Dark Matter and Dark Energy from the solution of the strong CP problem

1. 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) 121301 Mainini, Colombo & Bonometto (2004) Apj submitted

2. 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)

3. Dynamical DE models to ease CDM problems Tracking quintessence DE from a scalar field  self-interacting through an effective potential V() but…. …. at least1 more parameter required more complex models to try to unify DM and DE…. coupling parameter also required InteractingDM-DE models

4. 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 parameteras 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)

5. 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 θ is so small?

6. Peccei-Quinn solution and the axionPeccei & 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

7. - CP-violating terms generate a potential for the axion which acquires a mass m(T) (chiral symmetry break).From instantonic calculus: • FPQis a free parameter • Cosmological and astrophysical constraints require:

8. 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> Kolb & Turner 1990

9. 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 Φ variation cause a dependence of the axion mass on scale factor a Angular oscillations are still axions whileradial motion yields DE

10. AXION DARK ENERGY LAGRANGIAN THEORY Friction term modified: more damping than PQ case COUPLED QUINTESSENCE MODEL with a time dependent coupling C()=1/ Amendola 2000, 2003

11. 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 Background evolution

12. Background evolution coupling term settles on different tracker solution

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

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

15. 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

16. Fit to WMAP data Best fit parameters: -Main differences at low l - 2eff from 1.064 (uncoupled SUGRA) to 1.071 (C=1/) - SUGRA with C=1/ h=0.930.05 Uncoupled SUGRA SUGRA with C = cost SUGRA with C= 1/ SUGRA Dual-Axion

17. Conclusions - 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

18. 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

19. Two dark components required: • Dark Matter (DM): non-baryonic component to account for • dynamics in galaxies and galaxy clusters • Dark Energy (DE): smooth component with p<0 to account for cosmic acceleration 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)

20. 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, 123516

21. 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