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Valeria Pettorino SISSA, Trieste

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. D.F.Mota, V.Pettorino, G.Robbers, C.Wetterich 2008.

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Valeria Pettorino SISSA, Trieste

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  1. 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 D.F.Mota, V.Pettorino, G.Robbers, C.Wetterich 2008

  2. Valeria Pettorino, SISSA BCTP, 4th October 2010 Dark energy and neutrinos This particular role of the neutrinos can be clearly linked to the particular way how neutrino-masses are generated Here a small expectation value of a heavy SU(2)L-triplet field with mass Mt is induced by a cubic coupling ζ involving the triplet and two powers of the Higgs-doublet 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 neutrinos and cosmological selection C.Wetterich, 2007 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 Growing neutrino quintessence MAVANS: Fardon etal 2004, Afshordi etal 2005, Bjaelde etal 2008, Brookfield etal 2007

  3. 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

  4. Fixed coupling Growing()coupling 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 Wetterich 2007 …the neutrino mass grows

  5. 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 

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

  7. 2  Valeria Pettorino, SISSA BCTP, 4th October 2010 Effective attractive force Neutrinos feel a STRONG attractive interaction mediated by the dark energy scalar field (cosmon) Neutrinos feel an attractive interaction mediated by the dark energy scalar field (cosmon) Typical value today   50 502 stronger than gravitational attraction   Geff = G(1 + 2) Neutrinos can cluster!

  8. Valeria Pettorino, SISSA BCTP, 4th October 2010 Very large structures • Prediction: formation of neutrino lumps at supercluster scales • Non linearities appear at z ~ 1 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

  9. Valeria Pettorino, SISSA BCTP, 4th October 2010 Non-linear analysis Non-linear fluid equations Gives us information on kinetic energy, potential energy, gravitational potential, density profile of the lump as a function of time and scale. 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

  10. Can we estimate the effect on CMB? It is a non linear problem!

  11. Valeria Pettorino, SISSA BCTP, 4th October 2010 Linear analysis is NOT sufficient Implemented CMBEASY and CAMB to solve linear perturbations k = 0.1 h/Mpc [Mota,Pettorino,Robbers,Wetterich 2008]

  12. 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 Matching linear and non-linear VP, Wintergerst, Amendola, Wetterich 2010 Linear extrapolation would predict a huge ISW in CMB for l  100 Reasonable bounds complitely eliminate this feature at those scales.

  13. Valeria Pettorino, SISSA BCTP, 4th October 2010 Criteria for linear breaking • First criterium: • non-linear whenever 1 Linear evolution can break already before that!

  14. 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

  15. 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]

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

  17. Cross correlation Valeria Pettorino, SISSA BCTP, 4th October 2010 Space for observations • CMB: • effects on l < 100; enhanced ISW • oscillations at small multipoles? • LSS: effects at large scales 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 • Detecting time dependence of neutrino masses

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

  19. 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.

  20. 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

  21. 4th TRR33 Winter school in cosmology Register now on

  22. Valeria Pettorino, SISSA BCTP, 4th October 2010 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

  23. ~500Mpc ~20Mpc 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 • At small scales • neutrinos reduce CDM • structures • Stable neutrino lumps • Brouzakis etal 2007

  24. Valeria Pettorino, SISSA BCTP, 4th October 2010 Supernovae constraints Rubin etal 2008

  25. Valeria Pettorino, SISSA BCTP, 4th October 2010 Monte Carlo analysis in progress E.Carlesi, D.Mota, V.Pettorino, G.Robbers,…

  26. Valeria Pettorino, SISSA BCTP, 4th October 2010 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

  27. 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 Implementation of CMBEASY to include general coupling mass function m() [Bean etal 2008] Monte Carlo analysis in progress! [Robbers, Pettorino]

  28. Valeria Pettorino, SISSA BCTP, 4th October 2010 Gravitational potential Wintergerst etal 2009, astro-ph/09104985 Upper bound Linear extrapolation would predict a huge ISW in CMB for l  100 Reasonable bounds complitely eliminate this feature at those scales. Distribution of lumps in space? Merging? Much smaller than the linear extrapolation!

  29. Valeria Pettorino, SISSA SISSA, 17th March 2010 Observational constraints The effect of the scalar field on the gravitational force is negligible if the mass is so large (short range) that its effect is on scales smaller than the distance between bodies. However the filed is usually light so that it’s effect is highly constrained. 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-Farese 2001 The bound on does not imply a bound on 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

  30. Valeria Pettorino, SISSA SISSA, 17th March 2010 Observational constraints The effect of the scalar field on the gravitational force is negligible if the mass is so large (short range) that its effect is on scales smaller than the distance between bodies. However the filed is usually light so that it’s effect is highly constrained. 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. Cosmology can help reconstructing the whole A() Acquaviva et al 2004 (CMB and power spectrum bound) Esposito Farese et al 2001 In teorie in cui le costanti fondamentali variano, le costanti stesse possono assumere valori locali effettivi diversi da quelli su larga scala 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(). BBN, unico bound diretto per il valore del campo nella RDE La produzione di nuclidi leggeri prodotti a T circa 0.01-10 MeV è sensibile al valore di H Coc etal 2006, Iocco etal 2008, Mangano Miele Pettorino 2005

  31. Valeria Pettorino, SISSA BCTP, 4th October 2010 Pattern for the background similar to extended quintessence Non negligible amount of dark energy in the past RAD MAT DE

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

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

  34. Valeria Pettorino, SISSA SISSA, 17th March 2010 Present Neutrinos Scalar field

  35. Valeria Pettorino, SISSA SISSA, 17th March 2010 Future attractor Amendola, Baldi, Wetterich 2007

  36. Valeria Pettorino, SISSA BCTP, 4th October 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. In the JF multiplication for : =ln  corresponds to dilatation. If in JF 4, if not constant but function (), running, anomaly. At fixed point  tends to a constant * All fundamental constants approach fixed points and can be seen that they do it exponentially with some constant in the exponential (alpha for V) U() = (*+e-) U() In EF, devide by 4. Dilatation doesn’t tell how much is . Stability gives hints for =0. Wetterich 2007

  37. 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. In the JF multiplication for : =ln  corresponds to dilatation. If in JF 4, if not constant but function (), running, anomaly. At fixed point  tends to a constant * All fundamental constants approach fixed points and can be seen that they do it exponentially with some constant in the exponential (alpha for V) U() = (*+e-) U() In EF, devide by 4. Dilatation doesn’t tell how much is . Stability gives hints for =0. Wetterich 2008

  38. 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. In the JF multiplication for : =ln  corresponds to dilatation. If in JF 4, if not constant but function (), running, anomaly. At fixed point  tends to a constant * All fundamental constants approach fixed points and can be seen that they do it exponentially with some constant in the exponential (alpha for V) U() = (*+e-) U() In EF, devide by 4. Dilatation doesn’t tell how much is . Stability gives hints for =0. Wetterich 2007

  39. 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 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)

  40. 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 the attractor era Attractor solutions: Copeland, Liddle, Wands 1998, Steinhardt, Wang and Zlatev 1999, Liddle & Scherrer 1999, Wetterich 1995, Amendola 2000, …

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