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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 1012 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~2m2 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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