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Dark Energy

Dark Energy . L. News on CMB and Structure Formation. f. L. Dark Energy Evidence . f. L. Dark Energy Evidence . f. Spergel et al. 2003. WMAP+ACBAR+CBI+2dF+L . L. Cosmological Constant Problem . G  n = 8 p T mn. f. L. Cosmological Constant Problem . Geometry .

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Dark Energy

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  1. Dark Energy L News on CMB and Structure Formation f

  2. L Dark Energy Evidence f

  3. L Dark Energy Evidence f Spergel et al. 2003 WMAP+ACBAR+CBI+2dF+L

  4. L Cosmological Constant Problem Gn=8pTmn f

  5. L Cosmological Constant Problem Geometry Gmn+gmn=8pTmn+Vgmn f Quantum Vacuum

  6. L Cosmological Constant Problem : ? |-V|/M2Planck.10-123 f 2 V: ? M Planck

  7. L Cosmological Constant Problem : ? percent accuracy |-V|/M2Planck=10-123 f 2 V: ? M Planck

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

  9. L Dark Energy Models • 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) • 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) • 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) • 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) f

  10. L Quintessence Field L!f(t)+f(t,x), U(f) f

  11. f vs. L L Background energy density: r=constant Background energy density: p=-constant Constant equation of state, w=p/r=-1 No fluctuations Background energy density: dynamical, ft2/2+U(f) f Background pressure: dynamical, ft2/2-U(f) Dynamical equation of state, w=p/r>-1 Fluctuations, df(t,x)

  12. L Quintessence Field L!f(t)+f(t,x), U(f) U(f)/fa (Ratra & Peebles 1988) U(f)/ exp f(Wetterich 1988) U(f)/ cos f(Coble et al. 1997) U(f)/fa exp(f2)(Brax & Martin 2000) … f

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

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

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

  16. DEfast L A CMBfast plug-in for scalar field dark energy Features: Quintessence evolution in ordinary and scalar-tensor cosmology SUGRA and RP tracking trajectories Scalar field fluctuations User specifies WQ, w0, and the scenario to obtain the right trajectory f

  17. L Dark Energy & CMB power spectrum f

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

  19. CMB bispectrum L Q (W ) ´dT(W )/T alm=sQ (W )Ylm(W )dW Blm l`m`l``m``=alm al`m` al``m`` Bl l`l``=åm m` m`` (mlm`l`m``l``) alm al`m` al``m`` l f l`` l`

  20. CMB bispectrum & Structure Formation L < Blm l`m`l``m`` >=0 < Blm l`m`l``m`` >0 f

  21. CMB bispectrum & Structure Formation L Q (W ) =Qlss(W +dW)+QISW 'Qlss(W)+rQlss(W)¢dW QISW(W )=2s0decdr dY (r,W )/dh dW =2s0decdr[(r-rdec)/rdecr]Y(r,W) <Bl l`l``>=[(2l+1)(2l`+1)(2l``+1)/16p]1/2(0l0l`0``l``) ¢ ¢ [l(l+1)- l`(l`+1)+ l``(l``+1) ]Cl Q(l``) +Perm. D(z)=[r(zdec)-r(z)]/r(zdec)r(z)3 f Q(l)=s0dec D(z) F(z) dz F(z)=dPY/dz|k=l/r(z) PY=(3Wm0 /2)2(H0/ck)4P(k,z)(1+z)2 P(k,z)=AknT(k,z)2 Hu & White 1997, Bartelmann & Schneider 2001, Komatsu & Spergel 2001, Verde & Spergel 2002

  22. CMB bispectrum & Structure Formation L z r l =2p /k=r(z3)/l z3 r(z3) l =r(z2)/l z2 r(z2) l =r(z1)/l f z1 r(z1) l-1

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

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

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

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

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

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

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

  30. CMB bispectrum & Structure Formation < Blm l`m`l``m`` >=0 < Blm l`m`l``m`` >0 dW =2s0decdr[(r-rdec)/rdecr]Y(r,W) Giovi, Liguori et al. 2004, in preparation

  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 GADGET (Springel et al. 2001) initial box: 5123 particles, side = 479h-1M , s8 today fixed to 0.9 Dark energy in background expansion, linear growth rate Haloes fitted with NFW Dolag et al. 2003, A&A submitted

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

  34. N-body in Dark Energy Cosmology dtt+2Hdt –4p Grd =0, D+(z)=d(z)/d0 Dolag et al. 2003, A&A submitted

  35. N-body in Dark Energy Cosmology L c(M,z)=c0 /(1+z)(M/1014h-1M)a f Dolag et al. 2003, A&A submitted

  36. N-body in Dark Energy Cosmology L is c0 dependent on the dark energy dynamics? can such dependence be predicted? f c(M,z)=[c0 /(1+z)](M/1014h-1M)a c0 ! c0L CDM¢ D+(zcoll) / D+L CDM(zcoll) Dolag et al. 2003, A&A submitted

  37. Dark Energy in Generalized Cosmologies L L=f(f ,R)/2-[w(f)/2]f;mf ;m-U(f )- -åk[y;m;m +V(yk)+W(f,yk)] G ,f ,y , ...

  38. Dark Energy in Generalized Cosmologies L Quintessence L=f(f ,R)/2-[w(f)/2]f;mf ;m-U(f )- -åk[y;m;m +V(yk)+W(f,yk)] G ,f ,y , ...

  39. Dark Energy in Generalized Cosmologies L Extended Quintessence L=f(f ,R)/2-[w(f)/2]f;mf ;m-U(f )- -åk[y;m;m +V(yk)+W(f,yk)] G ,f ,y , ...

  40. Dark Energy in Generalized Cosmologies L L=f(f ,R)/2-[w(f)/2]f;mf ;m-U(f )- -åk[y;m;m +V(yk)+W(f,yk)] Coupled Quintessence G ,f ,y , ...

  41. Dark Energy in Generalized Cosmologies L k-essence L=f(f ,R)/2-[w(f)/2]f;mf ;m-U(f )- -åk[y;m;m +V(yk)+W(f,yk)] G ,f ,y , ...

  42. Dark Energy in Generalized Cosmologies L New Gravity L=f(f ,R)/2-[w(f)/2]f;mf ;m-U(f )- -åk[y;m;m +V(yk)+W(f,yk)] G ,f ,y , ...

  43. Bravely facing the Coincidence Cosmic acceleration is a recent occurrence, say z of order unity … What happens at that epoch? 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 L H2 = (8p G/3)[r + stuff ] stuff = (1/8p GF)[r(1-8p G F) +ft2/2+(RF-f)/2+V-3HFt] F=¶ f /¶ R Ht = - 4p G[r + p + stuff ] stuff = (1/8p GF)[(r+p)(1-8p G F) +ft2+Ftt-HFt] G non-minimal coupling: f=F¢ R ,f new gravity: f(R) R/8p G ,y , ... Hwang 1991, generalized cosmologies

  45. Extended Quintessence L d Gmn=d Tmn Perrotta, Baccigalupi, Matarrese, PRD 2000, Baccigalupi, Matarrese, Perrotta, PRD 2000 dk2=4p k3(dr /r)k2 m c2eff,  1 Perrotta, Baccigalupi 2002 G ,f ,y d Gmn=D Tmn , ... Perrotta et al. 2003, PRD submitted

  46. Non-linear Clustering in Extended Quintessence L d Gmn=D Tmn ds2=a2[(-1+2F)dh2+(1-2Y)gijdxidxj] r2Y = (1/2F)[a2Drm+a2D U+r 2(D F)+|r(Df) |2/2] r2F=(1/2F)[a2Drm-2a2D U-r 2(D F)] r2(Df) =a2D U-(dF/df /2F)[a2Drm+4a2D U+3r 2(D F)+|r(Df) |2/2]-a2D (dF/df )R G ,f ,y , ... Perrotta et al. 2003, PRD submitted

  47. Non-linear Clustering in Extended Quintessence L d Gmn=D Tmn ds2=a2[(-1+2F)dh2+(1-2Y)gijdxidxj] r2Y = (1/2F)[a2Drm+a2D U+r 2(D F)+|r(Df) |2/2] r2F=(1/2F)[a2Drm-2a2D U-r 2(D F)] r2(Df) =a2D U-(dF/df /2F)[a2Drm+4a2D U+3r 2(D F)+|r(Df) |2/2]-a2D (dF/df )R G ,f ,y , ... Perrotta et al. PRD 2004

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

  49. L Dark Energy f

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