profiles
- Galaxies of different types cluster differently
- Void phenomenon
• Biasing relation depends in principle on some “hidden” variable ...
g=g(, A1, A2, A3 ... t)

Stochasticity in the plane g 
From an observational point of view....
• Biasing must exist on both small and large cosmological scales!
- Halo and galaxy profiles
- Galaxies of different types cluster differently
- Void phenomenon
• Biasing relation depends in principle on some “hidden” variable ...
g=g(, A1, A2, A3 ... t)
Stochasticity in the plane g 

• Up to now most measurement methods constrain
i.e. measure only linear bias (scalar parameter)
g  b
Where do we stand with observations
No bias locally. At present time ligh follows matter
Where do we stand with observations
At high z , blue galaxies more correlated than matter
Where do we stand with observations
Extremely red objects at z~1 more clustered w/r to blue
Where do we stand with observations
Where do we stand with observations
Conflicting evidences about biasing evolution!
Outline
• Galaxy bias
- Biasing from a theoretical & observational
perspective
• The
survey of the LSS at high z
- Results : biasing properties up to z=1.5
• Cosmological implication of our results
- Test of the Gravitational Instability Paradigm (GIP)
The
: Vimos-VLT Redshift Survey
French-Italian team : P.I. Olivier LeFèvre
– Laboratoire d ’Astrophysique (Marseille): Adami,
Arnouts, Foucaud, Ilbert, Le Brun, Mazure, Meneux,
Paltani, Tresse
– OABo, IRA-CNR (Bologna): Bardelli, Bondi, Bongiorno,
Cappi, Ciliegi, Marano, Pozzetti,Scaramella (Rome),
Vettolani, Zamorani, Zanichelli, Zucca
– IASF, OABr (Milan): Bottini, Cucciati, Franzetti, Garilli,
Guzzo, Iovino, Maccagni, Marinoni, Pollo, Scodeggio
– IAP (Paris): Charlot (MPA), Colombi, McCracken,
Mellier
– OAC (Naples): Arnaboldi, Busarello,Radovich
– OMP (Toulouse): Contini, Mathez, Pello, Picat,
Lamareille
The
in a nutshell
Imaging Survey (CFHT, ESO-MPI 2.2, ESO-NTT)
McCracken et al 2004, Radovich et al. 2004, Iovino 2005



16 sq.deg in 4 fields 22 deg
2
L~100h-1 Mpc at z~1
6
(U)BVRI(K) filters, ~3x10 objects
Spectroscopic Survey (Vimos at VLT):
LeFèvre et al 2004 AA in press (astroph/0409133)



Purely flux -limited survey, No preselections
16 deg down to I=22.5, z<1.3, 36000 observed
1 deg down to I=24,z<2, 13000 observed
Public data release on http://cencosw.oamp.fr
Sample:
Deep “cone”
(2h Field: first-epoch data)
• ~7000 galaxies with
secure redshifts, IAB24
z=1.5
• Coverage:
0.7x0.7 sq. deg
(40x40 Mpc at z=1.5)
• Volume sampled:
2x106 Mpc3 (~CfA2)
(1/16th of final goal)
•Mean inter-galaxy
separation at z=0.8
<l>~4.3 Mpc (~2dF at z=0.1)
•Sampling rate: 1 over 3
galaxies down to I=24
z=0
The
Density Field
(smoothing R=2Mpc)
2DFGRS/SDSS stop here
The Probability Distribution Function (PDF)
of galaxy overdensities
Probability of having a density fluctuation in the range
(,+d) within a sphere of radius R randomly located
in the survey volume
fR()
High density
Low density

Time Evolution of the galaxy PDF
The 1P-PDF of galaxy overdensities g ()
R
Z=1.1-1.5
• The PDF is different
at different cosmic
epochs
Z=0.7-1.1
• Systematic shift of the

peak towards low
density regions as a
function of cosmic time
• Cosmic space
becomes dominated by
low density regions at
recent epochs
Volume limited sample M<-20+5log h
A possible Interpretation
Gravitational
instability
in an
expanding
universe ???

(r)
v   2 dV
r
The PDF of mass overdensities f(): Shape
Z=1.1-1.5
Z=0.7-1.1

Lognormal!
(Coles & Jones 1991)
Conclusion:
Galaxies are
Spatially
distributed in
a different
way (biased)
with respect
to dark
matter at
high z

Measuring the galaxy bias up to z=1.5 with the VVDS
Bias: difference in distribution of DM and galaxy fluctuations
Linear Bias Scheme:
Our goal:

Strategy
g  b
g  b(z,,R)
(Kaiser 1984)
• Redshift evolution
• Non linearity
• Scale dependence
g(g )dg   ( )d
 Derive the biasing function
Sigad et al 2000
Marinoni & Hudson 2002
Ostriker et al. 2003
g  g ( )
The PDF of galaxy overdensities g (): Shape
Z=1.1-1.5
Z=0.7-1.1
 g   g ( )

The biasing function: Time evolution
• Scale independent
on 5 < R(Mpc) < 10
2dF
(Norberg et al. 04)
• Galaxies were
progressively more
biased mass tracers
in the past
• Evolution:
weak for z < 0.8
stronger for z > 0.8
The biasing function: 2) Shape b()
L
15 Mpc Smoothing
• Non linearity at a level <10% on scales 5<R<10 Mpc
(Local slope is steeper (bias stronger) in underdense regions)
• Also at high z, galaxy bias depends on luminosity: More luminous
galaxies are more spatially segregated with respect to DM
• Luminous galaxies do not form in underdense regions
The biasing function: 2) Shape b()
z
• At present epochs galaxies form also in low density regions, while
at high z the formation process is inhibited in underdensities
The Problem: Formation and Evolution of luminous matter
Dynamics of galaxy fluctuations 
• Where do
galaxies form?
In the high density
peaks of the dark
matter distribution

• How do they
evolve:
As time goes by
they start forming
also in low density
regions
Theoretical Interpretation: Which is the physical
mechanism governing biasing evolution?
Merging
(Mo & White `96
Matarrese et al `97)
Istantaneous
Star Formation
(Blanton et al `02)
Gravity
(Dekel and Rees `88
Tegmark & Peebles `98)
Outline
• Cosmological bias (definition)
- Biasing from a theoretical perspective
- Biasing from an observational point of view
• The VVDS survey of the LSS at high z
- A new method to measure biasing
- Results : biasing properties up to z=1.5
• Cosmological implication of our results
- Test of the Gravitational Instability Paradigm
Test of the Gravitational Instability Paradigm
~ costant with z

decrease with z
Volume limited sample M<-20+5log h
Test of the Gravitational Instability Paradigm
 g ( z )  bL ( z ) D( z ) (0)
Peebles 1980


b2 
S (z)  b (z)S3  3 
b1 

g
3
1
1
S3  34 /7  (n  3)

Juskiewicz et al. 1993
Conclusions
• Determination of the PDF of galaxy fluctuations
from a complete Volume-limited redshift survey
covering the range 0.5< z <1.5 (large connected sky
regions, all the galactic populations).
• The bias function is complex! First time
detection of non linearity on large scales (10% effect).
• Significant evolution of the `linearized’ bias 0.7<z<1.5.
• No single simple physical model is able to describe the
observed evolution.
• Low order moments of the galaxy PDF evolve as
predicted by the linear and second order perturbation
theory. GIP predictions consistent over 9,000,000,000 years
Reconstruction Completeness
Is the lognormal PDF of mass a good approximation of reality?

CDM Hubble Volume simulation (Virgo cons.)
Test of the Gravitational Instability Paradigm :
Motivation
The Origin of the Large Scale Structure is one of the
key issue in Cosmology.
A plausible assumption is that structures grow
via gravitational collapse of density fluctuations
that are small at early times, but is vital to test
this hypothesis.

J.A.Peacock, Nature 2002
Is gravity the engine of the cosmic factory?
Growth of Cosmic Structures

Fundamental variable for LSS studies:
The Matter Fluctuation Field
  (r,t) R  ( t) 

( t)
-1
r
The Evolution
of the LSS in linear approximation......
Continuity eq. + Poisson eq. + Poisson eq.
a
 (t )   (0)  a 3da
a

Initial Condition: Primordial Power Spectrum
P(k , t  0)   k2 (t  0)  k n
Assume knowledge of cosmological background
SNIa+Wmap measurements
a(t,)
n 1
Friedmann eq.
Harrison Zel’dovich.
Reconstruction of the Galaxy Density Field
• Top-Hat smoothing on various scales R (5-15 Mpc)
• Correction for radial selection function of the sample
• Correction for the VVDS sampling rate
• Shot noise minimization (Wiener-filter in Fourier space)


The PDF of mass: ()
Real Space Model Cole 1992
 (y) 
1
[ln y   2 /2]2
Exp{
}
2
2 y
2
2
1
y 1 
  ln[1  r (R,z) ]
2
2

Problem: we measure galaxies in redshift space!
2
1
2

 z (z)   r (0)D(z)[1 f (z)  f (z) ]
3
5

 z (R,z)
Kaiser 87