Which physics for the Invisible Universe?

**Which** **physics** **for**

**the** **Invisible** **Universe**?

André Füzfa!

!

Namur Center **for** Complex Systems (naXys),!

University of Namur (Belgium)!

and!

Center **for** Cosmology, Particle Physics and Phenomenology (CP3)!

Louvain University (Belgium)!

Part I:

BASICS OF PHYSICAL

COSMOLOGY

The equivalence principles

Universality!

of gravitation!

Weak Equivalence Principle WEP!

(Einstein Equivalence Principle)!

gravitation is mediated !

by one universal metric g µ!"

+!

Strong Equivalence Principle SEP!

Non-linear dynamics

of g µ!"

Acceleration!

Weight!

Anywhere !

in space-time,!

far from matter!

Covariance:!

Laws of **physics** !

are independent !

on **the** general motion !

of **the** observer!

Earth!

There is no way to discriminate locally !

between acceleration and gravitation!

with non-gravitational experiments!

…even with gravitational experiments!!

SEP!

!

Generalised !

principle !

of relativity!

General Relativity in a Nutshell

! The Equivalence Principles (EPs):

# Weak: gravitation is mediated by one universal metric g µ!

" In free-fall, laws of **physics** are those of special relativity

# SEP rules **the** non-linear dynamics of gravitation (notably g µ! is **the** only one canonical

gravitational field)

" Machian view of general relativity :

« Laws of Physics are independent of any general motion of **the** observer »

! Generalised Covariance:

# Gauge principle : field equations are invariant under arbitrary non-linear coordinate change

(Poincare gauge trans**for**m)

# Pseudo-riemanian differential geometry with Levi-Civita connexion

! Einstein-Hilbert gravity:

G µν = R µν − 1 2 Rg µν = 8πG

c 4 T µν

Derivatives of g Stress-energy tensor "

µ!"

Gauge principle : Invariance under

difféomorphisms

The perfect cosmological principle

! The large-scale **Universe** is isotropic (no privileged direction)

! Universality principle : conclusions drawn here and now are everywhere and

everytime valid (Copernic principle)

! Noprivileged location: **the** **Universe** is homogeneous and isotropic at a given time

! No privileged epoch : **the** **Universe** does not evolve

! Static **Universe**s:

! Isotropy: spherical symmetry

! **Universe** filled with self-gravitating fluids in gravitational/**the**rmal equilibrium

! Equlibrium is unrealistic:

! Einstein’s **Universe**: unstable equilibrium (guaranteed by cosmological constant)

! de Sitter’s **Universe** : an expanding vacuum universe

! Lemaître’s cosmological syn**the**sis (1927):

! A dynamical universe linking Einstein’s static universe (a=cst in t!-$) and de

Sitter (a~exp(t) in t!-$)

! Cosmic expansion explains runaway galaxies (Hubble diagram)

! Conclusion : **the** perfect cosmological principle has to be relaxed!

The (restricted) cosmological principle

! The properties of **the** **Universe** do not depend on **the** particular location

of **the** observer

! The **Universe**, at any given time, is homogeneous and isotropic

! Its averaged properties evolve with time

! Friedmann-Lemaître-Robertson-Walker metric

with

R: curvature radius

d%: solid angle element

a(t): scale factor

! 3D spatial homogeneous and isotropic geometries

k=+1

Elliptic geometry

k=0

Euclidean geometry

k=-1

Hyperbolic Geometry

The restricted cosmological principle

On large-scales (10 24 m), **the** **Universe** is roughly

HOMOGENEOUS and ISOTROPic

1.6x10 6 IR galaxies (~2005)

2x10 6 galaxies (~1990)

Friedmann-Lemaître cosmological models

! Einstein equations: Friedmann and acceleration equations

! Ingredients : conservation equation"

Matter : p=0 => &~a -3 :

Radiation : p=&c 2 /3 => &~a -4 4

Cosmological constant : p=-&c 2 => &~cst

! Cosmological parameters

! Hubble parmeter (expansion rate):

! Critical density :

! Density parameters:

! Acceleration parameters

Classification of Friedmann-Lemaître **Universe**s

Reality:

Open **Universe**s k=-1 or 0

(hyperbolic or flat)

a

'(0 : **Universe** with accelerated

expansion:

Lemaître-Eddington

'"

'=0 et k=0: "

Einstein-de Sitter **Universe**

'

Classification of Friedmann-Lemaître **Universe**s

Reality:

a

Closed **Universe**s k=+1

(elliptic)

L-Ed

Lemaître’s

**Universe**

(primeval atom)

Osc.

Einstein’s **Universe**

Lemaître’s primeval atom

'"

a E

Lemaître’s

Hesitating

**Universe**

Osc.

'>' E : Eddington-Lemaître **Universe**

'!' E : Lemaître’s hesitating **Universe**

(galaxy **for**mation)

0

Successes of **the** Hot Big Bang Scenario

! Three classical proofs:

! Hubble diagram and cosmological redshift

! Existence and **physics** of **the** cosmic microwave background (CMB)

! Light-elements abundance and Big Bang Nucleosyn**the**sis

! Indirect « proofs »:

! Galaxy counts and cosmological principle

! Galaxy **for**mation in an expanding universe

! Number of elemntatry particle generation

! Gravitational lensing on large-scales

! Failure of alternative cosmologies (e.g., steady-state)

Now we can go fur**the**r:

In which **Universe** do we live?

What is **the** **Universe** made of?

Part II:

A PUZZLING INVISIBLE

UNIVERSE

What’s wrong with **the** large-scale **Universe**?

Total=!

NGC 1090!

Picture: D. W. Hogg, M. R. Blanton (SDSS)!

Data from Gentile et al., MNRAS 351 (2004)!

Dark Matter!

+!

Stars!

+!

gas!

! Stars and clusters rotate too fast around galaxies

! Galaxies also rotate too fast inside clusters (F. Zwicky 1930)

What’s wrong with **the** large-scale **Universe**?

Gravitational Lensing!

Bullet Cluster!

Ordinary (luminous) matter is not enough!!

Cosmic

Microwave

Background

Galaxy Formation!

! Large-scale Gravitational lensing

! There should exist a large amount of invisible matter between galaxies

! Cosmic Microwave Background:

! Dark Matter= 5x Ordinary (baryonic) matter

Dark Matter or Modified Gravity?

MOND!

Wiggles?!

Newton!

a 0 ~10 -10 m/s

Newton:!

a~1/r 2!

!

MOND:!

a~1/r!

si

a>>a 0!

2 Broeils 1992 A&A 256 19!

Famaey et al. 2007 PRD 75 063002!

MOND:!

a~1/r!

si a

Modern Measurement

of Cosmic Expansion

New Standard Candles :

type Ia supernovae

Supernovae appear

fainter than

expected!

!"#$%%$&

Original

Hubble

Diagram

" HST Gold Sample

" 1st year SNLS collaboration

" « Old » Cosmology (SCDM, % m =1)

" Matter + DE ('CDM, % m =0.24 ; % ' =0.76)

! Riess et al., ApJ, 607, 665

(2004)

! P. Astier et al., A&A 447

(2006)

" Deceleration (100% Matter)

" Acceleration (Matter and Dark Energy)

SNe are fainter than expected

#

They are fur**the**r than expected

#

Cosmic expansion has accelerated! (fixed expansion rate)

or (and?)!

Supernovae are not standard candles !

(including nonuniversal **physics**)

!"#$%%$&

Angular Fluctuations of CMB

! Geometry:

Flat **Universe** (% T ~1)

! Present Energy Content:

! Matter : ~24%

! Baryons: ~4%

Intensity of fluctuations ($K%)

Geometry % T h%

Total Matter % m h%

Baryons % b h%

Angular size of fluctuations (°)

=> Dark Matter : ~ 20 %

=> Missing DE: ~76%!

" Old Cosmology (100% Matter)

" Baryons, Dark Matter and Dark Energy

! D.N. Spergel, et al., 2003, ApJ S, 148, 175

! D.N. Spergel et al., Astrophys. J. Suppl. 170 377 (2007)

! Baryon Acoustic Oscillation:

Large-scale Structures

2-point correlation function

" SDSS Luminous Red Galaxies

" 'CDM, % m =0.24 ; % ' =0.76

" OCDM, % m =0.24

Distance r (h -1 Mpc)

! Large-Scale distribution of galaxies (Power Spectrum)

2dFGRS : 0.65

The Concordance Model 'CDM

Present amount of ' (dark energy)!

http://supernova.lbl.gov Atoms ~4% "

Present amount of pressureless matter

Energy Content

of **the** **Universe** Today

(>95% C.L.)

Cosmological

Constant '"

(DE)~76%

'CDM

Age of **the** **Universe** :

~ 14 billion years

Geometry : flat

Dark Matter

~20%

Radiations

~0.01%

**Invisible** **Universe**?

! Observational evidence requiring a dark sector:

« Dark Matter »:!

" Galaxy rotation curves, CMB anisotropies, Galaxy cluster properties, Gravitational

lensing, Structure **for**mation & galaxy distribution, etc.!

« Dark Energy »:!

" SNe Ia Hubble diagram, CMB energy balance, distance to last scattering surface,

baryon acoustic oscillation, large-scale galaxy distribution, etc.!

! Observational evidence NOT requiring a dark sector:

High-precision tests of GR:!

" light elements abundance (BBN), light deflexion, perihelion shift, time delay, binary

pulsars orbital decay, etc.!

! Three options **for** **the** dark sector:

Observational problems?!

COSMOLOGICAL SCALES!

LOCAL SCALES / ORDINARY MATTER PROFUSION

Misinterpretations? (e.g. : relaxation of cosmological principle)!

New **physics**? (gravitation + exotic matter-energy components)

Part III:

THE DARK ENERGY

CHALLENGE

The Unbearable Lightness of Vacuum

! **Which** vacuum **for** gravitation?

Trivial (g µ! =0) or non-trivial (Minkowski, de Sitter, Schwarzschild, Kerr, etc.)!

! Weight of vacuum energy? " quantum gravity and quantum field **the**ory!

! ' provides cosmic acceleration:

" Why is **the** cosmological constant so small?

Fine-tuning problem!

" Why is vacuum energy of **the** order of a present cosmological property?

Coincidence problem!

Why going beyond 'CDM?"

! What is Dark Matter (DM) AND what is Dark Energy (DE)?

DE: cosmological constant ' #vacuum energy # fine-tuning & exp ' ~(1028 eV) 4 !

DM: yet-undiscovered faintly interacting heavy particle!

CDM and DE not physically related !

Triple coincidence on % baryons , % CDM and % ' !

! Negative Pressures of DE

Violation of **the**

Strong Energy Condition

(SEC)

Gravitational collapse of DE!!

Effect of structure **for**mation!!

Beyond **the** ' ...?"

! Coincidence Problem & obs ' ~ (10-3 eV) 4

Why is vacuum energy of **the** order of a present cosmological property?!

A cosmological mechanism behind DE? Low-energy **physics**? !

Frozen Vacuum

Energy:

cosmological

constant '"

What lies behind **the** '?

'"

Gravitation g µ!"

Space-time independent

interactions

(Minimal Coupling)

**Invisible** Sector

Dark Matter

A Dynamical Cosmological Constant?

"New degrees of freedom!

'CDM

Visible Sector

Baryons Photons

Quintessence: Matter and DE conserved separately, only gravitational interaction

Modified Gravity: Matter interacting with DE (non-minimal coupling)!

What lies behind **the** '? Quintessence?!

! Quintessence, k-essence:

Minimal Coupling

'"

Gravitation g µ!"

Varying

Dark Energy *"

(Effective) Potential

**Invisible** Sector

Dark Matter

(!

)

VV(*)!

Visible Sector

Baryons Photons

Cosmic acceleration

if violation of

Strong Energy Condition

(p

What lies behind **the** '? Interacting DE?!

Dark Energy *"

coupling non-minimally:

space-time dependent

universal interactions

'"

Gravitation

G m (*)! G m (*)!

! Bare Space-time g* µ!

! Running coupling G m (*)"

**Invisible** Sector

Visible Sector

Violation of **the** Strong Equivalence Principle

(tensor-scalar gravitation):

Varying G N !

(are SNe Ia still Standard Candles?)!

Adequacy with constraints on SEP?!

Why is SEP violated?!

! P. Jordan, Nature 164, 637 (1949)

! M. Fierz, Helv. Phys. Acta 29, 128 (1956)

! C. Brans and R. H. Dicke, Phys. Rev. 124, 925 (1961)

SEP violation

=Effective metric felt by matter,

suited by **the** scalar field

Cosmic acceleration through

deviation from GR

Space-time dependent!

nonuniversal interactions!

What lies behind **the** '? AWE!

+"

Abnormally Weighting

**Invisible** Sector

Gravitation

G awe (*)! G m (*)!

! Bare Space-time g* µ!

! Running couplings G m , G awe"

Normally Weighting

Visible Sector

Does Dark Matter

fall in **the** usual way?

Weak Equivalence Principle

violation

No WEP " no SEP

Transient deviation from GR

" cosmic acceleration

The Dark Cosmology Iceberg

Cosmological Constant

Coincidence? " cosmological mechanism (*)!

Quintessence

Only gravitational interactions?

" Non-Minimal couplings!

Scalar tensor gravity

Universality of NM couplings?

" No uniersality of free-fall!

Coupled DM-DE models

DM-DE unification…?

«!(Please not) Yet ano**the**r DE model!!»

! Numerous interpretations of cosmic acceleration have been proposed

YES, BUT

! DE candidates often originate from long-standing and deep ideas in Physics

': Einsteinʼs attempt to incorporate Mach Principle in general relativity!

Quintessence : particle **physics**-motivated scalar fields (like inflation)!

Coupled DE : variation of physical constants!

Backreactions: Lemaître-Tolman inhomogeneous universe!

Brane cosmology: extra-dimensions à la Kaluza-Klein!

F(R)-gravity : Einstein unitary field **the**ory (so called « Palatiniʼs method »)!

AWE: Brans-Dicke approach to Machʼs Principle!

Etc.!

! We are now offered a unique opportunity to test **the**se ideas

! Confidence into a **the**ory is also gained by discarding rival explanations

! **Invisible** **Universe**: new bridges between HEP & cosmology!

Part IV:

UNIFIED APPROACHES TO

DARK MATTER-DARK

ENERGY

Why Dark Matter-Dark Energy interactions?"

! Are **the** nature of DM and DE really physically disconnected?

! A cosmological mechanism **for** DE?

Dynamical DE " new degrees of freedom!

Separately conserved: QUINTESSENCE

(only gravitational interaction)

Conserved toge**the**r: COUPLED DE

! New interactions: toward a unified **physics** of **the** dark sector?

DM-DE of same physical nature!

Coincidence: DE is related to **the** dominance of DM!

Allows new tests of **the** nature of DE!

! Violation of **the** Equivalence Principles (EPs):

Matter – DE energy exchange is viewed as an energy loss through an invisible

channel!

If so, local physical laws does not seem to be those of special relativity…!

Some examples of coupled DE models"

! Extended quintessence / Tensor-scalar gravity

Same coupling DE-baryons & DE-DM!

Variation of G N " solar system constraints (Strong Equivalence Principle)!

! Coupled DM-DE"

Non-universality of free-fall: violation of Einstein Equivalence Principle!

DE scalar field drives **the** DM mass!

Well-shaped

potential

requested!

cosmic acceleration

DM mass

variation

! Neutrinos DE (Mass-Varying Neutrinos, Growing !)

Motivation : vicinity of DE coincidence with ! **physics** energy scale!

Dependence of ! mass upon **the** acceleron field:!

Energy density of !: & ! =m ! n ! = & ! (A(x µ ))!

Effective potential and equation of state: V eff (A)= & ! (A)+V(A)!

! Perrotta, et al., PRD 61 (2000)

! Amendola, PRD 62 (2000)

! Farrar, Peebles, ApJ 604 (2004)

! Fardon, Nelson, Weiner, JCAP0410 (2004)

! Peccei, PRD 71 (2005)

! Wetterich, Phys.Lett.B 655 (2007)

! Amendola, Baldi, Wetterich PRD78 (2008)

Dark sector: questionning **the** equivalence principles

! The EPs **for**mulate **the** universality of gravitation

# Weak Equivalence Principle (WEP) : all non-gravitational binding energies

# Strong Equivalence Principle (SEP): any type of energies (inc. grav. ones)

# SEP " WEP (**the**re**for**e No WEP " No SEP)

+!

! How can we know if DM violates **the** EPs?

" DM-induced Modified gravity effects on ordinary matter!

DM-induced violation of

WEP!

(non-universality of free-fall)!

DM-induced violation of SEP!

(varying G N )!

Ordinary !

matter!

Not so Dark !

Matter virtual !

particles!

Dark Scalar!

(fifth **for**ce)!

! Carroll, Mantry, Ramsey-Musolf, Stubbs, PRL 2009! ! Füzfa, Alimi, JCAP 2008, PRD 2007, PRL 2006!

“AWE Hypo**the**sis”!

The Abnormally Weighting Energy Hypo**the**sis

! The AWE action:

Induced SEP violation!

(varying G, modified gravity)!

WEP violation!

(mass-variation of DM)!

# Gravitation = admixture of spin-2 (g µ! ) and spin 0 (,) fields (!propagation!)"

# Local laws of **physics** **for** matter are those of special relativity (geodesic free-fall)

! Induced SEP violation:

# Modified gravity : not Friedmann-Lemaître cosmic expansion

# No need **for** negative pressures nor well-shaped potential as in DM-DE

models

# Relaxation toward **the** EP during cosmic expansion

! Let’s apply this mechanism to a (mass-varying) DM candidate

! Damour, et al. PRL 64, 123 (1990)!

! Alimi, Füzfa, JCAP 0809 (2008); PRD 75

123007 (2007); PRL 97, 061301 (2006)!

A famous example of mass-varying DM : **the** axion

! Global U(1) symmetry (eg.: Peccei-Quinn, B-L, etc.) and new complex scalar"

% &"' (

! Spontaneous and explicit symmetry breaking :

# - acquires a vev . s

# / acquires a mass and becomes **the** axion

# Effective mass term **for** / of perturbative nature

# Residual discrete symmetry

! Cosmological implications

# Axion-like dark matter and joint DM (/)/DE (0) models

# pNGB quintessence model :

• . s ~ m Pl ; . e ~ m !

! Axion-like DM has a varying mass

# violation of **the** equivalence principle during phase transition

# Why not a gravitational mechanism **for** vev stabilisation?

! Peccei, Quinn PRL (1977), Weinberg PRL (1978),

Wilczek PRL (1978), Chikasige et al. PLB (1981)!

! J. Frieman et al., PRL 75 (1995)!

! R. Mainini, S. Bonometto, PRL 93 (2004)!

Spontaneous!

V(/)!

Spontaneous + explicit!

« DE »!

« DM »!

! A. Arbey, PRD 74 (2006)!

! S. Das, N. Weiner, astro-ph/0611353!

! Kolb, Turner, 1992!

! Copeland, Sami, Tsujikawa, IJMP D (2006)!

/"

An effective action **for**

Gravitational Symmetry Breaking (GSB)

! Effective potential **for** **the** complex scalar:"

! " #$ % &"' (

! " #$%

Violation of WEP !

! Non-minimal gravitational coupling **for** 0"

! "#$% & ' ()*+ , - ()*. / ). / )

Violation of SEP!

! Ordinary matter not charged under U(1)

# no (or weak) explicit couplings between matter and -

! Total action: AWE Hypo**the**sis

Ordinary matter follow !

geodesics of metric !

that does not propagate!

like in general relativity!

SEP violation!

(varying G)!

WEP violation!

(mass-variation of DM)!

The cosmological mechanism of GSB

! New **physics** of dark sector:

# Dark Matter : **the** axion (pNGB) /"

# Dark Energy : cosmic acceleration through non FLRW expansion (0 dynamics)

! Gravitational stabilisation of 0:"

# Tensor-scalar gravitation have convergence mechanism toward general relativity"

# 0 has non canonical propagators (« gravitational scalar »)

# Dynamics of 0 more intuitive in Einstein frame (*=0 « disentangled » from g µ! )

Effective potential!

Attractors: EPs ok (GR-like)!

High & DM /& m!

Low & DM /& m!

*"

Matter-dominated era:!

m DM decreases such that !

& DM & baryons when a$!

!

(GR-like)!

Cosmological evolution:!

A quest **for** **the** EP!!

Radiation-dominated era:!

* attracted toward GR!

! Radiative era : 0 frozen close to GR value, / slowly rolls **the**n becomes DM

! Matter era: 0 is driven toward attractor, DM mass decreases to balance baryons

! Transient phases of cosmic acceleration during 0 stabilisation

! Coincidences:

Cosmic history of GSB

# & b ~ & DM : fixed by energy scales (. e , . g )

# & DM ~ & DE : naturally explained by characteristic evolution time of 0

Today!

Why cosmic expansion accelerates?

Standard FLRW

expansion:

AWE DM-driven cosmic expansion:

Effective G eff awe

% awe!

Predictions on cosmological parameters

HST Gold !

Sample!

SNLS!

Combined HST & SNLS data sets!

! R i =0.13 +0.23 -0.08 !

! % m =0.05 +0.06 -0.03!

! % awe =0.24 +0.03 -0.04!

! % * =0.71 +0.04 -0.06!

! t 0 =13.85Gyr +0.19 -0.38 !

!(**for** h=0.7) !

!

!1 2 /dof(AWE)=1.12, 1 2 /dof('CDM)=1.11!

!

Matter "baryons!

AWE " CDM!

* dynamics " DE!

!

% m!

! Measurement of baryons and DM distribution

from SNe Ia alone!

! Consistent with CMB & BBN constraints (though

obtained in **the** 'CDM framework)

! Non-minimal dynamics can be translated in terms

of exotic fluid p=w& with w

Predictions on energy scales

m / ~10 -15 GeV !

UNION data set!

U B-L (1)!

m(! L )

Application to neutrino mass generation

! ! oscillations: ! mass eigenstates ! ! flavour eigenstates (interactions)

" Lepton number is a global broken symmetry

" Physical ingredients:

! A new scalar particle 2 charged under U B-L (1) couples to right neutrinos ! R

! " # $ % &" # ' " #

! " !

# $ % &" ' " !

Yukawa coupling "Majorana mass term!

! No direct couplings of 2 to Standard Model particles (L - =-2)

!! R couples directly to ! L (Dirac mass) ! " !

# $ % &" ' " !

!! mixing : Seesaw mechanism

! " #

$ ! % & '! " ( ! " # $ % & '

! Lightness of ! L requires a huge vacuum expectation value **for** - (large m !R )

# Usually : spontaneous symmetry breaking of U B-L (1) (at Planck scale)

# Here: gravitational symmetry breaking (stabilisation with non-minimal couplings)

! " #$ " % & ' ( ) * ! + #+% " + ,-. -/& ' ( ) *

0

" ( 1 ,-. -/ 23 *

0

" ( 4 ,-. -/ 23

SM **physics** is B-L

invariant: !

No dependence on 2!

! " # $% $ ! " # $ %& %

Majoron!

! " # $

%

&' &

! Chikashige, Mohapatra, Peccei, Phys.Lett. B98, 265 (1981).!

Variation of neutrino masses

! L!

Majoron /"

! R!

Example:!

"

. e ~10 -5 GeV"

. g ~10 15 GeV!

!

!

« Bare » masses:!

m / =. 2 e /. g ~10-25 GeV!

!

m R ~. g ~10 15 GeV !

!

m L =(v EW )²/m R ~0.01 eV!

! A mass scaling of ~30% of Majoron DM accounts **for** cosmic acceleration

! Numerous impacts on large-scale structure **for**mation! (CDM&WDM)

! The mass scaling is density-dependent => DM-induced modified gravity

! SM couplings induces violation of WEP in **the** ordinary matter sector

(cf. Carroll, Mantry, Ramsey-Musolf, Stubbs)

**Which** Physics **for** **the** **Invisible** **Universe**?

! Observational evidence

« missing matter » or « stronger gravity »!

« missing energy » or « antigravity »!

! Options:

Observational problems?`!

Cosmological problems?!

New **physics**? (new gravitational laws, exotic matter-energy components)!

! Theoretical interpretations:

Cosmological constant leads to intricate problems!

Investigating a cosmological mechanism **for** DE naturally leads to

sophisticated **physics**!

! Toward unified **physics** **for** **the** dark sector…

DM-induced modification of gravity due to new interaction in **the** dark

sector

Observational features: cosmic acceleration, rotation curves, solar

system => NEED FOR COMBINED CONSTRAINTS ON GR!

New tests of **the** nature of DM and gravity!