valeria pettorino sissa, trieste

Valeria PettorinoSISSA, Trieste

Growing neutrino quintessence:large structures and CMB

04.10.10 BCTP Workshop, Bonn

In collaboration with:

Christof Wetterich, Luca Amendola (Heidelberg) Nico Wintergerst (Munich)

Dark energy and neutrinosNew role for neutrinos: significant influence in

cosmology?

Connection between neutrinos and dark energy propertiesGrowing matterL.Amendola, M.Baldi, C.Wetterich 2007 Growing neutrinos and cosmological selectionC.Wetterich, 2007Neutrino clustering in growing neutrino quintessenceD.Mota, V.P., G.Robbers, C.Wetterich, Feb 2008 Very large scale structures in growing neutrino quintessenceN.Wintergerst, V.P., D.Mota, C.Wetterich, Oct. 2009 Neutrino lumps and the Cosmic Microwave BackgroundV.P. N.Wintergerst, L.Amendola, C.Wetterich, Sept.2010

Valeria Pettorino, SISSA BCTP, 4th October 2010

Growing neutrino

quintessence

MAVANS: Fardon etal 2004, Afshordi etal 2005, Bjaelde etal 2008, Brookfield etal 2007

Coupled dark energy cosmologies


Many (observable) things can happen when you have

dynamical dark energy interacting with other species

Coupling between DE and

The mass of the coupled species is a function of the cosmon

For a multicomponent system, the stress energy tensor of the single species is in general not conserved.

Wetterich 2007

DE as a scalar field

Kodama&Sasaki 1984, Ma & Bertschinger 1995, Wetterich 1995, Amendola 2000, …


…the neutrino mass grows

Fixed coupling Growing () coupling

Cosmological trigger for dark energy

Dark energy in an exponential potential + coupling

Neutrino mass grows

Neutrinos become non relativistic


Without coupling, dark energy tracks the background (attractor)

The coupling almost stops

Large scale structures


Effective attractive force

Neutrinos feel an attractive interaction mediated by the dark energy scalar field (cosmon)

Geff = G(1 + 2)

2


Neutrinos feel a STRONG attractive interaction mediated by the dark energy scalar field (cosmon)

Typical value today 50

502 stronger than gravitational attraction

Neutrinos can cluster!

Very large structures

Wintergerst, Pettorino, Mota, Wetterichastro-ph/09104985 & PRD

• Prediction: formation of neutrino lumps at

supercluster scales

Non linear investigation of individual neutrino lumps


• Non linearities appear at z ~ 1

Stable neutrino lumps: typical scale 10 – 100 Mpc …and beyond

Non-linear analysis

Wintergerst, Pettorino, Mota, Wetterich 2009astro-ph/09104985

Non-linear fluid equations


Combination of a gravitational potential

and a neutrino induced potential

which depends on the value of the cosmon

Can we estimate the effect on CMB?

It is a non linear problem!

Linear analysis is NOT sufficient

Implemented CMBEASY and CAMBto solve linear perturbations

k = 0.1 h/Mpc[Mota,Pettorino,Robbers,Wetterich 2008]


Matching linear and non-linear


Relevant scales for CMB: possible effects on l < 100 via ISWLarge uncertainties: reliable NBody simulations not yet

available

VP, Wintergerst, Amendola, Wetterich 2010

linear non-linear

Criteria for linear breaking


First criterium:

non-linear whenever 1

Linear evolution can break already before that!

Backreaction


• Neutrino mass inside the lump is different (smaller) from the cosmological neutrino mass

• Backreaction of small scale fluctuations on large scale fluctuations (close to the horizon)

• Smaller effective coupling

• Once smaller lumps form, backreaction effects slow down the growth of larger size neutrino lumps

Pettorino, Wintergerst, Amendola, Wetterich 2010

Criteria for linear breaking

k = 0.1 h/Mpc[Mota,Pettorino,Robbers,Wetterich 2008]


Second criterium: backreaction effects

• Non-linear when the local induced potential 1

• Evaluate the cosmological induced potential 10-3

• Stop growth of all modes with k < kb where kb is the first mode (smallest length scale) to reach the bound

Effect on the CMB


Space for observations • CMB:

- effects on l < 100; enhanced ISW- oscillations at small multipoles?

• LSS: effects at large scales

• Detecting time dependence of neutrino masses


Cross correlation

In general, Dark energy interactions can have significant

effects at the non-linear level (high-z massive clusters, …)

Baldi, VP, Robbers, Springel 2008

Baldi, VP 2010

Conclusions• Dark energy interactions can give important observable

effects


Conclusions• Dark energy interactions can give important observable

effects

• Interaction with neutrinos can play a crucial role in cosmology!

- Dark energy properties related to a cosmological event.

- Dark energy and neutrino properties are related.

- Neutrinos cluster at z ~ 1 at supercluster scales and beyond.


Conclusions• Dark energy interactions can give important observable effects

• Interaction with neutrinos can play a crucial role in cosmology!

- Dark energy properties related to a cosmological event.

- Dark energy and neutrino properties are related.

- Neutrinos cluster at z ~ 1 at supercluster scales and beyond.

• Linear analysis not sufficient: non-linear effects related to the cosmon. Backreaction.

• Non-linear effects (very large scales and a mapping at z > 1) can distinguish between a cosmological constant and dynamical (interacting) dark energy


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Dark energy - neutrino connection

Dark energy and neutrino properties are related!

DE- fluid equation of state

The present amount of DE is set by a cosmological event and not by ground state properties


Neutrino clustering

• Neutrino structures become non linear at z ~ 1 for supercluster scales

• Stable neutrino lumps Brouzakis etal 2007

• At small scales neutrinos reduce CDM structures

Mota,Pettorino,Robbers,Wetterich 2008

~500Mpc ~20Mpc


Supernovae constraints

Rubin etal 2008


E.Carlesi, D.Mota, V.Pettorino, G.Robbers,…

Monte Carlo analysis in progress


Conclusions for Quintessence - CDM

• Interaction keeps DE and DM closer in the background evolution

• Attractor solutions

• Constrains by CMB

• Three features implemented in the Nbody code:

bigger gravitational ‘constant’ felt by DM particles varying mass of DM extra friction term in the direction of the velocity

• Three main results: less clumpy inner profiles, smaller halo concentrations, scale dependent bias

See also Mangano, Miele, Pettorino 2005


CMB constraints

Constraints to the coupling from CMB data 0.1 (for a constant coupling)

[Bean etal 2008]

WARNING: constraints for constant

coupling models

Implementation of CMBEASY to include general coupling

mass function m()

[Bean etal 2008]

Monte Carlo analysis in progress![Robbers, Pettorino]


Gravitational potentialWintergerst etal 2009, astro-ph/09104985

Upper bound


Distribution of lumps in space?Merging?

Much smaller than the linear extrapolation!

Observational constraints

Bounds on the variation of the gravitational constant and/or on the coupling to (baryonic) matter

Solar system experiments

Binary pulsars

The effect of the scalar field on the gravitational force is highly constrained within the solar system: deviations from GR are parametrized via: Bertotti et

al2005

Esposito-Farese2004

Pulses of rapidly rotating neutron stars constrain 0> 4.5

The bound on does not imply a bound on

For example if A() = cos then GNeff = G*(1+(A,)2)= G* (cos2 + sin2 ) = G*

GG/.

FF/. Esposito-

Farese2001

112.

106/ yrGG NeffNeff

Valeria Pettorino, SISSA SISSA, 17th March 2010

Observational constraints

Cosmological observations

It is not straightforward to extend limit to cosmological scales. Cosmology will provide bounds on the underlying theory of gravity which are complementary to the ones found in the solar system.

120JBD2)( F

Acquaviva et al2004

(CMB and power spectrum bound)

Cosmology can help

reconstructing the whole A()

Esposito Farese et al

2001

BBN constraints

The amount of light nuclides produced when 0.01 < T < 10 MeV and in particular the nn/np number density ratio is sensitive to the value of the Hubble parameter at that time and to the cosmological expansion.

Bounds on the value of 4He mass fraction (Yp) and D, whose amount increase with H for a fixed baryonic amount, can be used to constrain F(). Coc etal 2006, Iocco etal 2008, Mangano Miele Pettorino

2005Valeria Pettorino, SISSA SISSA, 17th March 2010

Pattern for the background similar to extended

quintessence

Non negligible amount of dark energy in the past

RAD

MAT

DE


Linear perturbations


More perturbations

k = 0.1 h/Mpc(Supercluster scales) Mota, Pettorino, Robbers, Wetterich 2008


Present

Neutrinos

Scalar field


Future attractor

Amendola, Baldi, Wetterich 2007


Variable coupling

Wetterich 2007

• Neutrinos get a mass contribution through the cascade mechanism– Massive triplet with a cubic coupling to the Higgs doublet,

assuring a small VEV– The triplet gives mass to neutrinos: the mass term decreases

with the square of the triplet mass

m=…+MB-Ld2/Mt2

• If Mt2 depends on and crosses zero at t admitting a Taylor

expansion, then

and as approaches t the mass m increases.


Dilatation symmetry

Wetterich 2008

• Dilatation symmetry: /M /M +

– Flat potential, m = 0

• Small anomaly introduced by the potential V: in dilation, anomalies tend to vanish when a fixed point is approached.

• As approaches the flat direction exact dilatation symmetry is almost restored and the mass m keeps small

• A too naive computation of quantum fluctuations (m~2m

2 and spoils flatness) doesn’t respect dilatation

symmetry: if it’s respected than the potential stays flat and remains massless.


Variable coupling

Wetterich 2007

• Neutrinos get a mass contribution through the cascade mechanism

– SU(2)L triplet field with heavy mass Mt with a cubic coupling to the Higgs doublet

Mt2 2+Mt HH to get a small VEV < >~H2/Mt

– Then triplet gives mass to neutrinos

m=…+MB-Ld2/Mt2

• If Mt2 depends on and crosses zero at t and admits a Taylor expansion,

then

m= m/(- t )

and as approaches t the mass m increases.


Weyl scaling

]~;~[)(

~)(

~

2

1

24

gLVgZ

RgxdS mfluid

Two equivalent representations connected via ametric transformation and a redefinition of matter fields. The scaling function A() is a function of the coupling f(, R)

Coupling a scalar field to gravity is equivalent to

coupling the scalar field universally to all matter fields


• V() = M4 exp(- )

• Solutions independent of the initial conditions

• DE scales as a constant fraction tracking the background:= n/2

with n = 3(4) in MDE (RDE)

Exponential potential

Attractor solutions: Copeland, Liddle, Wands 1998,Steinhardt, Wang and Zlatev 1999, Liddle & Scherrer 1999, Wetterich 1995,

Amendola 2000, …

Need a cosmological event that triggers the end of the attractor era


valeria pettorino sissa, trieste

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