IBERICOS2016
11th Iberian Cosmology Meeting
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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. JoΓ£o 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
β’ We propose: oscillating scalar field as DM candidate, coupled to the Higgs boson;
β’ Previous works: βHiggs-portalβ DM models: abundance of DM is set by the decoupling and
freeze-out from thermal equilibrium π ~ πΊππ β πππ (Weakly Interacting Massive
Particles - WIMPs) [Silveira, Zee 1985; Bento, Bertolami, Rosenfeld 2001; Burgess, Pospelov, ter Veldhuis 2001;
Tenkanen 2015];
β’ 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
β’ Oscillating scalar field, Ο, as DM candidate;
β’ Ο acquires mass through the Higgs mechanism;
β’ Ο starts to oscillate whenπΟ ~ π», after the electroweak phase transition;
β’ Weakly interactions with the Higgs boson πΟ βͺ ππ , 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
πΟ,0 =1
2
πΟ2
π03 Οπ
2
Energy density
Ξ©Ο,0 β‘πΟ,0
ππ,0
DM abundance
πΟ Οπ =
π»πΈπ~10β5 ππ
2 Γ 10β5πβ100
1/2 Οπ1013 πΊππ
β4
ππ , πΟ> π»πΈπ.
3 Γ 10β5πβ100
1/2 Οπ1013 πΊππ
β4
ππ, πΟ < π»πΈπ.
β’ Light fields during inflation quantum fluctuations do not respect the limit of the Cold
Dark Matter (CDM) isocurvature perturbations.
β’ Gravitational interactions during inflation ππππ‘=π
2
Ο2π Ο
πππ2 πΟ~ π»πππ CDM
isocurvature perturbations compatible with observations [Planck Collaboration 2015] ;
β’ Constraints on CDM isocurvature perturbations lead to:
β’ π»πππβ 2.5 Γ 1013 π
0.01
1
2πΊππ, π < 0.11. [Planck Collaboration 2015].
30/03/2016 Scalar field dark matter and the Higgs field 5
Initial conditions
Οπ β Ξ± π»πππ, Ξ± β 0.1 β 0.25;
π β‘βπ‘2
βπ‘2
30/03/2016 Scalar field dark matter and the Higgs field 6
Initial conditions β Results
πΟ < π»πΈπ
πΟ > π»πΈπ
πΟ~ 10β6 ππ
πΟ~ 10β5 ππ
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
ππππ‘ =π62
2β 4
Ο2
π2 πΟ = π6
π£2
π~ 2.5 Γ 10β5 π6
π
ππ
β1
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
Ο
π£ β πβππΏπππβππΏ ~ 10β16
π = π4π₯ ππ¦ βπΊ1
2πΊππππΞ¦ππΞ¦β
1
2πΞ¦2Ξ¦2 + πΏ π¦ β πΏ πΊππππβ
β ππβ β π β +1
2π52Ξ¦2β2
[L. Randall, R. Sundrum 1999]
ππ 2 = πβ2π π¦ ππΞ½ππ₯πππ₯Ξ½ + ππ¦2Metric:
30/03/2016 Scalar field dark matter and the Higgs field 9
Warped extra-dimension model
β’ Decompose Ξ¦ in Kaluza-Klein modes: Ξ¦ π₯π , π¦ =1
2πΏ π=0β Οπ π₯
π ππ π¦ ;
β’ Ξ¦0 π₯π , πΏ =
1
2πΏΟ0 π₯
π 2ππΏ
π4 ~ π52ππβ2ππΏ β πͺ 1 Γ
π£
ππ~10β16
ππππ‘ =1
2π52ππβ2ππΏΟ0
2β2
πΟ ~π£2
ππ~ 10β5 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.
β’ DM candidate: oscillating scalar field Ο, which acquires mass through the Higgs
mechanism.
β’ Lower bound: πΟ β³ 10β6 β 10β5 ππ ;
β’ πΟ~π£2
ππ~10β5 ππ obtained through either non-renormalizable interactions
between Ο 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
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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
ClΓ‘udio Gomesβ Universidade do Porto and Centro de FΓsica do Porto
IberiCos 2016, Vila do Conde, 30 March 2016
β In collaboration with Orfeu Bertolami and JoΓ£o RosaFundação para a CiΓͺncia 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:Ο+ 3HΟ+ V β²(Ο) = 0 (1)
Inflation occurs in the so-called slow-roll approximation:
V β« Ο2/2 =β Ο β V (Ο) (2)
V β const. (3)This is the same as stating that the slow-roll parameters are:
Ο΅Ο =M2
P
2
(V β²
V
)2
βͺ 1 (4)
Ξ·Ο = M2P
V β²β²
Vβͺ 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, BΓΆhmer, 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 =
β«[ΞΊf1 (R) + f2 (R)L]
ββgd4x , (6)
where ΞΊ = M2P /2 = 1/16ΟG.
Varying the action relatively to the metric g¡ν :
2 (ΞΊF1 β F2Ο)
(R¡ν β 1
2g¡νR
)=f2T¡ν + ΞΊ (f1 β F1R) g¡ν+
+ F2ΟRg¡ν + 2β¡ν (ΞΊF1 β F2Ο)
(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:
βΒ΅T¡ν =
F2
f2(g¡νL β T¡ν)βΒ΅R (8)
For a perfect fluid, the extra force due to the NMC can be expressedas:
fΒ΅ =1
Ο+ p
[F2
1 + f2(Lm β p)βΞ½R+βΞ½p
]h¡ν , (9)
with h¡ν = g¡ν + u¡uν being the projection operator.
2. Alternative theories of gravity 7/11
Degeneracy-lifting of the Lagrangian choice [O. Bertolami, F. S. N.Lobo, J. PΓ‘ramos, 2008]
Mimicking Dark Matter (galaxies, clusters) [O. Bertolami, J. PΓ‘ramos,2010; O. Bertolami, P. FrazΓ£o, J. PΓ‘ramos, 2013]
Cosmological Perturbations [O. Bertolami, P. FrazΓ£o, J. PΓ‘ramos,2013]
Preheating scenario after inflation [O. Bertolami, P. FrazΓ£o, J.PΓ‘ramos, 2011]
Modified Friedmann equation [O. Bertolami, J. PΓ‘ramos, 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:
Ο+ 3HΟ+ V β²(Ο) β 0 (10)
In the slow-roll regime, and for f1(R) = R, we have a modifiedFriedmann equation:
H2 β f2
1 + 2F2ΟM2
P
Ο
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 β₯ 3 the modified Friedmann equation becomes (An, Bn β R)
H2 = An β Bn
Ο(13)
whilst in the low density regime, this model gives a smallcorrection to the Friedmannβs 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 Gonçalves
3. Scalar field inflation with a matter-curvature NMC 11/11
IBERICOS2016
11th Iberian Cosmology Meeting
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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 AstrofΔ±sica 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 (g¡ν , Ο) + Smatter(g(m)¡ν ) + SEM(AΒ΅, g
(r)¡ν )
The metrics g(m)¡ν and g
(r)¡ν are related to g¡ν via a disformal transformation:
g(m)¡ν = Cm(Ο)g¡ν +Dm(Ο)Ο,Β΅Ο,Ξ½
g(r)¡ν = Cr(Ο)g¡ν +Dr(Ο)Ο,Β΅Ο,Ξ½ .
Cr and Cm are conformal factorsDr and Dm are disformal factorsWe can also write,
g(r)¡ν =CrCm
g(m)¡ν +
(Dr β
CrDm
Cm
)Ο,Β΅Ο,Ξ½ β‘ Ag(m)
¡ν +BΟ,Β΅Ο,Ξ½
Electromagnetic sector
The action
SEM = β1
4
β«d4x
ββg(r)h(Ο)g¡ν(r)g
Ξ±Ξ²(r)F¡αFΞ½Ξ² β
β«d4x
ββg(m)g¡ν(m)jΒ΅AΒ΅
- F¡ν is Faraday tensor; jΒ΅ is the fourβcurrent;- h(Ο) is the coupling between the electromagnetism and Ο.
In the frame in which matter is decoupled from the scalar field
SEM = β1
4
β«d4x
ββg(m)hZ
[g¡ν(m)g
Ξ±Ξ²(m) β 2Ξ³2g¡ν(m)Ο
,Ξ±Ο,Ξ²]F¡αFΞ½Ξ²
ββ«d4x
ββg(m)g¡ν(m)jΒ΅AΒ΅
where
Z =(
1 + BA g
¡ν(m)βΒ΅ΟβΞ½Ο
)1/2, Ξ³2 = B
A+Bg¡ν(m)
βΒ΅ΟβΞ½Ο
The field equation for AΒ΅
Varying the action with respect to AΒ΅
βΞ΅ (hZF Ξ΅Ο)β βΞ΅(hZΞ³2Ο,Ξ²
(gΡν(m)Ο
,Ο β gΟΞ½(m)Ο,Ξ΅)FΞ½Ξ²
)= jΟ
With g(m)¡ν = η¡ν , and Ei = F i0
β Β·E =ZΟ
h
where Ο = j0. Integrating this equation over a volume V using, E = ββV , we get theelectrostatic potential
V (r) =ZQ
4Οhrβ Ξ± β Z
h
The fine structure constant depends on Z.
The evolution of Ξ±
For FLRW Universe,
Z =
(1β Dr
CrΟ2
1β DmCm
Ο2
)1/2
Time derivative of Ξ±,Ξ±
Ξ±=
1
Z
(βZ
βΟΟ+
βZ
βΟΟ
)β 1
h
dh
dΟΟ
Redshift evolution of Ξ±,
βΞ±
Ξ±(z) β‘ Ξ±(z)β Ξ±0
Ξ±0=h0Z
hZ0β 1
Constrains on the evolution of Ξ±
1 Atomic Clocks at z = 0,
Ξ±
Ξ±
β£β£β£β£0
= (β1.6Β± 2.3)Γ 10β17 yrβ1
2 Oklo at z β 0.16,|βΞ±|Ξ±
< 1.1Γ 10β8
3 187Re meteorite at z β 0.43,
βΞ±
Ξ±= (β8Β± 8)Γ 10β7
4 CMB at z ' 103βΞ±
Ξ±= (3.6Β± 3.7)Γ 10β3
Astrophysical constrains on the evolution of Ξ±
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 Ο compatible with constraints on the evolution of Ξ±?
S =
β«d4xββg(
1
2Rβ 1
2g¡νβΒ΅ΟβΞ½Οβ V (Ο)
)+ Smatter(g
(m)¡ν )
with the equation of motion
Ο+ 3HΟ+ V β² = Qm +Qr,
Οm + 3H(Οm + pm) = βQmΟ,Οr + 3H(Οr + pr) = βQrΟ,
where Qm and Qr are complicated functions of Οm, Οr, Ο, Cr, Cm, Dr, Dm and theirfield derivatives.
Couplings and parameters
We specify to exponential couplings and potential and to linear direct coupling h(Ο):
Ci(Ο) = Ξ²iexiΟ, Di(Ο) = Mβ4i eyiΟ,
h(Ο) = 1β ΞΆ(Οβ Ο0), V (Ο) = M4V eβΞ»Ο.
Parameters xi, yi, Ξ», Ξ²i, Mi, MV and ΞΆ are tuned such that their are in agreementwith constraints on Ξ± and on the cosmological parameters from Planck.
Parameter Estimated valuew0,Ο β1.006Β± 0.045
H0 (67.8Β± 0.9) km sβ1Mpcβ1
Ξ©0,m 0.308Β± 0.012
Disformal and electromagnetic couplings
Mr Mm MV Ξ²m xm |ΞΆ| Ξ»βΌ 1 meV βΌ 1 meV 2.69 meV 1 0 < 5Γ 10β6 0.45
Disformal and conformal couplings
Mr Mm MV Ξ²m xm |ΞΆ| Ξ»25-27 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 10β21 yrβ1.
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
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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 AstrofΓsica e CiΓͺncias do EspaΓ§o
arXiv:1507.01064
DOMAIN WALLS
DOMAIN WALLS ARE FORMED WHEN DISCRETE SYMMETRIES ARE SPONTANEOUSLY BROKEN IN
PHASE TRANSITIONS.
V (Ο)
ΟβΒΏΟ+ ΒΏ
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 ΞΌ Ξ½ββg=Οβ« d 3ΞΎΞ΄
4[ xΞΌ
βxΞΌ(ΞΎ
a)]ββhhab x , a
ΞΌ x , bΞ½
ΒΏ
S=βΟβ« d3ΞΎββhNAMBU-GOTO ACTION:
WE NEED TO COMPUTE THE ENERGY-MOMENTUM TENSOR FOR EACH OF THESE SECTIONS.
xΞΌ=xΞΌ(ΞΎa) , a=0,1 ,2WITH
WORLD-VOLUME
ENERGY-MOMENTUM TENSOR
ΞΈ00=4Ο Ξ³ β2cos(kβ x+vk Ο)sin (kl x3
' (1)/2)sin (kl x3
' (2)/2)
k 2 x3' (1) x3
' (2)
x=x0+ΞΎ1 x' (1)
+ΞΎ2 x' (2)
+v Ο x
ΞΈij=ΞΈ00 [v2 Λx i Λx jβ(1βv2
) x i' (1) x j
' (1)+ x i
' (2) x j' (1)
]
FORTUNATELY, IN THIS CASE
ANALYTICAL SOLUTIONS:
ENERGY-MOMENTUM TENSOR
2ΞΈS=ΞΈ00[v2(3 Λx3
Λx3β1)β(1βv2)(3 x3
' (1) x3' (1)
+3 x3' (2) x3
' (2)β2)]
THE REST FOLLOWS FROM E-M CONSERVATION...
ΞΈV=ΞΈ00[v2 Λx1
Λx3β(1βv2)( x1
' (1) x3' (1)
+ x1' (2) x3
' (2))]
ΞΈT=ΞΈ00[v2 Λx1
Λx2β(1βv2)( 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
GΞΌ=G Ο L0=10β7
THE RESULTS: CONSTRAINTS
FRACTIONAL CONTRIBUTION TO THE TT-
POWER SPECTRUM
ENERGY SCALE OF THE DOMAIN-WALL-FORMING
PHASE TRANSITIONΞ·<0,92MeV
f dw<0,2
THERE IS STILL OBSERVATIONAL ROOM FOR DOMAIN WALLS:
THE RESULTS: CONSTRAINTS
β¦ AND THEY MAY PRODUCE SIGNIFICANT B-MODES!
IBERICOS2016
11th Iberian Cosmology Meeting
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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. AchΓΊcarro, A. Avgoustidis, C.J.A.P. Martins, A.S. Nunes, J. Urrestilla
Evolution of String Networks
Numerical Simulations Analytic Models
β’ Evolve true eom
β’ High computational cost
β’ Limited dynamical range
β’ Approximate models
β’ Simples
β’ More tractables
β’ Need input from Num. Sim.
TWO methods to analyse the evolution:
OBJECTIVE: CALIBRATE analytic models for SL
Semilocal Strings (A. Achucarro & Vachaspati 1999)
β’ Extension of Abelian-Higgs (AH): U(1)l SU(2)g x U(1)l
β’ They are not topological
β’ They can have ends
β’ This ends are effectively global monopoles
Abelian-HiggsSemilocal
Semilocal Strings (A. Achucarro & Vachaspati 1999)
β’ The stability of the strings depends on the parameter Ξ² =mscalar2/mgauge2:
β’ Ξ² > 1 Unstable
β’ Ξ² = 1 Neutrally stable
β’ Ξ² < 1 Stable
β’ For lower Ξ² they behave more like AH
S =
Z
d
4x
nh
@Β΅ iAΒ΅
i2
1
4F
2
4(+
2)2o
Velocity-one-scale Model
β’ 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
β’ Compare simulations with analytic models
β’ Obtain the best values for the parameters
Model A Model B
Hybrid Networks: strings + monopoles
Field Theory Simulationsβ’ 10243 lattices in radiation and matter eras in expanding universe
β’ 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
β’ We perform Ο2 analysis to determine the best values for the parameters
Summary
β’ TWO VOS models for Semilocal string networks
β’ We perform X2 analysis:
β’ Determine the best values of the parameters
β’ Conclude which model describes better the network
Future Workβ’ Improve parameter analysis:
β’ Obtaining vs distribution from simulations
β’ Obtain segment end (monopole) velocities
IBERICOS2016
11th Iberian Cosmology Meeting
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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
ΞΎΞΎ
Introduction
Kibble mechanism
[Kibble,J.Phys.A9(1976),1387-1398ICTP/75/5]
L = 12 (βΟ)
2 β V (Ο)
V (Ο) = V0
(1β Ο2
Ο20
)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
ΞΎ ΞΎ
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.
Ξ» 1/10
1/5
1/4
1/3
2/5
1/2
3/5
2/3
3/4
4/5
9/10
19/20
Ο
Ο
Ο Ο
(Ξ³ Ο
)2
Ξ» 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)]
β2ΟβΟ2
+ 3 d ln ad ln Ο
βΟβΟ β
β2Οβx iβxi
= ββVβΟ ,
Measured values (asymptotic):
β’ (Ξ³Ο )2 (Ο - velocity).
β’ ΞΎc/Ο (ΞΎc - correlation length βΌ 1Ο)
(for a βΌ tΞ»)
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 = βΟwβ« β
Gd2ΟdΟ ,[Sousa,Avelino,Phys.Rev.D,84,063502(2011)]
(averaged) β β« ...d2Ο
dLdt
=(1+ 3Ο 2
)HL+ cwΟ ,
dΟ dt
=(1β Ο 2
) (kwLβ 3HΟ
),
Scaling solution is: L = Ξ΅t, Ο (Ξ΅, Ο - 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 (Ο ) = k01β(qΟ 2)
Ξ²
1+(qΟ 2)Ξ²
Physical restrictions:
β’ 0 β€ k0 β€ 2
β’ 0 < 1qβ€ Ο 2w = 2
3
k0 = 1.73Β± 0.01,
q = 4.27Β± 0.10 (< Ο >β 0.48),
Ξ² = 1.69Β± 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:
β’ creation of closed objects β’ scalar radiation (βΌ curvaturer )
cwΟ d [k0 β k(Ο )]r
r = 1.30Β± 0.02, d = 0.28Β± 0.01, cw = 0.00Β± 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+ 3Ο 2
)HL+ cwΟ + d (k0 β k(Ο ))r ,
dΟ dt
=(1β Ο 2
) (k(Ο )Lβ 3HΟ
),
k(Ο ) = k01β(qΟ 2)
Ξ²
1+(qΟ 2)Ξ²
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(Ο)aeq
=(ΟΟβ
)2+ 2
(ΟΟβ
),
where Οβ = Οeq/(β2β 1).
Simulations with dierent aeq, Οeq 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
SOCβANA ACHΓCARRO (LEIDEN/BILBAO), FERNANDO ATRIO-BARANDELA (SALAMANCA), MAR BASTERO-GIL (GRANADA), JUAN GARCIA-
-BELLIDO (MADRID), RUTH LAZKOZ (BILBAO), CARLOS MARTINS (PORTO), JOSΓ PEDRO MIMOSO (LISBON), DAVID MOTA (OSLO)
LOCβANA 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