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Neutrino clustering in interacting Dark Energy cosmologies

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Neutrino clustering in interacting Dark Energy cosmologies Powered By Docstoc
					   Growing neutrino quintessence:
     large structures and CMB

                     Valeria Pettorino
                           SISSA, Trieste

In collaboration with:

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


                     04.10.10 BCTP Workshop, Bonn
           Dark energy and neutrinos
   New role for neutrinos: significant influence in cosmology?

   Connection between neutrinos and dark energy properties

      Growing matter
      L.Amendola, M.Baldi, C.Wetterich 2007                          Growing
      Growing neutrinos and cosmological selection                    neutrino
      C.Wetterich, 2007
                                                                   quintessence
      Neutrino clustering in growing neutrino quintessence
      D.Mota, V.P., G.Robbers, C.Wetterich, Feb 2008
      Very large scale structures in growing neutrino quintessence
      N.Wintergerst, V.P., D.Mota, C.Wetterich, Oct. 2009
      Neutrino lumps and the Cosmic Microwave Background
      V.P. N.Wintergerst, L.Amendola, C.Wetterich, Sept.2010


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


Valeria Pettorino, SISSA                                             BCTP, 4th October 2010
                    Coupled dark energy
                        cosmologies

         Many (observable) things can happen when you have
        dynamical dark energy interacting with other species


Valeria Pettorino, SISSA                          BCTP, 4th October 2010
           Coupling between DE and 
                                   For a multicomponent system, the stress energy
                                   tensor of the single species is in general not
                                   conserved.
    Kodama&Sasaki 1984, Ma & Bertschinger 1995, Wetterich 1995, Amendola 2000, …




   DE as a scalar field


                                       

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

           Fixed  coupling                                   Growing () coupling



                                                                                   Wetterich 2007
                              …the neutrino mass grows
Valeria Pettorino, SISSA                                                   BCTP, 4th October 2010
 Cosmological trigger for dark energy
          Dark energy in an exponential potential + coupling




                                 Without coupling, dark energy tracks
                                     the background (attractor)

                                                   Neutrino mass grows

                                  Neutrinos become non relativistic



                                     The coupling almost stops 


Valeria Pettorino, SISSA                              BCTP, 4th October 2010
                  Large scale structures




Valeria Pettorino, SISSA             BCTP, 4th October 2010
           Effective attractive force
          Neutrinos feel a attractive interaction mediated
         Neutrinos feel an STRONG attractive interaction by
                the dark dark energy scalar field (cosmon)
         mediated by the energy scalar field (cosmon)


                                                      2     
    Typical value today   50

    502 stronger than                                     
    gravitational attraction
                                        Geff = G(1 + 2)


                       Neutrinos can cluster!

Valeria Pettorino, SISSA                            BCTP, 4th October 2010
                  Very large structures
   • Non linearities                  • Prediction: formation of
     appear at z ~ 1                       neutrino lumps at
                                          supercluster scales
       Stable neutrino lumps: typical scale 10 – 100 Mpc …and beyond

         Non linear investigation of individual neutrino lumps

                                         Wintergerst, Pettorino, Mota, Wetterich
                                         astro-ph/09104985 & PRD




Valeria Pettorino, SISSA                                    BCTP, 4th October 2010
                       Non-linear analysis
     Non-linear fluid equations



                                                       Combination of a
                                                    gravitational potential
                                                    and a neutrino induced
                                                   potential which depends
                                                      on the value of the
                                                            cosmon




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

Valeria Pettorino, SISSA                                    BCTP, 4th October 2010
Can we estimate the effect on
            CMB?


     It is a non linear problem!
      Linear analysis is NOT sufficient
                                          Implemented
                                          CMBEASY and CAMB
                                          to solve linear perturbations




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

Valeria Pettorino, SISSA                               BCTP, 4th October 2010
      Matching linear and non-linear
                VP, Wintergerst, Amendola, Wetterich 2010




                                linear                      non-linear

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

Valeria Pettorino, SISSA                                         BCTP, 4th October 2010
          Criteria for linear breaking

          First criterium:

          non-linear whenever 1


          Linear evolution can break already before that!




Valeria Pettorino, SISSA                           BCTP, 4th October 2010
                           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


Valeria Pettorino, SISSA                                   BCTP, 4th October 2010
          Criteria for linear breaking

    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




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

Valeria Pettorino, SISSA                          BCTP, 4th October 2010
                      Effect on the CMB




Valeria Pettorino, SISSA              BCTP, 4th October 2010
                Space for observations
   • CMB:
        - effects on l < 100; enhanced ISW
        - oscillations at small multipoles?
                                                   Cross correlation

     • LSS: effects at large scales




     In general, Dark energy interactions
      can have significant effects at the     Baldi, VP, Robbers, Springel 2008
        non-linear level (high-z massive
                                                       Baldi, VP 2010
                  clusters, …)


   • Detecting time dependence of neutrino masses


Valeria Pettorino, SISSA                                     BCTP, 4th October 2010
                           Conclusions
    • Dark energy interactions can give important observable effects




Valeria Pettorino, SISSA                               BCTP, 4th October 2010
                            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.




Valeria Pettorino, SISSA                                     BCTP, 4th October 2010
                            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

Valeria Pettorino, SISSA                                     BCTP, 4th October 2010
4th TRR33 Winter school in cosmology




Register now on
Dark energy - neutrino connection

           Dark energy and neutrino properties are related!

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



         DE- fluid equation of
         state


Valeria Pettorino, SISSA                           BCTP, 4th October 2010
                     Neutrino clustering
                                 Mota,Pettorino,Robbers,Wetterich 2008
  • Neutrino structures
    become non linear at
    z ~ 1 for
    supercluster scales
                               ~500Mpc      ~20Mpc
  • At small scales
    neutrinos reduce CDM
    structures
 • Stable neutrino lumps
    Brouzakis etal 2007




Valeria Pettorino, SISSA                         BCTP, 4th October 2010
               Supernovae constraints




                                 Rubin etal 2008

Valeria Pettorino, SISSA           BCTP, 4th October 2010
                     Monte Carlo analysis in progress
                            E.Carlesi, D.Mota, V.Pettorino, G.Robbers,…
Valeria Pettorino, SISSA                                       BCTP, 4th October 2010
   Conclusions for Quintessence - CDM
  • Interaction keeps DE and DM closer in the background evolution
                                 See also Mangano, Miele, Pettorino 2005
  • 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
Valeria Pettorino, SISSA                                 BCTP, 4th October 2010
                           CMB constraints

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


  [Bean etal 2008]

             WARNING:
       constraints for constant
          coupling models
                                  [Bean etal 2008]
   Implementation of CMBEASY
    to include general coupling       Monte Carlo analysis in progress!
        mass function m()                        [Robbers, Pettorino]

Valeria Pettorino, SISSA                              BCTP, 4th October 2010
                 Gravitational potential
                                    Wintergerst etal 2009, astro-ph/09104985



                                               Upper bound




                       Distribution of lumps in space?
                                  Merging?
                  Much smaller than the linear extrapolation!
Valeria Pettorino, SISSA                                                BCTP, 4th October 2010
    Observational constraints
       Bounds on the variation of the gravitational constant and/or on the
       coupling to (baryonic) matter
                                   Solar system experiments
       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 al
                                                                                              2005

                                                                                             Esposito-
                                                                                              Farese
                                                                                               2004




                  .                                .             .
                                                                                                  Esposito-
  The bound on G/ G does not imply a bound on F/ F              G Neff / GNeff  6 1012 yr 1    Farese
                                                                                                    2001
  For example if A() = cos then GNeff = G*(1+(A,)2)= G* (cos2 + sin2 ) = G*
                                         Binary pulsars
        Pulses of rapidly rotating neutron stars constrain 0>  4.5

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.
        JBD  120     Acquaviva et al        Cosmology can help
                            2004               reconstructing the     Esposito Farese et al
       F ( )   2   (CMB and power               whole A()                2001
                      spectrum bound)

                                         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 2005

Valeria 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




Valeria Pettorino, SISSA                 BCTP, 4th October 2010
                     Linear perturbations




Valeria Pettorino, SISSA                BCTP, 4th October 2010
                           More perturbations




     k = 0.1 h/Mpc
     (Supercluster scales)          Mota, Pettorino, Robbers, Wetterich 2008
Valeria Pettorino, SISSA                                 SISSA, 17th March 2010
                           Present


      Neutrinos



     Scalar field




Valeria Pettorino, SISSA             SISSA, 17th March 2010
                           Future attractor




                                      Amendola, Baldi, Wetterich 2007


Valeria Pettorino, SISSA                            SISSA, 17th March 2010
                           Variable coupling
    • 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.
                                                             Wetterich 2007

Valeria Pettorino, SISSA                                BCTP, 4th October 2010
                           Dilatation symmetry
    • 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.



                                                          Wetterich 2008
Valeria Pettorino, SISSA                              BCTP, 4th October 2010
                           Variable coupling
    • 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.
                                                                  Wetterich 2007

Valeria Pettorino, SISSA                                     BCTP, 4th October 2010
                            Weyl scaling


       Coupling a scalar field to gravity is equivalent to


                coupling the scalar field universally to all matter fields

                     R 1~                      ~                 ~ ; g ]
         S  d x  g
                  4
                          Z ( ) g      V ( )  L fluid [ m ~  
                                   

                      2 2                                                

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


Valeria Pettorino, SISSA                                         BCTP, 4th October 2010
                   Exponential potential
 • 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)


Need a cosmological event that triggers the end of
              Attractor solutions: Copeland, Liddle, Wands 1998,

                                attractor
                         the Amendola 2000, …era
  Steinhardt, Wang and Zlatev 1999, Liddle & Scherrer 1999, Wetterich 1995,

Valeria Pettorino, SISSA                                 BCTP, 4th October 2010

				
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