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

1. PART 2 Dark Matter-Baryon segregation in the non-linear evolution of coupled Dark Energy models Roberto Mainini Universita’ di Milano Bicocca Mainini (2005) Phys.Rev.D submitted PART 1 Dark Matter and Dark Energy from the solution of the strong CP problem Mainini & Bonometto Phys.Rev.Lett. 93 (2004) 121301 Mainini, Colombo & Bonometto (2004) Apj accepted Roberto Mainini, L. Colombo & S.A. Bonometto Universita’ di Milano Bicocca

2. 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)

3. 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?

4. 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

5. - 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:

6. 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

7. 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 whileradial motion yields DE

8. 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

9. 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

10. Background evolution coupling term settles on different tracker solution

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

12. 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

13. 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/)

14. Dark Matter-Baryon segregation in the non-linear evolution of coupled Dark Energy models Roberto Mainini Università di Milano Bicocca

15. Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Gravitational instability: present struture (galaxy, group, cluster) originated by small density perturbation Perturbation evolution: linear theory until  << 1 But…..for present structure  >> 1 Simplest approach to non-linearity is to follow an inhomogeneity with particularly simple form

16. Energy conservation between turn-around and virialization Virial theorem + Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Top-hat overdensity in SCDM: Initial expansion with Hubble flow, then separation from background universe and collapse …as a closed FRW universe Virial radius Assuming mass conservation …. Density contrast

17. Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Top-hat overdensity in CDM and uncoupled DE models: Assuming an homogeneous DE field….. Virial radius …again from virial theorem and energy conservation but…. Density contrast no longer constant Mainini, Macciò & Bonometto 2003, New Astron., 8, 173

18. Coupled Dark Energy (cDE) Basic equations Spatially flat FRW universe with: baryons, radiation, cold DM and DE (scalar field  with potential V()) Friedmann eq. Continuty equations: Interaction DM-DE parametrized by Usual eqs. for baryons andradiation

19. Coupled Dark Energy Coupling effects: modified DM dynamics -Variable mass for DM particles -Violation of equivalence principle -Newtonian interactions: DM-DM particles: effective gravitational constant DM-baryons or baryons-baryons: ordinary gravitational constant

20. Linear bias modified friction term modified source term N-body simulations indicate that the bias persists also at non-linear level Macciò, Quercellini, Mainini, Amendola & Bonometto 2004, Phys.Rev.D 69, 123516 Coupled Dark Energy (cDE) Coupling effects: DM-baryons bias From linear theory: DM and baryons density fluctuations described by 2 coupled Jeans’ equations:

21. Spherical collapse in cDE models Start with: -DM and baryons top-hat fluctuations of identical radius RTH,i expanding with Hubble flow -Fluctuation amplitudes in DM and baryons set by linear theory: then, consider a set of n concentric shells with radii Rnc (DM) Rnb (baryons) such that and initial conditions:

22. From T;= 0, using comoving radii and Eqs. in physical coordinates Usual Friedmann-like equation for baryon shells modified friction term modified source term Modified equation for DM shells Spherical collapse in cDE models: Time evolution of concentric shells stronger gravitational push for DM layers, also strengthened by modified friction term

23. Spherical collapse in cDE models: Time evolution of concentric shells -DM fluctuation expands more slowly and reach turn-around earlier -Baryons contraction at different times for different layers -Baryons gradually leak out from the fluctuation bulk As a consequence….. baryon component deviates from a top-hat geometry

24. Spherical collapse in cDE models Density profiles • - Top-hat geometry kept for DM • - Deviation from a top-hat geometry for baryons outside RTH • Perturbation also in material outside the boundary of fluctuation: • outside RTHbaryon recollapse fastened by increased density of DM

25. Spherical collapse in cDE models: Escaped baryon fraction - Barion fraction fb outside RTH at virialization: - Mildly dependence on the scale 

26. No virialization with all the materials of original fluctuation – and only them Virialization in cDE models - Slower gravitational infall for baryons: outer layers of halo rich of baryons - Gradually recollapse of external baryons onto the DM-richer core: DM materials outside the original fluctuation carried with them - Original DM / baryons ratio increased How to define virialization in cDE models? 1 - Only materials within top-hat considered: escaped baryon fraction neglected 2 - All materials inside original fluctuation plus intruder DM considered but……..any intermediate choice also alloweded

27. Virialization in cDE models Our choice: 1 - Only materials within top-hat considered: escaped baryon fraction neglected Virialization condition: Kinetic and potential energies: Potential energy made of three terms: self-interaction, mutual interaction, interaction with DE DM-DE energy exchange for fluctuation described by G*=G

28. …but different baryons layers have different growth rates not valid for Tb(RTH) Virialization in cDE models Performing integrals… Density contrast

29. Conclusions Spherical top-hat collapse model in cDE theories: Ambiguity of definition of halo virialization: difficulty in comparing simulations outputs or data with PS or similar prediction But…indipendently of the way how virialization is defined: 1 - Only materials within top-hat considered: escaped baryon fraction neglected 2 - All the materials inside the original fluctuation plus intruder DM considered (or any intermediate choice) Final virialized system is richer of DM

30. Conclusions DM-baryons segregation during spherical growth: a fresh approach in the treatment of a number of cosmological problems large scale: baryon enrichment of large clusters? intermediate scale: lost baryonic materials as intra-cluster light? (X-ray, EUV excess emission problem) small scale: systems likely to loose their outer layers because of close encounters with heavier objects (missing satellite problem solved?) -Simulations of DM-DE coupled cosmologies urgently required -Replacing constant coupling with 1/ coupling

31. 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