Dark Matter and Dark Energy from the solution of the strong CP problem
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Dark Matter and Dark Energy from the solution of the strong
CP problem
Roberto Mainini, L. Colombo & S.A. BonomettoUniversita’ di Milano Bicocca
Mainini & Bonometto Phys.Rev.Lett. 93 (2004) 121301Mainini, Colombo & Bonometto (2004) Apj submitted
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Most cosmological data (CMB, SNIa, LSS) fitted by‘concordance model’ (CDM)
H 70 km/s/Mpc , n 1
ΩDM 0.3 , ΩDE 0.7 , Ωbar 0.04
DE from cosmological constant but….
…. || < 10 -56 cm -2 why so small? (fine-tuning problem)
…. why ΩDM ΩDE ? (coincidence problem)
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Dynamical DE models to ease CDM problems
Tracking quintessence
DE from a scalar field self-interacting through an effective potential V() but…. …. at least 1 more parameter required
more complex models to try to unify DM and DE….
Interacting DM-DE models coupling parameter also required
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Dual-Axion Model
Axion: DM candidate from Peccei-Quinn (PQ) solution to the strong CP problem
modifying PQ model :
- strong CP problem solved (even better so…)
- DM and DE from single complex scalar field (exploit better the same fields as in PQ approach)
- no fine-tuning
- number of parameter as SCDM (even 1 less than LCDM…) DM an DE in fair proportion from one parameter
- DM and DE coupled (this can be tested) but ….. …..no extra parameter (coupling strength set by theory)
ie2
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Strong CP problem
Non-perturbative effects related to the vacuum structure of QCD leads a CP-violating term in LQCD :
Neutron electric dipole moment
Experimental limits on electric dipole moment
GGs ~
2
L
1010
Why θ is so small?
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Peccei-Quinn solution and the axion Peccei & Quinn 1977
PQ idea: CP-violating term is suppressed making a dynamical variable driven to zero by the action of its potential
- Additional global U(1)PQ symmetry in SM
- U(1)PQ is spontaneously broken at the scale FPQ
- -parameter is now the NG boson due to sym.br. : the axion Weinberg 1978; Wilczek 1978
with NG potential ie
2 222 )|(||)(| PQFV
PQF
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- CP-violating terms generate a potential for the axion which acquires a mass m(T) (chiral symmetry break). From instantonic calculus:
- FPQ is a free parameter
- Cosmological and astrophysical constraints require:
22222
2
1)cos1()( PQPQ FmFmV
)
0)1
PQQCD
QCD
FΛm(T
Λm(T
GeVFGeV PQ1210 1010 eVTmeV 36 102.6)0(102.6
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Axion cosmology
- Equation of motion (θ <<1):
- Coherent oscillations for
- Oscillations are damped by the expansion of the universe
- Axions as Dark Matter candidate
Averaging over cosmological time <Ekin> = <Epot>
HTm 2)(
0)(2 22 Tmaa
a
0 potkin EEp )(3 3 Tmaa
a
m
m
30 amT QCD Kolb & Turner 1990
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Can a single scalar field account for both DM and DE?
NG potential Tracker quintessence potential with a complex scalar field
no longer constant but evolves over cosmological times
|)(|V
||
PQ model Dual-Axion Model
1)( QCDΛTm
cost
Angular oscillations are still axions while radial motion yields DE
PQF1)( PQQCD FTm
Φ variation cause a dependence of the axion mass on scale factor a
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LAGRANGIAN THEORY
AXION DARK ENERGY
)cos1(),()(
2
1 222
TmVgL
0sin)(2 22
Tma
a
a 22 )(2 Va
a
a
)()(3 Cpa
a
022 ma 2)( aC
13 a
)( 3 Ca
a
Friction term modified: moredamping than PQ case
COUPLED QUINTESSENCE MODEL with a time dependent coupling C()=1/
Amendola 2000, 2003
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Background evolution
We use SUGRA potential
Note: in a model with dynamical DE (coupled or uncoupled) once ΩDM is assigned can be arbitrarily fixed.
Here is univocally determined
244
)(
GeV
GeVDM10103.0
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Background evolution
coupling term settles on different tracker solution
Va 22
22 )(2 Vaa
a
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Background evolution
After equivalence the kinetic energy of DE
is non-negligible during matter era
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*4
4
DM DM DM DM b b
b b DM DM b b
aC G G
a
aG
a
* 241
3G G
Density fluctuations: linear evolution
modified friction term
DM and baryons fluctuations described by 2 coupled Jeans’ equations:
modified dynamical term
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Density fluctuations: linear evolution
Red: dual axion C()=1/Blue: Coupled DE C=cost=<C()>Black: CDM
Differences from CDM:- objects should form earlier - baryons fluct. keep below DM fluct. until very recently
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Uncoupled SUGRASUGRA with C = costSUGRA with C= 1/SUGRA Dual-Axion
Fit to WMAP data
- Main differences at low l- 2
eff from 1.064 (uncoupled SUGRA) to 1.071 (C=1/)- SUGRA with C=1/ h=0.930.05
Uncoupled SUGRA
x <x> x
Ωbh2 0.025 0.001
Ωdmh2 0.12 0.02
h 0.63 0.06
0.21 0.07
ns 1.04 0.04
A 0.97 0.13
Log 3.0 7.7
SUGRA with C=cost
x <x> x
Ωbh2 0.024 0.001
Ωdmh2 0.11 0.02
h 0.74 0.11
0.18 0.07
ns 1.03 0.04
A 0.92 0.14
Log -0.5 7.6
0.10 0.07
SUGRA with C= 1/
x <x> x
Ωbh2 0.025 0.001
Ωdmh2 0.11 0.02
h 0.93 0.05
0.26 0.04
ns 1.23 0.04
A 1.17 0.10
Log 4.8 2.4
Best fit parameters:
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- One complex scalar field yields both DM & DE
- Fair DM-DE proportions from one parameter : /GeV~1010
- Strong CP problem solved
- DM-DE coupling fixed (C=1/)
- Fluctuation growth is fair
- Structure formation earlier than in CDM
- Fair fit to WMAP data, constraining in the expected range
- SUGRA potential large H0 (~90 10 km/s/Mpc)
- Halo concentration and distribution to be tested, smaller concentrations expected
Conclusions
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Dynamical DE models to ease CDM problems
Tracking quintessence
DE from a scalar field self-interacting through an effective potential V() but…. …. at least 1 more parameter required
Ex. : RP model
4
V we have to set the energetic scale
more complex models to try to unify DM and DE….
Interacting DM-DE models
coupling parameter also required
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1. Dark Matter (DM): non-baryonic component to account for
dynamics in galaxies and galaxy clusters
1. Dark Energy (DE): smooth component with p<0 to account for cosmic acceleration
Most cosmological data (CMB, SNIa, LSS) fitted by‘concordance model’ (CDM)
Two dark components required:
H 70 km/s/Mpc , n 1
ΩDM 0.3 , ΩDE 0.7 , Ωbar 0.04
DE from cosmological constant but….
…. || < 10 -56 cm -2 why so small? (fine-tuning problem)…. why ΩDM ΩDE ? (coincidence problem)
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Axion mass
Φ variation cause a dependence of the axion mass on scale factor aRebounce at z=10 could be critical for structure formation
Maccio’ et al 2004, Phys. Rev. D69, 123516
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Some features of coupled quintessence model
• DM particles don’t follow geodesics:
00 xm
mxp
violation of equivalence principle
• Newtonian interactions:
- DM-DM particles - DM- baryons or baryons-barions
2*
3
41GG = effective gravitational constant
ordinary gravitational constant
Modified DM dynamics could be critical for structure formation