1. Dark Energy News on CMB and Structure Formation

2. Dark Energy Evidence

3. WMAP+ACBAR+CBI+2dF+L  Spergel et al. 2003

4. Cosmological Constant Problem

5. G+g=8T+VgG+g=8T+VgG+g=8T+VgG+g=8T+Vg Geometry Quantum Vacuum

6. Cosmological Constant Problem |  -V|/M 2 Planck. 10 -123 :::: V:

7. Cosmological Constant Problem |  -V|/M 2 Planck =10 -123 :::: V: percentaccuracy

8. for Physics for Physics Why so small with respect to any particle physics scale Why comparable to the cosmological critical density today Two Two

9. Dark Energy Models Trans-Planckian: energy stored in perturbations with wavenumber beyond the Planck scale (Mersini et al. 2001)Trans-Planckian: energy stored in perturbations with wavenumber beyond the Planck scale (Mersini et al. 2001) Spacetime microstructure: self-adjusting spacetime capable to absorbe vacuum energy (Padmanabhan, 2002)Spacetime microstructure: self-adjusting spacetime capable to absorbe vacuum energy (Padmanabhan, 2002) Matter-Energy Transition: dark matter undergoes a phase transition to dark energy at low redshifts (Basset et al. 2003)Matter-Energy Transition: dark matter undergoes a phase transition to dark energy at low redshifts (Basset et al. 2003) Brane worlds: brane tension (Shani & Sthanov 2002); cyclic-ekpyrotic cosmic vacuum (Steinhardt &Tutok 2001)Brane worlds: brane tension (Shani & Sthanov 2002); cyclic-ekpyrotic cosmic vacuum (Steinhardt &Tutok 2001) Exotic particle physics: photons oscillating in something else at cosmological distances (Csaki et al. 2002)Exotic particle physics: photons oscillating in something else at cosmological distances (Csaki et al. 2002) Chaplygin gas: dark matter and energy described by a single gas having variable equation of state (Den et al. 2003, Carturan & Finelli 2003)Chaplygin gas: dark matter and energy described by a single gas having variable equation of state (Den et al. 2003, Carturan & Finelli 2003) Scale-dependent Gravity: Gravity weaker on large scales (Dvali et al. 2003)Scale-dependent Gravity: Gravity weaker on large scales (Dvali et al. 2003) Quintessence: tracking scalar fields (Ratra & Peebles, Wetterich 1988, Coble et al. 1997, Ferreira & Joyce 1998, Liddle & Scherrer 1999, Steinhardt et al. 1999, Perrotta & Baccigalupi 1999, Brax & Martin 2000, Masiero et al. 2001, Doran et al. 2001, Corasaniti & Copeland 2003, ) Extended Quintessence: non-minimal coupling to Gravity (Chiba, Uzan 1999, Perrotta et al. 2000, Baccigalupi et al. 2000, Faraoni 2000, Bartolo & Pietroni 2000, Esposito-Farese & Polarski 2001, Perrotta & Baccigalupi 2002) Coupled Quintessence: coupling with dark matter (Carroll 1998, Amendola 2000, Matarrese et al. 2003) k-essence: modified kinetic scalar field energy (Aramendariz-Picon et al. 2001, Caldwell 2002, Malquarti et al. 2003)

10. Quintessence Field  !  (t)+   (t,x), U(  )

11.  vs.  Background energy density: dynamical,  t 2 /2+U(  ) Background pressure: dynamical,  t 2 /2-U(  ) Fluctuations,  (t,x) Background energy density:  =constant Background energy density: p=-constant No fluctuations Constant equation of state, w=p/  Dynamical equation of state, w=p/ 

12. Quintessence Field  !  (t)+   (t,x), U(  ) U(  ) /   (Ratra & Peebles 1988) U(  ) / cos   (Coble et al. 1997) U(  ) / exp   (Wetterich 1988) … U(  ) /   exp(  2 )(Brax & Martin 2000)

13. w today WMAP+ACBAR+CBI+2dF+Ly  Spergel et al. 2003 w < -0.8 (2  )

14. Effects on the CMB Power Spectrum Projection Projection Integrated Sachs-Wolfe Integrated Sachs-Wolfe

15. Dark Energy & CMB power spectrum Balbi et al. 2001, Baccigalupi et al. 2002:evidence for w ' –0.8, h fixed and  =1 Balbi et al. 2001, Baccigalupi et al. 2002:evidence for w ' –0.8, h fixed and  =1 Efstathiou 2002: tensor degeneracy for cosmological parameters Efstathiou 2002: tensor degeneracy for cosmological parameters Bean & Melchiorri 2002: degeneracy with hBean & Melchiorri 2002: degeneracy with h Balbi et al. 2003: degeneracy with Balbi et al. 2003: degeneracy with 

16. A CMBfast plug-in for scalar field dark energy DE fast Features: Quintessence evolution in ordinary and scalar-tensor cosmology SUGRA and RP tracking trajectories Scalar field fluctuations User specifies  Q, w 0, and the scenario to obtain the right trajectory

17. Dark Energy & CMB power spectrum

18. Dark Energy & CMB: beyond C l s Giovi et al. 2003, PRD in press, astro-ph/0308118

19. CMB bispectrum B l m l` m` l`` m`` =a lm a l`m` a l``m`` a lm = s  (  )Y lm (  )d  B l l`l`` =  m m` m`` ( m l m` l` m`` l`` ) a lm a l`m` a l``m`` l l` l``  (  ) ´  T(  )/T

20. CMB bispectrum & Structure Formation =0 =0  0  0

21. CMB bispectrum & Structure Formation =[(2l+1)(2l`+1)(2l``+1)/16  ] 1/2 ( 0 l 0 l` 0`` l`` ) ¢ =[(2l+1)(2l`+1)(2l``+1)/16  ] 1/2 ( 0 l 0 l` 0`` l`` ) ¢ ¢ [l(l+1)- l`(l`+1)+ l``(l``+1) ] C l Q(l``) +Perm. Q(l)= s 0 dec D(z) F(z) dz D(z)=[r(z dec )-r(z)]/r(z dec )r(z) 3 F(z)=dP  /dz| k=l/r(z) P  =(3  m0 /2) 2 (H 0 /ck) 4 P(k,z)(1+z) 2 P(k,z)=Ak n T(k,z) 2  (  ) =  lss (  +  )+  ISW '  lss (  )+ r  lss (  ) ¢   ISW (  )=2 s 0 dec dr d  (r,  )/d   =2 s 0 dec dr[(r-r dec )/r dec r]  r,  ) Hu & White 1997, Bartelmann & Schneider 2001, Komatsu & Spergel 2001, Verde & Spergel 2002

22. CMB bispectrum & Structure Formation l -1 =2  /k=r(z 3 )/l =2  /k=r(z 3 )/l =r(z 2 )/l =r(z 2 )/l =r(z 1 )/l =r(z 1 )/l r(z 1 ) r(z 2 ) r(z 3 ) z1z1z1z1 z2z2z2z2 z3z3z3z3 z r

23. CMB bispectrum line of sight chronology l -1 horizon crossing,  decaying linearly, dQ/dz>0 z !1 :super-horizon scales in a flat CDM universe, dP  /d  =0, dQ/dz ! 0 z r Non-linearity,  grows, dQ/dz<0 z ! 0, vanishes, dQ/dz ! 0 onset of acceleration, change in cosmic equation of state,  decaying linearly, dQ/dz>0

24. CMB bispectrum line of sight distribution Giovi et al. 2003, PRD in press, astro-ph/0308118

25. CMB bispectrum & Dark Energy Quintessence reference models SUGRA RP

26. CMB bispectrum & Dark Energy Giovi et al. 2003, PRD in press, astro-ph/0308118 Ma et al. 1999, Smith et al. 2003

27. CMB bispectrum & Dark Energy Giovi et al. 2003, PRD in press, astro-ph/0308118

28. CMB bispectrum & Dark Energy Giovi et al. 2003, PRD in press, astro-ph/0308118

29. CMB bispectrum & Dark Energy Giovi et al. 2003, PRD in press, astro-ph/0308118

30. CMB bispectrum & Structure Formation =0 =0  0  0 Giovi, Liguori et al. 2004, in preparation  =2 s 0 dec dr[(r-r dec )/r dec r]  r,  )

31. N-body in Dark Energy Cosmology Dolag et al. 2003, A&A submitted, see also Klypin et al. 2003, Linder & Jenkins 2003

32. N-body in Dark Energy Cosmology Dolag et al. 2003, A&A submitted GADGET (Springel et al. 2001) initial box: 512 3 particles, side = 479h -1 M ,  8 today fixed to 0.9 Dark energy in background expansion, linear growth rate Haloes fitted with NFW

33. N-body in Dark Energy Cosmology Dolag et al. 2003, A&A submitted Quintessence reference models

34. N-body in Dark Energy Cosmology Dolag et al. 2003, A&A submitted  tt +2H  t –4  G   =0, D + (z)=  (z)/  0

35. N-body in Dark Energy Cosmology Dolag et al. 2003, A&A submitted c(M,z)=c 0 /(1+z)(M/10 14 h  M  ) 

36. N-body in Dark Energy Cosmology Dolag et al. 2003, A&A submitted c(M,z)=[c 0 /(1+z)](M/10 14 h  M  )  is c 0 dependent on the dark energy dynamics? can such dependence be predicted? c 0 ! c 0  CDM ¢ D + (z coll ) / D +  CDM (z coll )

37. Dark Energy in Generalized Cosmologies L=f( ,R)/2-[  (  )/2]  ;   ;  -U(  )- -  k [  ;  ;  +V(  k )+W( ,  k )] -  k [  ;  ;  +V(  k )+W( ,  k )]

38. Dark Energy in Generalized Cosmologies L=f( ,R)/2-[  (  )/2]  ;   ;  -U(  )- -  k [  ;  ;  +V(  k )+W( ,  k )] -  k [  ;  ;  +V(  k )+W( ,  k )] Quintessence

39. Dark Energy in Generalized Cosmologies L=f( ,R)/2-[  (  )/2]  ;   ;  -U(  )- -  k [  ;  ;  +V(  k )+W( ,  k )] -  k [  ;  ;  +V(  k )+W( ,  k )] Extended Quintessence

40. Dark Energy in Generalized Cosmologies L=f( ,R)/2-[  (  )/2]  ;   ;  -U(  )- -  k [  ;  ;  +V(  k )+W( ,  k )] -  k [  ;  ;  +V(  k )+W( ,  k )] Coupled Quintessence

41. Dark Energy in Generalized Cosmologies L=f( ,R)/2-[  (  )/2]  ;   ;  -U(  )- -  k [  ;  ;  +V(  k )+W( ,  k )] -  k [  ;  ;  +V(  k )+W( ,  k )] k-essence

42. Dark Energy in Generalized Cosmologies L=f( ,R)/2-[  (  )/2]  ;   ;  -U(  )- -  k [  ;  ;  +V(  k )+W( ,  k )] -  k [  ;  ;  +V(  k )+W( ,  k )] New Gravity

43. Bravely facing the Coincidence What happens at that epoch? Cosmic acceleration is a recent occurrence, say z of order unity … funny physics: the formation of cosmological clumps affects the cosmological vacuum state matter over-densities move the dark energy field out of the potential minimum

44. Extended Quintessence & New Gravity H 2 = (8  G/3)[  + stuff ] stuff = (1/8  GF)[  (1-8  G F) +  t 2 /2+(RF-f)/2+V-3HF t ] H t = - 4  G[  + p + stuff ] stuff = (1/8  GF)[(  p)(1-8  G F) +  t 2 +F tt -HF t ] non-minimal coupling: f=F ¢ R new gravity: f(R)  R/8  G Hwang 1991, generalized cosmologies F=  f /  R

45. Extended Quintessence  k 2 =4  k 3 (  /  ) k 2 Perrotta, Baccigalupi, Matarrese, PRD 2000, Baccigalupi, Matarrese, Perrotta, PRD 2000   m  m  m  m c 2 eff,   1  G= T G= T G= T G= T Perrotta, Baccigalupi 2002  G= T  G= T  G= T  G= T Perrotta et al. 2003, PRD submitted

46. Non-linear Clustering in Extended Quintessence  G= T  G= T  G= T  G= T ds 2 =a 2 [(-1+2  )d  2 +(1-2  )  ij dx i dx j ] r 2  = (1/2F)[a 2  m +a 2  U+ r 2 (  F)+| r (  | 2 /2] r 2  =(1/2F)[a 2  m -2a 2  U- r 2 (  F)] r 2 (  ) =a 2  U-(dF/d  /2F)[a 2  m +4a 2  U+3 r 2 (  F)+| r (  | 2 /2]-a 2  (dF/d  )R Perrotta et al. 2003, PRD submitted

47. Non-linear Clustering in Extended Quintessence  G= T  G= T  G= T  G= T ds 2 =a 2 [(-1+2  )d  2 +(1-2  )  ij dx i dx j ] r 2  = (1/2F)[a 2  m +a 2  U+ r 2 (  F)+| r (  | 2 /2] r 2  =(1/2F)[a 2  m -2a 2  U- r 2 (  F)] r 2 (  ) =a 2  U-(dF/d  /2F)[a 2  m +4a 2  U+3 r 2 (  F)+| r (  | 2 /2]-a 2  (dF/d  )R Perrotta et al. PRD 2004

48. Continua… CMB & bispectrum,*observability*, vary cosmological parameters, non-linearity, … CMB & bispectrum,*observability*, vary cosmological parameters, non-linearity, … N-body, gain statistics, check concentration dependence on w(z), *lensing*… N-body, gain statistics, check concentration dependence on w(z), *lensing*… Generalized cosmologies, are *dark haloes* affected? If so, check with N-body, …Generalized cosmologies, are *dark haloes* affected? If so, check with N-body, …

49. Dark Energy