The dark universe
P. Binétruy
AstroParticule et Cosmologie, Paris
Second Sino-French Workshop, Beijing, 28 August 2006
The twentieth century legacy
Two very successful theories :
• General relativity
A single equation, Einstein’s equation, successfully predicts tiny deviations from classical physics and describes the universe at large as well as its evolution.
R - (R/2) g = 8GN T
geometry matterQuickTime™ et un
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Describes nature at the level of the molecule, the atom, the nucleus,the nucleons, the quarks and the electrons .
• Quantum theory
Difficult to reconcile general relativity with the quantum theory: bestillustration is the vacuum problem ( cosmological constant pb)
Classically, the energy of the fundamental state (vacuum) is not measurable. Only differences of energy are (e.g. Casimir effect).
Einstein equations: R - R g/2 = 8G T
geometry energy
Hence geometry may provide a way to measure absolute energies i.e. vacuum energy:
R - R g/2 = 8G T + 8G < T >
vacuum energy
similar to the cosmological term introduced by Einstein :
R - R g/2 = 8G T + g
Such a term tends to accelerate the expansion of the universe :
H2 = 8 G ( + ) /3 - k/a2 / (8 G )
curvature term
Present observations (k=0, < ) yield ~ H02 / 8 G
~ (10-3 eV)4
Computing the vacuum energy associated with the SM
vac ~ MW4 ~ (1011 eV)4 to be compared with ~ (10-3 eV)4
The electroweak scale MW ( lW = 10-18 m)
or the Planck scale mP = √ hc/8GN = 2.4 1018 GeV ( lP = 10-34 m)
obviously do not provide the size of the Universe.
Horizon scale : H0 -1 =1026 m
Critical energy density c = 3H02 /8 GN c
4
c = 10-3 eV
From the experimental and observational point of view,
• exploration of the infinitely small
electron, neutrino; up and downquarks make the proton/neutron
Why do we need a muon?
• exploration of the infinitely large
First only detecting visible light, then all electromagnetic spectrum
But also particles…
Cosmic rays
Neutrinos
And other types of waves … gravitational waves
Also indirect ways allow to identify new components of the Universe
First example: rotation curves of galaxies dark matter
e.g. spiral galaxies
astro-ph/9506004
Also indirect ways allow to detect new components of the Universe
First example: rotation curves of galaxies dark matter
luminous matter
e.g. spiral galaxies
astro-ph/9506004
Also indirect ways allow to detect new components of the Universe
First example: rotation curves of galaxies dark matter
luminous matter
exponential halo
e.g. spiral galaxies
astro-ph/9506004
Also indirect ways allow to detect new components of the Universe
First example: rotation curves of galaxies dark matter
luminous matter
exponential halo
total contribution
e.g. spiral galaxies
astro-ph/9506004
also detected through gravitational lensing
Second example: measuring cosmic distances with supernovae explosions dark energy
• Supernovae of type Ia
magnitude versus redshift
mB = 5 log(H0dL) + M - 5 log H0 + 25
luminosity distance dL = lH0 z ( 1 + ------- z + …)1-q0
2
q0 deceleration parameter q0 = M /2 - for a -CDM model
M M / c / c
Unknown component of equation of state p = w , w < 0
(cosmological constant w= -1)
Need for dark matter from the study of the universe at cosmological distance scales
Why are we so excited about this field?
Theoretical ideas
Experiments and observations
Theoretical ideas
Theories beyond the Standard Model provide many new fields :
Dark matter New fermions or vector fields
Dark energy New scalar fields
We have a good candidate for the unification of gravity with quantum theory : string theory.
Modifies drastically our view of spacetime : hopes to solvethe vacuum energy problem . But no clear solution in view!
Models for dark matter
Dark matter Modification of gravity
MOND TeVeSbaryonic non-baryonic
Clumped Hydrogen
dustMACHO
Primordial Black holes
Exotic particles
Extradimensions
thermal nonthermal
Light WIMPS SuperWIMPS axion Wimpzillas
Experiments and observations
• present
Acoustic series in P(k) becomes a single peak in (r)
Pure CDM model has no peak.
mh2 = 0.12
mh2 = 0.13
mh2 = 0.14
CDM with baryons is a good fit: 2 = 16.1 with 17 dof.Pure CDM rejected at 2 = 11.7
Baryon Acoustic OscillationsAcoustic oscillations are seen in the CMB . Look for the the same waves in the galaxy correlations.
M
= 0.88, v=0.12, H
0 = 46
SNe ignored.cannot accommodate with baryon acoustic peak.
CDM
Baryon oscillations are really discriminating for dark energy
Blanchard, Douspis, Rowan-Robinson, Sarkar 2005
Blanchard et al 2003
w=-1
Tot=1
BAO: Baryon Acoustic Oscillations(Eisenstein et al 2005, SDSS)
68.3, 95.5 et 99.7% CL
Confidence Contours
See R. Pain’s talk
DE
(z)
• future
Dark matter
See G. Gerbier’s talk
Indirect detection
Through annihilation of wimps accumulated in the center of massive objects : Earth, Sun, galactic center.
HESS, GLAST, AMS, ANTARES/AMANDA/KM3NET, ….
Energy (keV)500 505 515510 520 525
Inte
nsity
(10
-4 p
hoto
n cm
-2 s
-1 s
r-1)
0,0
0.5
2.5
1.5
3.0
-0.5
1.0
2.0
3.5
Position:FWHM:
511.06 ± 0.18 keV2.95 ± 0.5 keV
Are we heading for surprises?G
alac
tic la
titud
e (d
egre
es)
20
10
0
-20
-10
FWHM: 9° (-3° / +7°)
200
Difficult to understand if :
• Decay of massive particles
• Positrons injected by compact jet sources
• + decay of radioactive nuclei released by novae• + decay of 56Co released by thermonuclear (type Ia) supernovae
More adequate :• + decay of 56Co released by gravitational supernovae/hypernovae
• Annihilation of a new form of dark matter, scalar and light (Boehm, Hooper, Silk, Cassé & Paul, PRL 92, 101301)
The intensity of the 511 keV line emission (10-3 photons s-1) implies the annihilation
of ~1043 positrons per second in the Galactic bulge.
INTEGRAL/SPI spectrum of the Galactic center region
Dark energy
Future programs both in space (SNAP/JDEM/DUNE)and on the ground (SDSS, LSST, SKA/FAST,…)
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Expected Planck performance on dark energy equation of state
Huterer & Turner 2001
Seo & Eisenstein 2003w = w0 + w1 z
Other standard candles
Gamma ray bursts
coalescence of supermassive black holes
Determine the luminosity through a relation between the collimation corrected energy E and the peak energy
cf. SVOM/ECLAIRs
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Inspiral phase
Key parameter : chirp mass M = (m1 m2)3/5
(m1 + m2)1/5(z) (1+z)
Inspiral phase
Key parameter : chirp mass M = (m1 m2)3/5
(m1 + m2)1/5
Amplitude of the gravitational wave:
h(t) = F (angles) cos (t) M(z)5/3 f(t)2/3
dL
Luminosity distance
frequency f(t) = d/2dt
(z) (1+z)
Inspiral phase
Key parameter : chirp mass M = (m1 m2)3/5
(m1 + m2)1/5
Amplitude of the gravitational wave:
h(t) = F (angles) cos (t) M(z)5/3 f(t)2/3
dL
Luminosity distance poorly known in the case of LISA
~ 10 arcmin 1 HzSNR fGW
(z) (1+z)
z = 1 , m1 = 105 M, m2 = 6.105 M
(arcminutes)
dL/dL
3°
5%
Holz & Hughes
Using the electromagnetic counterpart
Allows both a measure of the direction and of the redshift
Limited by weak gravitational lensing?
Holz and HughesdL/dL
0.5%
My own theoretical prejudices :
• dark energy : back reaction models
• dark matter: WIMP connected with the electroweak symmetry breaking issue
Connecting the naturalness of the electroweak scale with the existence of WIMPs
STEP 1 : naturalness
mh2 = t
2 - g2 - h
23mt
2
22v2
6MW2 + 3MZ
2
8 2v2
3mh2
8 2v2
Naturalness condition : |mh2 | < mh
2
v = 250 GeV
Introduce new physics at t or raise mh to 400 GeV range
STEP 2 : stable particles in the MEW mass range
E
New local symmetry
New discrete symmetry
Standard Modelfermions
New fields
Lightest odd-parityparticle (LOP) is stable
Example 1: low energy SUSY
E
R symmetry
R parity
Standard Modelfermions
Supersymmetricpartners
Stable LSP
Example 2: extra compact dimension (orbifold)
E
5-dimensionalLorentz invariance
KK parity
Standard Modelfermions
KK modes
Stable lightestKK mode (B(1))
A(m) + B(n) C(p) + D(q)
m+n=p+q
(-)n
Example 3: Inert Doublet Model
E
?
H2 -H2
Standard Modelfermions
Inert scalars
Stable LightestInert Particle
Introduce a second Higgs doublet H2
which is not coupled to fermions (symmetry H2 -H2)
Barbieri, Hall, Rychkov, hep-ph/0603188
STEP 3 : compute relic density
LOP h02 ~
109 GeV-1 xf
g*1/2 MP < ann v >
25
Number of deg. of freedom at time of decoupling
LOP mass ~ MEW < ann v > ~ EW/MEW 2 LOP h02 ~ 1
to be compared with DM h02 = 0.112 0.009
mSUGRA
Co-annihilation 0
Near-resonant s-channel anni-hilation through heavy Higgs states A and H (b b, + -)
Focus point (WW,ZZ)
tan=5
tan=35
tan=50-
~
Y. Mambrini,, E. Nezri
STEP 4 : search for the LOP at LHC
As the LSP, missing energy signal
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STEP 5: search LOP through direct detection
e.g. minimal sugra model
Dark energy : back reaction models
The cosmological constant is small because the universe is old
cf. Dirac : large numbers should be considered as resultingfrom the evolution of the Universe. Applied to fundamental constants (but yields time variation difficult to reconcile with constaints)
The cosmological constant is (almost) cancelled by back-reaction effects on the expanding space.
Conclusion
A lively field where many fruitful collaborations maybe envisaged both on the theory and observational fronts
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