1. Fluctuations in models with sterile-  WDM Silvio Bonometto Physics Dep., Trieste Univ. & INAF, Trieste Observatory Conca Specchiulla, sep 10, 2014 Paper in collaboration with 3M’s R.Mainini, A. Macciò, I.Musco LWDM cosmologies, “spiced” with a pinch of strongly coupled CDM, meet all data LCDM fits, as well as data LCDM fails to fit sterile mass predicted?

2. LCDM cosmologies meet cosmological data down to galactic scale Problems below galactic scale: Milky Way satellite abundance LCDM N-body simulations yield 20 times more satellites than observed, for a galaxy of the MW size Klypin et al ApJ 522 (1999) 82, Moore et al. ApJ 524 (1999) L19 Dwarf galaxies exhibit a core radial density not NFW in the central region Moore, Nature 370 (1994) 629, Flores & Primack, ApJ 427 (1994) L1, Diemand et al MNRAS 364 (2005) 665, Macciò et al MNRAS 378 (2007) 55, Springel et al., MNRAS 391 (2008) 1685, de Block et al., ApJ 552(2001) L23, Oh et al., AJ 141 (2011) 193 Dwarf galaxy abundance in large voids …. hydro sim. including baryon physics reduce discrepancy to factor 2-3 bigger galaxies also found to have core M-ind’nt size 500-1000 pc more controversial

3. LWDM cosmologies halos with core e.g. Macciò et al., MNRAS 428 (2013) Core radius related to DM particle mass: To have a core around 500-1000 pc need m = 80-110 eV STERILE NEUTRINO with m \sim 90eV ?

4. a catch-22 problem: to have a dwarf galaxies with a 500-1000 pc core we cannot have dwarf galaxies however… cores & dwarfs do exist !!!

5. New class of models : LWDM spiced with a grain of DARK pepper s-LWDM models not ad-hoc deriving from finding a new tracker solution in coupled-DE models

6. galaxies clusters As previous plot in terms of power spectrum P(k)

7. Spiced LWDM cosmologies Summary Background A dual component in a stationary primeval Universe Connecting DE with inflation Stationarity break and rise of present cosmic environment Inhomogenities Linear theory Simulations: satellites and profiles Problems Early non linearity, DE-CDM decoupling Bonometto S.A., La Vacca G., Sassi G., JCAP08 (2012) 015 Bonometto S.A. & Mainini R., JCAP03 (2013) 038 Macciò A.V., Bonometto S.A., Mainini R., Musco I. (in preparation) Strong CDM-DE coupling allows fluctuations to persist also on dwarf galaxy and MW substructure scales preliminary

8. Background metric Quintessential DE covariant form Cou.DE : J.Ellis et al., PL 228B (1989) 264 C.Wetterich, A&A 301 (1995) 321 L.Amendola, PRD 69 (1999) 043501 L.A. & Tocchi-Valentini D., PRD 66 (2002)043528 …. and many many others In FRW space  data (hopefully) to yield w(a) [sooner than V(F)] coupling allows DE to keep signif. density also at high z

9. We shall forget the potential shape, just assuming w  +1 at large z, w  -1 at small z, transition at zd results mildly dependent on a d &  results mildly dep. on z d scarse dep. on  classical approaches assume cou.CDM to be only DM, then  << 1 here CDM is a tiny component main DM is uncoupled this allows quite large  w=+1 at large z is a generic feature for any choice of self-inter. potential

10. Kinetic field would dilute as a CDM would dilute as a Energy flow from CDM to DE makes both component to dilute as a --4 -- 3 -6  = (m p /b) ln(  ) f=exp[-ln(  )]=1/  L = (  )  “…. mass redshifting” density parameters during radiative expansion

12. The solution found is an ATTRACTOR Conformal Invariance

13. At high z all components share similar densities (reminding similar decoupling redshifts) in a fully stationary expansion Eve of the present epoch: T approaches m w apologies for different color choice Coupling persists down to z=0 Coupling fades after invariance break  =10

14. slow tentative …

15. fluctuation evolution equations dispersion relation

17. WDM fluc.’ns restarted & baryon fluc.’ns enhanced by large ampl. cou-CDM fluc.’ns ” Cou.CDM : NO meszaros’ effect fluc’ns in CDM continue to grow after entering the horizon, over any scale Creating deep “potential wells”

18. CMB spectra almost identical to standard LCDM even for very high  Plots obtained with modified CMBFAST

19. Transfer functions (CMBFAST)

20. A typical spectrum (m w =220 eV  = 20)

21. A possible model pathology: coup’d CDM fluc.ns may become >>1 Simplest solution: coupling should fade at low z necessarily after conformal inv. break by wdm derelativization this preserves wdm fluc’n restoration delay=Log[a(dec’g)/a(der’l’n)]

22. delay = 4 decoup’g approximatively when w shifts from +1 to -1 delay = 2 shown in the plot after dec’g sufficient that CDM+bar fluc’ns are linear however :  c<<  b models with non-linear CDM fluc’s could still be physical just hard to compute structure formation early non-linearity to modify pop III predictions 2

23. m w /eV 96.80 48.51 g*/m w = 0.980 Simulated model delay=4 decoupling at +/- transition very little changes for delay=2

24. Original simul.: L box =20 Mpc/h, N pa =300^3 zoom grid: N pa =7200^3=3.73x10^11  N pa,halo =13.1x10^6,m pa =1500 M s /h Same halo: 2.07x10^10 M s /h (within R 200 ) CDM particles (v=0) WDM particles (thermal vel) CDM pa.m w =95eV (thermal velocities)

25. Same halo: 2.07x10^10 M s /h CDM particles (v=0) 5 WDM part :1 part v=0

26. Original simul.: L box = 90 Mpc/h, N pa =300^3 zoom grid: N pa =4800^3, N pa,halo =2.4x10^6, m pa =4.57x10^5 M s /h M_halo = 1.1x10^12 M s /h (not a lucky halo choice) CDM particles WDM particles only NO small halos

27. M = 10^10 M s /h Density profiles 1kpc/h

28. MW size halo : almost overlapping profiles (but resolution is different) 1 kpc/h

29. LCDM “MW” sLWDM “MW” Satellites in 10^12 M s halo s-LWDM : reduction factor 2 / 3

30. PRELIMINARY CONCLUSIONS FROM SIMULATIONS s-LWDM LCDM 1:6 cold 10^10 profile forming core NFW intermediate Dwarf closer to NFW Galaxy satellites almost 0 in excess intermediate just a few 10^12 profile NFW in all cases Milky fattening blobs Way satellites massive satellites remain small ones vanish BUT: small halo component proportions ? reso- lution....

31. Conclusions Sub-galactic scale features hard to explain by LCDM LWDM can help: critical feature warm particle mass LWDM with particle 80-110 eV meets rotation curves, satellites, etc. LWDM spectrum for such mass unsuitable New tracker solution for cou-DE models (background) Primeval conformal invariance 2 DM component already widely considered in literature here CDM coupled + WDM uncoupled, similar primeval densities LWDM models spiced with a pinch of cold dark pepper …. tracker solution holding since inflation possible connection with inflationary dynamics linear fluctuation evolution solved Cou-CDM does not feel Meszaros effect CMB spectra identical to LCDM CDM fluc’ns re-create WDM fluc’ns excessive amplitude of CDM fluctuations: a computational problem however: once conformal invariance brocken, decoupling harmless Simulations based on s-LWDM cosmologies confirm : rotation curves, satellite problems solved Pop III physics to be revisited: early seeds mostly

32. Thanks for your attention

34. when coupling switched on w  +1 at high z for any potential Small values of  to be coherent with observational data  DE decreases when w close -1, then almost parallel to  CDM

35. 11 eq (cold uncoupled…)

37. obtained with 11 eq ad-hoc program (uncoupled DM is cold)