Marco Baldi

Tuesday, July 6, 2010 

Marco Baldi 

Excellence Cluster Universe, Garching 

structure formation in the 

presence of dark 

interactions 

MGADS - Strasbourg, 1 VII 2010

Introduction 

outline 

Standard Model and non-standard models of the Universe 

Dynamic and interacting DE: 

- constant couplings [MB, V. Pettorino, G. Robbers, V. Springel - 0812.3901 (2010)] 

- time dependent couplings [MB - 1005.2188] 

Numerical methods for N-body simulations of interacting dark energy 

- assumptions, approximations, and their range of validity 

Results from high-resolution N-body runs: 

- Large Scale Structure: Halo Mass Function [MB, V. Pettorino - 1006.3761], Bias 

- Collapsed objects: Density Profiles, Concentrations, Baryon Fraction 

Next steps in a resurrected topic 


Marco Baldi - MGADS, Strasbourg 16 VI 2010

The beginning of the story: evidence for DE 

The last decade (well, actually a bit more than that...) has provided 

us with a hardly doubtable evidence of the existence of some 

accelerating component in the Universe, dubbed Dark Energy 








Large Scale Structure 

[APM, 2dF, SDSS, ...] 

Supernovae Ia 

[high-z SNS, SN Cosmology Project, ...] 

CMB anisotropies 

[COBE, WMAP, ...] 

Gravitational Lensing 

[HST, ...] 








Supernovae Ia 





[HST, ...] 

The theoretical effort to cast all these data into a simple and 

consistent picture of the Universe has led to the establishment of a 

STANDARD MODEL... 









Supernovae Ia 





[HST, ...] 

The theoretical effort to cast all these data into a simple and 

consistent picture of the Universe has led to the establishment of a 

STANDARD MODEL... 




Standard model and non-standard models 



Which is the standard model? 






ΛCDM 





ΛCDM 

1) GR is the correct and complete theory of gravity 





ΛCDM 


2) The Cosmological Principle holds (FLRW metric) 





ΛCDM 



3) The acceleration of the Universe is driven by a Cosmological Constant 




ΛCDM 




What is a non-standard model? 





ΛCDM 






Anything ≠ ΛCDM 




ΛCDM 







Dropping 1) Modified Gravities (ST theories, f(R) theories, TeVeS, extra dimensions, String...) 




ΛCDM 








Dropping 2) Inhomogeneous Universe (LTB models, Backreaction, ...) 




ΛCDM 








Dropping 2) Inhomogeneous Universe (LTB models, Backreaction, ...) 

Dropping 3) 

Dynamic Dark Energy models (Quintessence, k-essence, phantom, ...) 

Interactions of Dark Energy (Coupled DE, Unified DM, Chaplygin gas, ...) 


Why bothering with non-standard models? (I) 

The “standard” model is standard for a reason: 





fits well most of the data 





fits well most of the data easy 







Marco Baldi - MGADS, Strasbourg 16 VI 2010 

economic




So why looking for something more “exotic”? 



economic




So why looking for something more “exotic”? 

Easy BUT highly fine-tuned (cosmological issues): 

1) Only one number (Λ) but unnaturally small: FINE TUNING 

2) Λ domination is very recent: COINCIDENCE 


ρΛ 

ρm 


economic 

ρΛ 

ρpl 

∼ 10 −123 

< 10 −3 for z > 6

Why bothering with non-standard models? (II) 

NOT everything fits (astrophysical issues): 

1) Cusp-Core problem: OBSERVED CDM HALOS SHALLOWER THAN NFW 

[e.g. Flores & Primack 1994, Salucci & Burkert 2000, Newman et al. 2009] 

2) Satellite Problem: MANY FEWER SATELLITES OBSERVED THAN PREDICTED 

[e.g. Klypin et al. 1999, Springel 2008, (but see also e.g Maccio’ et al. 2009 MAYBE SOLVED?)] 

3) Void Phenomenon: TOO FEW GALAXIES FOUND IN VOIDS 

[e.g. Peebles 2000, Peebles & Nusser 2010] 

4) Cluster Baryon Fraction: SYSTEMATICALLY LOWER THAN EXPECTED 

[e.g. Allen et al. 2006 (but see also Giodini et al 2009!!)] 

5) Bulk Flows: TOO LARGE GALAXY VELOCITIES ON LARGE SCALES 

[e.g. Watkins et al. 2008, (but see also Erdogdu & Lahav 2009)] 

6) High-z massive clusters: VERY UNLIKELY TO FORM IN ΛCDM 

[e.g. Jee et al. 2009, Rosati et al 2009] 

7) The Bullet Cluster: EXCEEDINGLY RARE OBJECT IN A ΛCDM UNIVERSE 

[Lee & Komatsu 2010] 



Dynamic and interacting 

Dynamic DE: a scalar field in a self-interaction potential 



Dynamic and interacting 

Dynamic DE: a scalar field in a self-interaction potential 

¨φ +3H ˙ φ + dV 

dφ =0 


[Wetterich 1988] 



Time dependent couplings [MB 1005.2188] 



Why consider time variations of the coupling? 





1) There is no reason why β should be a constant. β(ϕ) is a more natural assumption 

2) A varying (growing) β could have larger effects on astrophysical observables at late 

times with a weaker impact on CMB and background expansion: INTERESTING. 








What changes with a time dependent coupling? 









There is no general analytic solution. 

Assume some generic forms of coupling evolution and find numerical solutions: 













β = β0a β1 

β = β0e β1φ/M









 

1.000 

0.100 

0.010 

Background evolution 

MDE 

Growing MDE 

0.001 

-10 -8 -6 -4 -2 0 

N ln a 


RP5 in Baldi et al. (2010) 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

w 

1.0 

0.5 

0.0 

-0.5 

-1.0 

Equation of state 

RP5 in Baldi et al. (2010) 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

1 10 

z + 1 


β = β0a β1 

β = β0e β1φ/M


Features of interacting dark energy 



1) MASS VARIATION 

of coupled matter particles 



m c 




1.4 

1.3 

1.2 

1.1 

1.0 

Mass correction for different coupled dark energy models 

CDM ( = 0, c=0) 

RP1 ( = 0.143, c=0.04) 

RP2 ( = 0.143, c=0.08) 

RP3 ( = 0.143, c=0.12) 

RP4 ( = 0.143, c=0.16) 

RP5 ( = 0.143, c=0.2) 

0.9 

0 10 20 30 40 50 

z 



m c 

1.4 

1.3 

1.2 

1.1 

1.0 





CDM ( = 0, c=0) 

RP1 ( = 0.143, c=0.04) 

RP2 ( = 0.143, c=0.08) 

RP3 ( = 0.143, c=0.12) 

RP4 ( = 0.143, c=0.16) 

RP5 ( = 0.143, c=0.2) 

0.9 

0 10 20 30 40 50 

z 



2) MODIFIED EXPANSION 

due to the Early DE component

m c 

1.4 

1.3 

1.2 

1.1 

1.0 





CDM ( = 0, c=0) 

RP1 ( = 0.143, c=0.04) 

RP2 ( = 0.143, c=0.08) 

RP3 ( = 0.143, c=0.12) 

RP4 ( = 0.143, c=0.16) 

RP5 ( = 0.143, c=0.2) 

0.9 

0 10 20 30 40 50 

z 


2) MODIFIED EXPANSION 

due to the Early DE component 

3•10 4 

2•10 4 

1•10 4 


H (km s -1 Mpc -1 ) 

Hubble functions for different coupled dark energy models 

CDM ( = 0, c=0) 

RP1 ( = 0.143, c=0.04) 

RP2 ( = 0.143, c=0.08) 

RP3 ( = 0.143, c=0.12) 

RP4 ( = 0.143, c=0.16) 

RP5 ( = 0.143, c=0.2) 

0 20 40 60 80 100 

z


How to implement all this in a code? (III) 



How to implement all this in a code? (III) 

Particle-Particle 

+ 

Particle-Mesh 

= 

GADGET-3 


Results (I): halo mass function and cluster counts 

Number counts in coupled dark energy models: CONSTANT and 

VARIABLE couplings [MB & V. Pettorino, 1006.3761] 

The recent detection [Jee et al (2009)] of a massive custer at z~1.4 might be a challenge for the 

standard model: the probability of such an object in ΛCDM has been estimated to be ~0.005. 

N(>M) (h -1 Mpc) -3 

N/N CDM 

10 -3 

10 -4 

10 -5 

10 -6 

10 -7 

10.0 

1.0 

0.1 

10 12 


N=256 3 

L=320Mpc/h 

DM only 

M max=3.05E+15 

M max=1.46E+15 

M max=9.56E+14 

z = 0.0 

10 13 

10 14 

MFoF [h -1 M O• 

] 

= 0.25 

= 0.5 e 2 

CDM 

10 15 

10 16 

Maybe non gaussianity? 

[Jimenez&Verde (2009)] 

NEED A LARGE fNL (~300) 


INTERACTING DE: 

The extra force acting between CDM 

particles and the extra friction term 

determine a faster growth of density 

perturbations. 

The number density of halos above a 

given mass M at any redshift z is 

correspondingly enhanced.

Results (II): bias 

The fifth-force determines an “effective” violation of the Weak 

Equivalence Principle for CONSTANT and VARIABLE couplings 



N=2x512 3 , L=80Mpc/h, Hydro




R(k)/R CDM(k) 

1.0 

0.9 

0.8 

0.7 

0.6 


CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM CDM 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

0.1 1.0 10.0 100.0 

k [ h Mpc -1 z=3.00000 

0.5 

] 


GRAVITATIONAL BIAS 

Since baryons are not coupled 

they do not feel any fifth-force. 

Baryon and CDM perturbations 

grow with a different rate, and the 

two components develop a purely 

gravitational bias at all scales. 

The bias is enhanced by 

nonlinearities at small scales and 

grows with time. 




R(k)/R CDM(k) 

1.0 

0.9 

0.8 

0.7 

0.6 



EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 


0.1 1.0 10.0 100.0 

k [ h Mpc -1 z=1.00000 

0.5 

] 















R(k)/R CDM(k) 

1.0 

0.9 

0.8 

0.7 

0.6 



EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 


0.1 1.0 10.0 100.0 

k [ h Mpc -1 z=0.200000 

0.5 

] 















R(k)/R CDM(k) 

1.0 

0.9 

0.8 

0.7 

0.6 



EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 


0.1 1.0 10.0 100.0 

k [ h Mpc -1 z=0.00000 

0.5 

] 













Results (III): baryon fraction 

The first hydrodynamical high-resolution N-body simulations for a weak 

DE-CDM CONSTANT interaction: [Baldi et al., MNRAS 2010] 


N=2x512 3 , L=80Mpc/h, Hydro 





Y b 

1.00 

0.95 

0.90 

0.85 

0.80 


Evolution of the relative baryon fraction with mass 

10 13 


M200 [h -1 M O• 

] 

!CDM 

RP1 

RP2 

RP5 

10 14 

BARYON FRACTION 

The different dynamics of 

(uncoupled) baryons and 

(coupled) CDM leads to a linear 

and nonlinear bias between the 

two species 

As a consequence, the baryon 

fraction of large halos is reduced 

in proportion to the coupling 

strength: RINGS A BELL? 

Yb ≡ 


fb 

Ωb/ΩM


DE-CDM VARIABLE interaction: [Baldi, arXiv:1005.2188] 

Y b 

1.00 

0.95 

0.90 

0.85 

0.80 

0.75 

0.70 

0.65 



10 13 

Relative baryon fraction 


M200 [h -1 M O• 

] 

10 14 

CDM 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

BARYON FRACTION 

The different dynamics of 

(uncoupled) baryons and 

(coupled) CDM leads to a linear 

and nonlinear bias between the 

two species 

As a consequence, the baryon 

fraction of large halos is reduced 

in proportion to the coupling 

strength: RINGS A BELL? 

Yb ≡ 


fb 

Ωb/ΩM

Resuts (IV): halo density profiles 








! / ! crit 

10 5 

10 4 

10 3 

10 2 

10 1 


Halo Density profiles for CDM and baryons for Group nr. 0 

N=2x512 3 

L=80Mpc/h 

Hydro 

"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc) 


DENSITY PROFILES 

The combination of the friction 

term and of the mass variation of 

(coupled) CDM particles affects 

the virial equiibrium of collapsed 

objects. 

The two effects induce a global 

increase of the total energy of the 

systems which slightly expand. This 

produces shallower density 

profiles in the inner regions of 

CDM halos: RINGS A BELL?

This result is in stark contrast with previous claims, which found the 

opposite behavior for the density profiles of CDM halos 

! / ! crit 

MB et al., 0812.3901 (MNRAS 2010) 

10 5 

10 4 

10 3 

10 2 

10 1 




"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc) 


Macciò et al., 2004



! / ! crit 

10 5 

10 4 

10 3 

10 2 

10 1 



N=2x512 3 

L=80Mpc/h 

Hydro 


"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc) 







objects. 









! ! / / ! crit 

10 5 

10 5 

10 4 

10 4 

10 3 

10 3 

10 2 

10 2 

10 1 

10 1 




N=2x512 3 

L=80Mpc/h 

Hydro 

"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M200("CDM) = 2.82510e+14 h M O• 

-1 M O• 

10 100 

R (h 

1000 

-1 10 100 

R (h kpc) 

1000 

-1 kpc) 







objects. 








Are NFW density profiles too steep also at cluster scales? 

! / ! crit 

10 5 

10 4 

10 3 

10 2 

10 1 



"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc) 

[Newman et al. 2009] 


Abell 611



M / crit 

10 5 

10 4 

10 3 

10 2 

10 1 


CDM 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

z = 0.00000 


Density profiles for Group nr. 6 

M200(CDM) = 1.44298e+14 h -1 M O• 

N=2x512 3 

L=80Mpc/h 

Hydro 

10 100 1000 

r [ h -1 kpc ] 






the virial equilibrium of collapsed 

objects.... BUT: 

If the coupling grows in time, 

there is also a decrease of the 

gravitational potential energy of 

halos. Two effects are competing, 

and can determine both shallower 

and steeper density profiles 

depending on the existence of a 

“Growing ϕMDE” phase.

Some first results (IV) 








c mean 

7 

6 

5 

4 

3 

2 


10 13 

M200 [h -1 M O• 

] 

!CDM 

RP1 

RP2 

RP5 

RP5 NO GF 

10 14 

N=2x512 3 

L=80Mpc/h 

Hydro 


CONCENTRATIONS 

Consistently with the results on 

density profiles, the 

concentrations of halos are found 

to be lower in coupled 

cosmologies with constant 

couplings than in ΛCMD. 

This confirms the picture: mass is 

moving outwards from the 

innermost regions of halos due to 

the extra physics coming from the 

DE-CDM interaction. 

Possible observational effects for 

strong lensing and galactic dynamics.




c mean 

14 

12 

10 

8 

6 

4 

2 


N=2x512 3 

L=80Mpc/h 

Hydro 

10 13 

M200 [h -1 M O• 

] 

10 14 

CDM 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 


CONCENTRATIONS 

Consistently with the results on 

density profiles, the concentrations 

of halos are found to be lower or 

higher in coupled cosmologies than 

in ΛCMD, according to the 

presence of a “Growing ϕMDE” 

phase: 

GϕMDE → Friction at work → 

→ halo “heating” → 

→ lower concentrations 

NO GϕMDE → NO friction → 

→ Potential energy 

decreases in time → 

higher concentrations


the highlights 


Maccio’ et al 2004 

Constant β 





Constant β 



MB et al 2008 (2010) 

Constant β 


! / ! crit 

10 5 

10 4 

10 3 

10 2 

10 1 


"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc)


Constant β 

MB 2010 (1005.2188) 

Variable β 


M / crit 

10 5 

10 4 

10 3 

10 2 

10 1 

CDM 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

z = 0.00000 


M200(CDM) = 1.44298e+14 h -1 M O• 

10 100 1000 

r [ h -1 kpc ] 


MB et al 2008 (2010) 

Constant β 


! / ! crit 

10 5 

10 4 

10 3 

10 2 

10 1 


"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc)


Constant β 

MB 2010 (1005.2188) 

Variable β 


M / crit 

10 5 

10 4 

10 3 

10 2 

10 1 

CDM 

EXP010a2 

EXP015a3 

EXP010e2 

EXP010e3 

EXP015e3 

z = 0.00000 


M200(CDM) = 1.44298e+14 h -1 M O• 

10 100 1000 

r [ h -1 kpc ] 


MB et al 2008 (2010) 

Constant β 

Li & Barrow (1005.4231) 

Constant β 


! / ! crit 

10 5 

10 4 

10 3 

10 2 

10 1 


"CDM 

RP1 

RP2 

RP5 

M200("CDM) = 2.82510e+14 h -1 M O• 

10 100 1000 

R (h -1 kpc)


concluding... 



concluding... 

The standard cosmological model requires 

extreme fine tuning and still shows some 

problems at small scales; 



concluding... 




Baryonic physics might resolve these 

tensions, but would not address the fine 

tuning at all; 



concluding... 







Scalar field models without a coupling also 

fail in reproducing the present Universe 

even at the background level 



concluding... 







Scalar field models without a coupling also 

fail in reproducing the present Universe 

even at the background level 

Coupled dark energy models, with constant 

or variable couplings, provide possible 

solutions to both the fine tuning and the 

small scale problems of ΛCDM...

Marco Baldi

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