LOC FERNANDO MOUCHEREK, PAULO PORTUGAL, (ADMIN) 29 โฆย ยท Hidden sector Visible sector Heavy...
Transcript of LOC FERNANDO MOUCHEREK, PAULO PORTUGAL, (ADMIN) 29 โฆย ยท Hidden sector Visible sector Heavy...
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016
Catarina M. CosmePhD student under the supervision of
Prof. Joรฃo Rosa and Prof. Orfeu Bertolami
30 March 2016
arXiv: 1603.06242
Scalar field dark matter and the Higgs field
What is dark matter made of?
Introducing the problem
Scalar field dark matter and the Higgs field30/03/2016 2
โข We propose: oscillating scalar field as DM candidate, coupled to the Higgs boson;
โข Previous works: โHiggs-portalโ DM models: abundance of DM is set by the decoupling and
freeze-out from thermal equilibrium ๐ ~ ๐บ๐๐ โ ๐๐๐ (Weakly Interacting Massive
Particles - WIMPs) [Silveira, Zee 1985; Bento, Bertolami, Rosenfeld 2001; Burgess, Pospelov, ter Veldhuis 2001;
Tenkanen 2015];
โข Dark matter (DM) - 26.8 % of the mass-energy content of the Universe [Planck Collaboration 2015];
30/03/2016 Scalar field dark matter and the Higgs field 3
Oscillating scalar field as dark matter candidate
Our proposal
โข Oscillating scalar field, ฯ, as DM candidate;
โข ฯ acquires mass through the Higgs mechanism;
โข ฯ starts to oscillate when๐ฯ ~ ๐ป, after the electroweak phase transition;
โข Weakly interactions with the Higgs boson ๐ฯ โช ๐๐ , extremely small self-
interactions oscillating scalar condensate that is never in thermal equilibrium.
30/03/2016 Scalar field dark matter and the Higgs field 4
Oscillating scalar field as dark matter candidate
๐ฯ,0 =1
2
๐ฯ2
๐03 ฯ๐
2
Energy density
ฮฉฯ,0 โก๐ฯ,0
๐๐,0
DM abundance
๐ฯ ฯ๐ =
๐ป๐ธ๐~10โ5 ๐๐
2 ร 10โ5๐โ100
1/2 ฯ๐1013 ๐บ๐๐
โ4
๐๐ , ๐ฯ> ๐ป๐ธ๐.
3 ร 10โ5๐โ100
1/2 ฯ๐1013 ๐บ๐๐
โ4
๐๐, ๐ฯ < ๐ป๐ธ๐.
โข Light fields during inflation quantum fluctuations do not respect the limit of the Cold
Dark Matter (CDM) isocurvature perturbations.
โข Gravitational interactions during inflation ๐๐๐๐ก=๐
2
ฯ2๐ ฯ
๐๐๐2 ๐ฯ~ ๐ป๐๐๐ CDM
isocurvature perturbations compatible with observations [Planck Collaboration 2015] ;
โข Constraints on CDM isocurvature perturbations lead to:
โข ๐ป๐๐๐โ 2.5 ร 1013 ๐
0.01
1
2๐บ๐๐, ๐ < 0.11. [Planck Collaboration 2015].
30/03/2016 Scalar field dark matter and the Higgs field 5
Initial conditions
ฯ๐ โ ฮฑ ๐ป๐๐๐, ฮฑ โ 0.1 โ 0.25;
๐ โกโ๐ก2
โ๐ก2
30/03/2016 Scalar field dark matter and the Higgs field 6
Initial conditions โ Results
๐ฯ < ๐ป๐ธ๐
๐ฯ > ๐ป๐ธ๐
๐ฯ~ 10โ6 ๐๐
๐ฯ~ 10โ5 ๐๐
30/03/2016 Scalar field dark matter and the Higgs field 7
Non-renormalizable interactions model
DM fieldConformal symmetry
Higgs boson (and Standard Model fields)
Hidden sector Visible sector
Heavy messengers,
Gravitybroken by non-renormalizable
operators
๐๐๐๐ก =๐62
2โ 4
ฯ2
๐2 ๐ฯ = ๐6
๐ฃ2
๐~ 2.5 ร 10โ5 ๐6
๐
๐๐
โ1
eV;
Electroweak symmetry breaking
30/03/2016 Scalar field dark matter and the Higgs field 8
Warped extra-dimension model
Randall-Sundrum inspired model:
0 yL
Higgs
5D bulk
Visible/Infrared brane
Planck brane
ฯ
๐ฃ โ ๐โ๐๐ฟ๐๐๐โ๐๐ฟ ~ 10โ16
๐ = ๐4๐ฅ ๐๐ฆ โ๐บ1
2๐บ๐๐๐๐ฮฆ๐๐ฮฆโ
1
2๐ฮฆ2ฮฆ2 + ๐ฟ ๐ฆ โ ๐ฟ ๐บ๐๐๐๐โ
โ ๐๐โ โ ๐ โ +1
2๐52ฮฆ2โ2
[L. Randall, R. Sundrum 1999]
๐๐ 2 = ๐โ2๐ ๐ฆ ๐๐ฮฝ๐๐ฅ๐๐๐ฅฮฝ + ๐๐ฆ2Metric:
30/03/2016 Scalar field dark matter and the Higgs field 9
Warped extra-dimension model
โข Decompose ฮฆ in Kaluza-Klein modes: ฮฆ ๐ฅ๐ , ๐ฆ =1
2๐ฟ ๐=0โ ฯ๐ ๐ฅ
๐ ๐๐ ๐ฆ ;
โข ฮฆ0 ๐ฅ๐ , ๐ฟ =
1
2๐ฟฯ0 ๐ฅ
๐ 2๐๐ฟ
๐4 ~ ๐52๐๐โ2๐๐ฟ โ ๐ช 1 ร
๐ฃ
๐๐~10โ16
๐๐๐๐ก =1
2๐52๐๐โ2๐๐ฟฯ0
2โ2
๐ฯ ~๐ฃ2
๐๐~ 10โ5 eV
Mass in the required range;In agreement with non-renormalizableinteractions model.
Planck-suppressed non-renormalizable operator
Renormalizable interaction in a higher-dimensional warped geometry.
โข DM candidate: oscillating scalar field ฯ, which acquires mass through the Higgs
mechanism.
โข Lower bound: ๐ฯ โณ 10โ6 โ 10โ5 ๐๐ ;
โข ๐ฯ~๐ฃ2
๐๐~10โ5 ๐๐ obtained through either non-renormalizable interactions
between ฯ and the Higgs field or through a warped extra-dimension model.
30/03/2016 Scalar field dark matter and the Higgs field 10
Conclusions
Thank you for your attention!
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016
Scalar field inflation in the presence of anon-minimal matter-curvature coupling
Clรกudio Gomesโ Universidade do Porto and Centro de Fรญsica do Porto
IberiCos 2016, Vila do Conde, 30 March 2016
โ In collaboration with Orfeu Bertolami and Joรฃo RosaFundaรงรฃo para a Ciรชncia e a Tecnologia, SFRH/BD/102820/2014
1/11
Contents
1. Inflation
2. Alternative theories of gravityThe non-minimal coupling between matter and curvature (NMC)
3. Scalar field inflation with a matter-curvature NMC
2/11
Why Inflation?
Hot Big Bang model: Evolutionary Universe; CMB; BBN...
Leaves some conundrums: Large scale homogeneity and isotropy (horizon problem); Flatness problem; Absence of observed topological defects (monopole problem); Origin of the energy density fluctuations,...
Cosmic Inflation (paradigm, not theory) provides a suitable solution forthe above problems by a mechanism of accelerated expansion of theUniverse at early times (between Planck and GUT epochs).
1. Inflation 3/11
Scalar field inflation
Real scalar field with:ฯ+ 3Hฯ+ V โฒ(ฯ) = 0 (1)
Inflation occurs in the so-called slow-roll approximation:
V โซ ฯ2/2 =โ ฯ โ V (ฯ) (2)
V โ const. (3)This is the same as stating that the slow-roll parameters are:
ฯตฯ =M2
P
2
(V โฒ
V
)2
โช 1 (4)
ฮทฯ = M2P
V โฒโฒ
Vโช 1 (5)
1. Inflation 4/11
Why to go beyond GR?
Successes: Solar System constraints; GPS;
But there were still some conundrums: Not compatible with quantum mechanics; Existence of singularities; Cosmological constant problem; Large scale data requires DM and DE; Astrophysical data requires DM.
Alternative theories of gravity: f(R) Horndeski gravity; Jordan-Brans-Dicke; NMC [Bertolami, Bรถhmer, Harko, Lobo 2007]...
2. Alternative theories of gravity 5/11
Alternative theories of gravity: the NMC
Generalisation of f(R) theories[Bertolami, Bohmer, Harko, Lobo, 2007]:
S =
โซ[ฮบf1 (R) + f2 (R)L]
โโgd4x , (6)
where ฮบ = M2P /2 = 1/16ฯG.
Varying the action relatively to the metric gยตฮฝ :
2 (ฮบF1 โ F2ฯ)
(Rยตฮฝ โ 1
2gยตฮฝR
)=f2Tยตฮฝ + ฮบ (f1 โ F1R) gยตฮฝ+
+ F2ฯRgยตฮฝ + 2โยตฮฝ (ฮบF1 โ F2ฯ)
(7)
One recovers GR by setting f1(R) = R and f2(R) = 1.
2. Alternative theories of gravity 6/11
Using the Bianchi identities, one finds the non-covariant conservationof the energy-momentum tensor:
โยตTยตฮฝ =
F2
f2(gยตฮฝL โ Tยตฮฝ)โยตR (8)
For a perfect fluid, the extra force due to the NMC can be expressedas:
fยต =1
ฯ+ p
[F2
1 + f2(Lm โ p)โฮฝR+โฮฝp
]hยตฮฝ , (9)
with hยตฮฝ = gยตฮฝ + uยตuฮฝ being the projection operator.
2. Alternative theories of gravity 7/11
Degeneracy-lifting of the Lagrangian choice [O. Bertolami, F. S. N.Lobo, J. Pรกramos, 2008]
Mimicking Dark Matter (galaxies, clusters) [O. Bertolami, J. Pรกramos,2010; O. Bertolami, P. Frazรฃo, J. Pรกramos, 2013]
Cosmological Perturbations [O. Bertolami, P. Frazรฃo, J. Pรกramos,2013]
Preheating scenario after inflation [O. Bertolami, P. Frazรฃo, J.Pรกramos, 2011]
Modified Friedmann equation [O. Bertolami, J. Pรกramos, 2013]
Modified Layzer-Irvine equation and virial theorem [O. Bertolami, C.Gomes, 2014]...
2. Alternative theories of gravity 8/11
Scalar field inflation in the presence of a non-minimalmatter-curvature curvature
At first approximation:
ฯ+ 3Hฯ+ V โฒ(ฯ) โ 0 (10)
In the slow-roll regime, and for f1(R) = R, we have a modifiedFriedmann equation:
H2 โ f2
1 + 2F2ฯM2
P
ฯ
3M2P
(11)
3. Scalar field inflation with a matter-curvature NMC 9/11
Choosing the non-minimal coupling function to be:
f2(R) = 1 +
(R
Rn
)n
(12)
we find that for the large density limit: n = 2 we retrieve the Friedmann equation as in GR n โฅ 3 the modified Friedmann equation becomes (An, Bn โ R)
H2 = An โ Bn
ฯ(13)
whilst in the low density regime, this model gives a smallcorrection to the Friedmannโs equation.
We further note that modifications of the Friedmann equation havebeen well studied in the literature: brane models, loop quantumcosmology, ...
3. Scalar field inflation with a matter-curvature NMC 10/11
Thank you for your attention!
Rob Gonรงalves
3. Scalar field inflation with a matter-curvature NMC 11/11
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016
The variation of the fine-structure constant from disformalcouplings
Nelson NunesInstituto de Astrofฤฑsica e Ciencias do Espaco
in collaboration with: Jurgen Misfud and Carsten van de Bruck,arXiv:1510.00200
EXPL/FIS-AST/1608/2013UID/FIS/04434/2013
Disformal couplings
Let us consider the action
S = Sgrav (gยตฮฝ , ฯ) + Smatter(g(m)ยตฮฝ ) + SEM(Aยต, g
(r)ยตฮฝ )
The metrics g(m)ยตฮฝ and g
(r)ยตฮฝ are related to gยตฮฝ via a disformal transformation:
g(m)ยตฮฝ = Cm(ฯ)gยตฮฝ +Dm(ฯ)ฯ,ยตฯ,ฮฝ
g(r)ยตฮฝ = Cr(ฯ)gยตฮฝ +Dr(ฯ)ฯ,ยตฯ,ฮฝ .
Cr and Cm are conformal factorsDr and Dm are disformal factorsWe can also write,
g(r)ยตฮฝ =CrCm
g(m)ยตฮฝ +
(Dr โ
CrDm
Cm
)ฯ,ยตฯ,ฮฝ โก Ag(m)
ยตฮฝ +Bฯ,ยตฯ,ฮฝ
Electromagnetic sector
The action
SEM = โ1
4
โซd4x
โโg(r)h(ฯ)gยตฮฝ(r)g
ฮฑฮฒ(r)FยตฮฑFฮฝฮฒ โ
โซd4x
โโg(m)gยตฮฝ(m)jยตAยต
- Fยตฮฝ is Faraday tensor; jยต is the fourโcurrent;- h(ฯ) is the coupling between the electromagnetism and ฯ.
In the frame in which matter is decoupled from the scalar field
SEM = โ1
4
โซd4x
โโg(m)hZ
[gยตฮฝ(m)g
ฮฑฮฒ(m) โ 2ฮณ2gยตฮฝ(m)ฯ
,ฮฑฯ,ฮฒ]FยตฮฑFฮฝฮฒ
โโซd4x
โโg(m)gยตฮฝ(m)jยตAยต
where
Z =(
1 + BA g
ยตฮฝ(m)โยตฯโฮฝฯ
)1/2, ฮณ2 = B
A+Bgยตฮฝ(m)
โยตฯโฮฝฯ
The field equation for Aยต
Varying the action with respect to Aยต
โฮต (hZF ฮตฯ)โ โฮต(hZฮณ2ฯ,ฮฒ
(gฮตฮฝ(m)ฯ
,ฯ โ gฯฮฝ(m)ฯ,ฮต)Fฮฝฮฒ
)= jฯ
With g(m)ยตฮฝ = ฮทยตฮฝ , and Ei = F i0
โ ยทE =Zฯ
h
where ฯ = j0. Integrating this equation over a volume V using, E = โโV , we get theelectrostatic potential
V (r) =ZQ
4ฯhrโ ฮฑ โ Z
h
The fine structure constant depends on Z.
The evolution of ฮฑ
For FLRW Universe,
Z =
(1โ Dr
Crฯ2
1โ DmCm
ฯ2
)1/2
Time derivative of ฮฑ,ฮฑ
ฮฑ=
1
Z
(โZ
โฯฯ+
โZ
โฯฯ
)โ 1
h
dh
dฯฯ
Redshift evolution of ฮฑ,
โฮฑ
ฮฑ(z) โก ฮฑ(z)โ ฮฑ0
ฮฑ0=h0Z
hZ0โ 1
Constrains on the evolution of ฮฑ
1 Atomic Clocks at z = 0,
ฮฑ
ฮฑ
โฃโฃโฃโฃ0
= (โ1.6ยฑ 2.3)ร 10โ17 yrโ1
2 Oklo at z โ 0.16,|โฮฑ|ฮฑ
< 1.1ร 10โ8
3 187Re meteorite at z โ 0.43,
โฮฑ
ฮฑ= (โ8ยฑ 8)ร 10โ7
4 CMB at z ' 103โฮฑ
ฮฑ= (3.6ยฑ 3.7)ร 10โ3
Astrophysical constrains on the evolution of ฮฑ
1 Keck/ HIRES141 absorbers (MM method) [M.T. Murphy et al. 2004]
2 VLT/ UVES154 absorbers (MM method) [J.A. King et al. 2012]
3 Keck/ HIRES Si IV absorption systems (AD method) [M.T. Murphy et al. 2001]
4 Comparison of HI 21 cm line with molecular rotational absorption spectra [M.T.Murphy et al. 2001]
5 11 UVES absorbers [P. Molaro et al. 2013, T.M. Evans et al. 2014]
Gravity and matter field sector
Is the evolution of ฯ compatible with constraints on the evolution of ฮฑ?
S =
โซd4xโโg(
1
2Rโ 1
2gยตฮฝโยตฯโฮฝฯโ V (ฯ)
)+ Smatter(g
(m)ยตฮฝ )
with the equation of motion
ฯ+ 3Hฯ+ V โฒ = Qm +Qr,
ฯm + 3H(ฯm + pm) = โQmฯ,ฯr + 3H(ฯr + pr) = โQrฯ,
where Qm and Qr are complicated functions of ฯm, ฯr, ฯ, Cr, Cm, Dr, Dm and theirfield derivatives.
Couplings and parameters
We specify to exponential couplings and potential and to linear direct coupling h(ฯ):
Ci(ฯ) = ฮฒiexiฯ, Di(ฯ) = Mโ4i eyiฯ,
h(ฯ) = 1โ ฮถ(ฯโ ฯ0), V (ฯ) = M4V eโฮปฯ.
Parameters xi, yi, ฮป, ฮฒi, Mi, MV and ฮถ are tuned such that their are in agreementwith constraints on ฮฑ and on the cosmological parameters from Planck.
Parameter Estimated valuew0,ฯ โ1.006ยฑ 0.045
H0 (67.8ยฑ 0.9) km sโ1Mpcโ1
ฮฉ0,m 0.308ยฑ 0.012
Disformal and electromagnetic couplings
Mr Mm MV ฮฒm xm |ฮถ| ฮปโผ 1 meV โผ 1 meV 2.69 meV 1 0 < 5ร 10โ6 0.45
Disformal and conformal couplings
Mr Mm MV ฮฒm xm |ฮถ| ฮป25-27 meV 15 meV 2.55 meV 8 0.14 0 0.45
Summary
1 A variation in the fine-structure constant can be induced by disformal couplingsprovided that the radiation and matter disformal coupling strengths are notidentical.
2 Such a variation is enhanced in the presence of the usual electromagnetic coupling.
3 Laboratory measurements with molecular and nuclear clocks are expected toincrease their sensitivity to as high as 10โ21 yrโ1.
4 Better constrained data is expected from high-resolution ultra-stablespectrographs such as PEPSI at the LBT, ESPRESSO at the VLT and ELT-Hiresat the E-ELT.
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016
COSMIC MICROWAVE
BACKGROUND ANISOTROPIES
GENERATED BY DOMAIN
WALL NETWORKS
Lara SousaInstituto de Astrofรญsica e Ciรชncias do Espaรงo
arXiv:1507.01064
DOMAIN WALLS
DOMAIN WALLS ARE FORMED WHEN DISCRETE SYMMETRIES ARE SPONTANEOUSLY BROKEN IN
PHASE TRANSITIONS.
V (ฯ)
ฯโยฟฯ+ ยฟ
DOMAIN WALLS!
DOMAIN WALL CMB Q&A
WHY?- FOR EXISTING!- REPULSIVE GRAVITY
HOW? ACTIVE GENERATION OF PERTURBATIONS.
WHERE? - SUBDOMINANT CONTRIBUTIONS TO THE TEMPERATURE AND E-MODES - POSSIBLY SIGNIFICANT B-MODE CONTRIBUTION
WHAT DOES IS MEAN? SIGNIFICANT VECTOR
CONTRIBUTIONS
CMBACT CODE
ENERGY-MOMENTUM TENSOR IS CALCULATED USING THE UNCONNECTED SEGMENT MODEL:
- SET OF UNCORRELATED STRAIGHT STRING SEGMENTS;- RANDOMLY DISTRIBUTED AND MOVING IN RANDOM DIRECTIONS;- A FRACTION OF SEGMENTS DECAY IN EACH EPOCH (ENERGY LOSS DUE TO INTERACTIONS);- LENGTH AND VELOCITY OF THE SEGMENTS ARE DEFINED USING THE VOS MODEL;
PHENOMENOLOGICAL APPROACH:
CMBACT CODE
ENERGY-MOMENTUM TENSOR IS CALCULATED USING THE UNCONNECTED SECTION MODEL:
- SET OF UNCORRELATED FLAT AND SQUARE DOMAIN WALL SECTIONS;- RANDOMLY DISTRIBUTED AND MOVING IN RANDOM DIRECTIONS;- A FRACTION OF SECTIONS DECAY IN EACH EPOCH (ENERGY LOSS DUE TO INTERACTIONS);- AREA AND VELOCITY OF THE SECTIONS ARE DEFINED USING THE VOS MODEL;
PHENOMENOLOGICAL APPROACH:
ENERGY-MOMENTUM TENSOR
T ฮผ ฮฝโโg=ฯโซ d 3ฮพฮด
4[ xฮผ
โxฮผ(ฮพ
a)]โโhhab x , a
ฮผ x , bฮฝ
ยฟ
S=โฯโซ d3ฮพโโhNAMBU-GOTO ACTION:
WE NEED TO COMPUTE THE ENERGY-MOMENTUM TENSOR FOR EACH OF THESE SECTIONS.
xฮผ=xฮผ(ฮพa) , a=0,1 ,2WITH
WORLD-VOLUME
ENERGY-MOMENTUM TENSOR
ฮธ00=4ฯ ฮณ โ2cos(kโ x+vk ฯ)sin (kl x3
' (1)/2)sin (kl x3
' (2)/2)
k 2 x3' (1) x3
' (2)
x=x0+ฮพ1 x' (1)
+ฮพ2 x' (2)
+v ฯ x
ฮธij=ฮธ00 [v2 หx i หx jโ(1โv2
) x i' (1) x j
' (1)+ x i
' (2) x j' (1)
]
FORTUNATELY, IN THIS CASE
ANALYTICAL SOLUTIONS:
ENERGY-MOMENTUM TENSOR
2ฮธS=ฮธ00[v2(3 หx3
หx3โ1)โ(1โv2)(3 x3
' (1) x3' (1)
+3 x3' (2) x3
' (2)โ2)]
THE REST FOLLOWS FROM E-M CONSERVATION...
ฮธV=ฮธ00[v2 หx1
หx3โ(1โv2)( x1
' (1) x3' (1)
+ x1' (2) x3
' (2))]
ฮธT=ฮธ00[v2 หx1
หx2โ(1โv2)( x1
' (1) x2' (1)
+ x1' (2) x2
' (2))]
WE NOW HAVE 3 OF THE E-M COMPONENTS REQUIRED BY CMBFAST:
THE RESULTS: CDM POWER SPECTRUM
DOMAIN WALLS CONTRIBUTE MOSTLY ON LARGE SCALES...
THE RESULTS: CMB SPECTRA
Gฮผ=G ฯ L0=10โ7
THE RESULTS: CONSTRAINTS
FRACTIONAL CONTRIBUTION TO THE TT-
POWER SPECTRUM
ENERGY SCALE OF THE DOMAIN-WALL-FORMING
PHASE TRANSITIONฮท<0,92MeV
f dw<0,2
THERE IS STILL OBSERVATIONAL ROOM FOR DOMAIN WALLS:
THE RESULTS: CONSTRAINTS
โฆ AND THEY MAY PRODUCE SIGNIFICANT B-MODES!
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016
Evolution of Semilocal String Networks:
Asier Lopez-Eiguren (UPV/EHU)
Segment Evolution
Vila do Conde, 30/03/16
In collaboration with: A. Achรบcarro, A. Avgoustidis, C.J.A.P. Martins, A.S. Nunes, J. Urrestilla
Evolution of String Networks
Numerical Simulations Analytic Models
โข Evolve true eom
โข High computational cost
โข Limited dynamical range
โข Approximate models
โข Simples
โข More tractables
โข Need input from Num. Sim.
TWO methods to analyse the evolution:
OBJECTIVE: CALIBRATE analytic models for SL
Semilocal Strings (A. Achucarro & Vachaspati 1999)
โข Extension of Abelian-Higgs (AH): U(1)l SU(2)g x U(1)l
โข They are not topological
โข They can have ends
โข This ends are effectively global monopoles
Abelian-HiggsSemilocal
Semilocal Strings (A. Achucarro & Vachaspati 1999)
โข The stability of the strings depends on the parameter ฮฒ =mscalar2/mgauge2:
โข ฮฒ > 1 Unstable
โข ฮฒ = 1 Neutrally stable
โข ฮฒ < 1 Stable
โข For lower ฮฒ they behave more like AH
S =
Z
d
4x
nh
@ยต iAยต
i2
1
4F
2
4(+
2)2o
Velocity-one-scale Model
โข Two variables:
(Martins & Shellard 1996,2002)
dv
dt= (1 v2)
k
L v
ld
(4 n)dL
dt= (4 n)HL+ v2
L
ld+ cv
L4n =M
M n
1
ld= nH +
1
lf
rms Velocity
Typical Length ScaleInterdefect distance
Damping scale
particle friction
n= dim. of defect
Semilocal VOS Models
โข Compare simulations with analytic models
โข Obtain the best values for the parameters
Model A Model B
Hybrid Networks: strings + monopoles
Field Theory Simulationsโข 10243 lattices in radiation and matter eras in expanding universe
โข Magnetic energy to detect strings
arXiv:1312.2123/PhysRevD.89.063503: Large Scale properties were analysed
t=150
t=300
t=450
Field Theory Simulations
Segment Distribution
Model A
Model B
Simulations
Initial ls seed from simulations Phenomenological vs distribution
Evolve VOS models
Segment Distribution
โข We perform ฯ2 analysis to determine the best values for the parameters
Summary
โข TWO VOS models for Semilocal string networks
โข We perform X2 analysis:
โข Determine the best values of the parameters
โข Conclude which model describes better the network
Future Workโข Improve parameter analysis:
โข Obtaining vs distribution from simulations
โข Obtain segment end (monopole) velocities
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016
Extending the velocity-dependent one-scale modelfor domain walls.
I.Yu. Rybak,
CAUP, IA
in collaboration with
C.J.A.P. Martins,
A. Avgoustidis,
E.P.S. Shellard
Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)
Vila do Conde, IberiCos 2016I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
V0
-0
0
ฮพฮพ
Introduction
Kibble mechanism
[Kibble,J.Phys.A9(1976),1387-1398ICTP/75/5]
L = 12 (โฯ)
2 โ V (ฯ)
V (ฯ) = V0
(1โ ฯ2
ฯ20
)2
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
-0
0
V0
ฮพ ฮพ
Introduction
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Walls-0
0
V0
Introduction
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
ฮป 1/10
1/5
1/4
1/3
2/5
1/2
3/5
2/3
3/4
4/5
9/10
19/20
ฯ
ฯ
ฯ ฯ
(ฮณ ฯ
)2
ฮป 19/20
9/10
4/5
3/4
2/3
3/5
1/2
2/5
1/3
1/4
1/5
1/10
Field theory simulation (40963 boxes)
Scalar eld model:
[Press,Ryden,Spergel, Astrophys.J.347,590(1989)]
โ2ฯโฯ2
+ 3 d ln ad ln ฯ
โฯโฯ โ
โ2ฯโx iโxi
= โโVโฯ ,
Measured values (asymptotic):
โข (ฮณฯ )2 (ฯ - velocity).
โข ฮพc/ฯ (ฮพc - correlation length โผ 1ฯ)
(for a โผ tฮป)
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Velocity-depend one scale (VOS) model
Dirac-Nambu-Goto action: S = โฯwโซ โ
Gd2ฯdฯ ,[Sousa,Avelino,Phys.Rev.D,84,063502(2011)]
(averaged) โ โซ ...d2ฯ
dLdt
=(1+ 3ฯ 2
)HL+ cwฯ ,
dฯ dt
=(1โ ฯ 2
) (kwLโ 3Hฯ
),
Scaling solution is: L = ฮตt, ฯ (ฮต, ฯ - constants).
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Momentum parameter for VOS model
From the microscopic description
kw (ฯ ) = k01โ(qฯ 2)
ฮฒ
1+(qฯ 2)ฮฒ
Physical restrictions:
โข 0 โค k0 โค 2
โข 0 < 1qโค ฯ 2w = 2
3
k0 = 1.73ยฑ 0.01,
q = 4.27ยฑ 0.10 (< ฯ >โ 0.48),
ฮฒ = 1.69ยฑ 0.08.
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Energy loss for VOS model
Energy loss mechanisms:
โข creation of closed objects โข scalar radiation (โผ curvaturer )
cwฯ d [k0 โ k(ฯ )]r
r = 1.30ยฑ 0.02, d = 0.28ยฑ 0.01, cw = 0.00ยฑ 0.01.
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Extended VOS model
The whole model with found parameters
dLdt
=(1+ 3ฯ 2
)HL+ cwฯ + d (k0 โ k(ฯ ))r ,
dฯ dt
=(1โ ฯ 2
) (k(ฯ )Lโ 3Hฯ
),
k(ฯ ) = k01โ(qฯ 2)
ฮฒ
1+(qฯ 2)ฮฒ
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Radiation-matter transition
Scale factor
a(ฯ)aeq
=(ฯฯโ
)2+ 2
(ฯฯโ
),
where ฯโ = ฯeq/(โ2โ 1).
Simulations with dierent aeq, ฯeq to span the entire transition
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Results
The largest currently available eld-theory simulations;
Adjustment of the VOS model;
Direct comparison of energy loss mechanisms;
Description of the radiation-matter transition by the extended VOS model;
Interesting avenues for further study
To extend this analysis to the case of cosmic strings for better understanding the
dierences between Goto-Nambu and eld theory simulations;
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
Thank you for your attention!
SFRH/BD/52699/2014
I.Yu. Rybak, CAUP, IA in collaboration with C.J.A.P. Martins, A. Avgoustidis, E.P.S. Shellard Phys.Rev.D93(2016)no.4,043534, (arxiv[hep-ph] 1602.01322)Extending the velocity-dependent one-scale model for domain walls.
IBERICOS2016
11th Iberian Cosmology Meeting
SOCโANA ACHรCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSร PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCโANA CATARINA LEITE, CARLOS MARTINS (CHAIR), FERNANDO MOUCHEREK, PAULO PEIXOTO (SYSADMIN), ANA MARTA PINHO, IVAN RYBAK, ELSA SILVA (ADMIN)
VILA DO CONDE, PORTUGAL, 29-31 MARCH, 2016
SERIES OF MEETINGS WHICH AIM TO ENCOURAGE INTERACTIONS AND COLLABORATIONS BETWEEN RESEARCHERS WORKING IN COSMOLOGY AND RELATED AREAS IN PORTUGAL AND SPAIN.
www.iastro.pt/ibericos2016