Dark Matter and Dark Energy from the solution of the strong

CP problem

Roberto Mainini, L. Colombo & S.A. BonomettoUniversita’ di Milano Bicocca

Mainini & Bonometto Phys.Rev.Lett. 93 (2004) 121301Mainini, Colombo & Bonometto (2004) Apj submitted

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)

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)

ie2

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

GGs ~

2

L

1010

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 FPQ

- -parameter is now the NG boson due to sym.br. : the axion Weinberg 1978; Wilczek 1978

with NG potential ie

2 222 )|(||)(| PQFV

PQF

- 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:

22222

2

1)cos1()( PQPQ FmFmV

)

0)1

PQQCD

QCD

FΛm(T

Λm(T

GeVFGeV PQ1210 1010 eVTmeV 36 102.6)0(102.6

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>

HTm 2)(

0)(2 22 Tmaa

a

0 potkin EEp )(3 3 Tmaa

a

m

m

30 amT QCD 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

|)(|V

||

PQ model Dual-Axion Model

1)( QCDΛTm

cost

Angular oscillations are still axions while radial motion yields DE

PQF1)( PQQCD FTm

Φ variation cause a dependence of the axion mass on scale factor a

LAGRANGIAN THEORY

AXION DARK ENERGY

)cos1(),()(

2

1 222

TmVgL

0sin)(2 22

Tma

a

a 22 )(2 Va

a

a

)()(3 Cpa

a

022 ma 2)( aC

13 a

)( 3 Ca

a

Friction term modified: moredamping 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 ΩDM is assigned can be arbitrarily fixed.

Here is univocally determined

244

)(

GeV

GeVDM10103.0

Background evolution

coupling term settles on different tracker solution

Va 22

22 )(2 Vaa

a

Background evolution

After equivalence the kinetic energy of DE

is non-negligible during matter era

*4

4

DM DM DM DM b b

b b DM DM b b

aC G G

a

aG

a

* 241

3G G

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=<C()>Black: CDM

Differences from CDM:- objects should form earlier - baryons fluct. keep below DM fluct. until very recently

Uncoupled SUGRASUGRA with C = costSUGRA 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=0.930.05

Uncoupled SUGRA

x <x> x

Ωbh2 0.025 0.001

Ωdmh2 0.12 0.02

h 0.63 0.06

0.21 0.07

ns 1.04 0.04

A 0.97 0.13

Log 3.0 7.7

SUGRA with C=cost

x <x> x

Ωbh2 0.024 0.001

Ωdmh2 0.11 0.02

h 0.74 0.11

0.18 0.07

ns 1.03 0.04

A 0.92 0.14

Log -0.5 7.6

0.10 0.07

SUGRA with C= 1/

x <x> x

Ωbh2 0.025 0.001

Ωdmh2 0.11 0.02

h 0.93 0.05

0.26 0.04

ns 1.23 0.04

A 1.17 0.10

Log 4.8 2.4

Best fit parameters:

- 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

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

4

V 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

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)

Axion mass

Φ variation cause a dependence of the axion mass on scale factor aRebounce at z=10 could be critical for structure formation

Maccio’ et al 2004, Phys. Rev. D69, 123516

Some features of coupled quintessence model

• DM particles don’t follow geodesics:

00 xm

mxp

violation of equivalence principle

• Newtonian interactions:

- DM-DM particles - DM- baryons or baryons-barions

2*

3

41GG = effective gravitational constant

ordinary gravitational constant

Modified DM dynamics could be critical for structure formation