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
PART 1

• 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
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 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)

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 ? is so small?
4
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 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
• FPQ is a free parameter
• Cosmological and astrophysical constraints
  require

6
Axion cosmology

• - Equation of motion (? ltlt1)
• Coherent oscillations for
  
• Oscillations are damped by the expansion of the
  universe
• Axions as Dark Matter candidate
• Averaging over cosmological time
  ltEkingt ltEpotgt

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 while
radial motion yields DE
8
LAGRANGIAN THEORY

• AXION

• DARK ENERGY

Friction term modified more damping than PQ case
COUPLED QUINTESSENCE MODEL with a time
dependent coupling C(?)1/?
Amendola 2000, 2003
9
Background evolution

• We use SUGRA potential
• Note in a model with dynamical DE (coupled
  or uncoupled) once ODM is assigned ? can be
  arbitrarily fixed.
• Here ? is univocally determined

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
F variation cause a dependence of the axion mass
on scale factor a Rebounce at z10 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
  ?/GeV1010
• Strong CP problem solved
• DM-DE coupling fixed (C1/?)

14
Dark Matter-Baryon segregation in the non-linear
evolution of coupled Dark Energy models
Roberto Mainini Università di Milano Bicocca
15
Postlinear 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 ? ltlt 1
But..for present structure ? gtgt 1
Simplest approach to non-linearity is to
follow an inhomogeneity with particularly simple
form
16
Postlinear 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
Postlinear 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 and radiation
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
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
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 RTH baryon 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
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
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 Butindipendently 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