# 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 problemRoberto Mainini, L. Colombo & S.A. BonomettoUniversita di Milano Bicocca

Mainini & Bonometto Phys.Rev.Lett. 93 (2004) 121301Mainini, Colombo & Bonometto (2004) Apj submitted

Most cosmological data (CMB, SNIa, LSS) fitted byconcordance model (CDM)H 70 km/s/Mpc , n 1

DM 0.3 , DE 0.7 , bar 0.04

DE from cosmological constant but.. || < 10 -56 cm -2 why so small? (fine-tuning problem)

. why DM DE ? (coincidence problem)

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

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)

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

Why is so small?

Peccei-Quinn solution and the axion Peccei & Quinn 1977PQ 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

- 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:

Axion cosmology

- Equation of motion (

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

PQ model

Dual-Axion Model

Angular oscillations are still axions while radial motion yields DE variation cause a dependence of the axion mass on scale factor a

LAGRANGIAN THEORYAXION

DARK ENERGYFriction term modified: moredamping than PQ caseCOUPLED QUINTESSENCE MODEL with a time dependent coupling C()=1/

Amendola 2000, 2003

Background evolution We use SUGRA potential

Note: in a model with dynamical DE (coupled or uncoupled) once DM is assigned can be arbitrarily fixed. Here is univocally determined

Background evolution coupling term settles on different tracker solution

Background evolutionAfter equivalence the kinetic energy of DE is non-negligible during matter era

Density fluctuations: linear evolutionmodified friction termDM and baryons fluctuations described by 2 coupled Jeans equations:modified dynamical term

Density fluctuations: linear evolutionRed: dual axion C()=1/Blue: Coupled DE C=cost=Black: CDM Differences from CDM:- objects should form earlier - baryons fluct. keep below DM fluct. until very recently

Uncoupled SUGRASUGRA with C = costSUGRA with C= 1/SUGRA Dual-AxionFit to WMAP data- Main differences at low l- 2eff from 1.064 (uncoupled SUGRA) to 1.071 (C=1/)- SUGRA with C=1/ h=0.930.05Best fit parameters:

Uncoupled SUGRAxxbh20.0250.001dmh20.120.02h0.630.060.210.07ns1.040.04A0.970.13Log 3.07.7

SUGRA with C=costxxbh20.0240.001dmh20.110.02h0.740.110.180.07ns1.030.04A0.920.14Log -0.57.60.100.07

SUGRA with C= 1/xxbh20.0250.001dmh20.110.02h0.930.050.260.04ns1.230.04A1.170.10Log 4.82.4

- One complex scalar field yields both DM & DE- Fair DM-DE proportions from one parameter : /GeV~1010- Strong CP problem solvedDM-DE coupling fixed (C=1/)Fluctuation growth is fair - Structure formation earlier than in CDMFair fit to WMAP data, constraining in the expected rangeSUGRA potential large H0 (~90 10 km/s/Mpc)Halo concentration and distribution to be tested, smaller concentrations expected

Conclusions

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 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

- Dark Matter (DM): non-baryonic component to account for dynamics in galaxies and galaxy clustersDark Energy (DE): smooth component with p
Axion mass variation cause a dependence of the axion mass on scale factor aRebounce at z=10 could be critical for structure formationMaccio et al 2004, Phys. Rev. D69, 123516

Some features of coupled quintessence model DM particles dont follow geodesics:violation of equivalence principle Newtonian interactions:

- DM-DM particles - DM- baryons or baryons-barions= effective gravitational constantordinary gravitational constantModified DM dynamics could be critical for structure formation

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