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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 accepted PART 1 Dark Matter-Baryon segregation in the non-linear evolution of coupled Dark Energy models Roberto Mainini Universita’ di Milano Bicocca PART 2 Mainini (2005) Phys.Rev.D submitted
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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)
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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?
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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 F PQ - -parameter is now the NG boson due to sym.br. : the axion W einberg 1978; Wilczek 1978 with NG potential
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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: -F PQ is a free parameter -Cosmological and astrophysical constraints require:
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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 = 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 PQ modelDual-Axion Model Angular oscillations are still axions while radial motion yields DE
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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
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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
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Background evolution coupling term settles on different tracker solution
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Background evolution After equivalence the kinetic energy of DE is non-negligible during matter era
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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
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-One complex scalar field yields both DM & DE -Fair DM-DE proportions from one parameter : /GeV~10 10 -Strong CP problem solved -DM-DE coupling fixed (C=1/ ) Conclusions
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Dark Matter-Baryon segregation in the non-linear evolution of coupled Dark Energy models Roberto Mainini Università di Milano Bicocca
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Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Perturbation evolution: But…..for present structure >> 1 linear theory until << 1 Gravitational instability: present struture (galaxy, group, cluster) originated by small density perturbation Simplest approach to non-linearity is to follow an inhomogeneity with particularly simple form
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Post–linear evolution of density fluctuation: The spherical “top-hat” collapse Top-hat overdensity in SCDM: Assuming mass conservation …. Initial expansion with Hubble flow, then separation from background universe and collapse …as a closed FRW universe Virial radius + Virial theorem Energy conservation between turn-around and virialization Density contrast
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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
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Coupled Dark Energy (cDE) Basic equations Spatially flat FRW universe with: baryons, radiation, cold DM and DE (scalar field with potential V( )) Continuty equations: Friedmann eq. Interaction DM-DE parametrized by Usual eqs. for baryons and radiation
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Coupling effects: modified DM dynamics Coupled Dark Energy -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
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Coupled Dark Energy (cDE) Coupling effects: DM-baryons bias From linear theory: DM and baryons density fluctuations described by 2 coupled Jeans’ equations: 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 Linear bias
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Spherical collapse in cDE models -DM and baryons top-hat fluctuations of identical radius R TH,i expanding with Hubble flow -Fluctuation amplitudes in DM and baryons set by linear theory: a set of n concentric shells with radii R n c (DM) R n b (baryons) such that Start with: then, consider and initial conditions:
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Spherical collapse in cDE models: Time evolution of concentric shells From T ; = 0,using comoving radiiand modified friction term modified source term stronger gravitational push for DM layers, also strengthened by modified friction term Eqs. in physical coordinates Usual Friedmann-like equation for baryon shells Modified equation for DM shells
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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
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Spherical collapse in cDE models Density profiles - Top-hat geometry kept for DM - Deviation from a top-hat geometry for baryons outside R TH - Perturbation also in material outside the boundary of fluctuation: outside R TH baryon recollapse fastened by increased density of DM
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Spherical collapse in cDE models: Escaped baryon fraction - Barion fraction f b outside R TH at virialization: - Mildly dependence on the scale
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Virialization in cDE models 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 - 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 but……..any intermediate choice also alloweded No virialization with all the materials of original fluctuation – and only them
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Virialization in cDE models Our choice:1 - Only materials within top-hat considered: escaped baryon fraction neglected Potential energy made of three terms: self-interaction, mutual interaction, interaction with DE DM-DE energy exchange for fluctuation described by G*= G Virialization condition: Kinetic and potential energies:
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Virialization in cDE models Performing integrals… …but different baryons layers have different growth ratesnot valid for T b (R TH ) Density contrast
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Conclusions 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 Spherical top-hat collapse model in cDE theories:
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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 Conclusions
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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 1.064 (uncoupled SUGRA) to 1.071 (C=1/ ) - SUGRA with C=1/ h=0.93 0.05 Uncoupled SUGRA x xx Ωbh2Ωbh2 0.0250.001 Ω dm h 2 0.120.02 h0.630.06 0.210.07 nsns 1.040.04 A0.970.13 Log 3.07.7 SUGRA with C=cost x xx Ωbh2Ωbh2 0.0240.001 Ω dm h 2 0.110.02 h0.740.11 0.180.07 nsns 1.030.04 A0.920.14 Log -0.57.6 0.100.07 SUGRA with C= 1/ x xx Ωbh2Ωbh2 0.0250.001 Ω dm h 2 0.110.02 h0.930.05 0.260.04 nsns 1.230.04 A1.170.10 Log 4.82.4 Best fit parameters:
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