Dark Matter and Dark Energy from the solution of the strong CP problem Roberto Mainini, L. Colombo & S.A. Bonometto Universita’ di Milano Bicocca Mainini & Bonometto Phys.Rev.Lett. 93 (2004) Mainini, Colombo & Bonometto (2004) Apj submitted

Most cosmological data (CMB, SNIa, LSS) fitted by ‘concordance model’ (  CDM) H  70 km/s/Mpc, n  1 Ω DM  0.3, Ω DE  0.7, Ω bar  0.04 DE from cosmological constant  but…. …. |  | < cm -2 why  so small? (fine-tuning problem) …. why Ω DM  Ω 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 L QCD : Neutron electric dipole moment Experimental limits on electric dipole moment Why θ is so small?

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 F PQ -  -parameter is now the NG boson due to sym.br. : the axion W einberg 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: -F PQ is a free parameter -Cosmological and astrophysical constraints require:

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 = Kolb & Turner 1990

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

LAGRANGIAN THEORY AXIONDARK ENERGY Friction term modified: more damping than PQ case COUPLED 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 Ω DM is assigned  can be arbitrarily fixed. Here  is univocally determined

Background evolution coupling term settles on different tracker solution

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

Density fluctuations: linear evolution modified friction term DM and baryons fluctuations described by 2 coupled Jeans’ equations: modified dynamical term

Density fluctuations: linear evolution Red: 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 SUGRA SUGRA with C = cost SUGRA with C= 1/  SUGRA Dual-Axion Fit to WMAP data - Main differences at low l -  2 eff from (uncoupled SUGRA) to (C=1/  ) - SUGRA with C=1/  h=0.93  0.05 Uncoupled SUGRA x xx Ωbh2Ωbh Ω dm h h  nsns A Log  SUGRA with C=cost x xx Ωbh2Ωbh Ω dm h h  nsns A Log   SUGRA with C= 1/  x xx Ωbh2Ωbh Ω dm h h  nsns A Log  Best fit parameters:

- One complex scalar field yields both DM & DE - Fair DM-DE proportions from one parameter :  /GeV~ 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 H 0 (~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

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 Ω DM  0.3, Ω DE  0.7, Ω bar  0.04 DE from cosmological constant  but…. …. |  | < cm -2 why  so small? (fine-tuning problem) …. why Ω DM  Ω DE ? (coincidence problem)

Axion mass Φ variation cause a dependence of the axion mass on scale factor a Rebounce at z=10 could be critical for structure formation Maccio’ et al 2004, Phys. Rev. D69,

Some features of coupled quintessence model DM particles don’t follow geodesics: violation of equivalence principle Newtonian interactions: - DM-DM particles - DM- baryons or baryons-barions = effective gravitational constant ordinary gravitational constant Modified DM dynamics could be critical for structure formation