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Dark Energy Dark Energy News on CMB and News on CMB and Structure Structure FormationFormation
Dark Energy Evidence Dark Energy Evidence
Dark Energy Evidence Dark Energy Evidence
WMAP+ACBAR+CBI+2dF+LWMAP+ACBAR+CBI+2dF+L
Spergel et al. 2003Spergel et al. 2003
Cosmological Constant Problem Cosmological Constant Problem
GG==88TT
Cosmological Constant Problem Cosmological Constant Problem
GG++gg==88TT++VVgg
Geometry Geometry
Quantum VacuumQuantum Vacuum
Cosmological Constant Problem Cosmological Constant Problem
||-V|/M-V|/M22PlanckPlanck .. 10 10-123-123
::
V:V:
Cosmological Constant Problem Cosmological Constant Problem
||-V|/M-V|/M22PlanckPlanck =10 =10-123-123
::
V:V:
percent percent accuracyaccuracy
for Physics for Physics
Why so small with Why so small with respect to any respect to any
particle physics particle physics scalescale
Why Why comparable to comparable to
the the cosmological cosmological
critical density critical density todaytoday
Two Two
Dark Energy Models Dark Energy Models • Trans-PlanckianTrans-Planckian: : energy stored in perturbations with wavenumber beyond the energy stored in perturbations with wavenumber beyond the
Planck scale (Mersini et al. 2001)Planck scale (Mersini et al. 2001)• Spacetime microstructureSpacetime microstructure: self-adjusting spacetime capable to absorbe vacuum : self-adjusting spacetime capable to absorbe vacuum
energy (Padmanabhan, 2002)energy (Padmanabhan, 2002)• Matter-Energy TransitionMatter-Energy Transition: dark matter undergoes a phase transition to dark energy : dark matter undergoes a phase transition to dark energy
at low redshifts (Basset et al. 2003)at low redshifts (Basset et al. 2003)• Brane worldsBrane worlds: brane tension (Shani & Sthanov 2002); cyclic-ekpyrotic cosmic : brane tension (Shani & Sthanov 2002); cyclic-ekpyrotic cosmic
vacuum (Steinhardt &Tutok 2001)vacuum (Steinhardt &Tutok 2001)• Exotic particle physicsExotic particle physics: photons oscillating in something else at cosmological : photons oscillating in something else at cosmological
distances (Csaki et al. 2002)distances (Csaki et al. 2002)• Chaplygin gasChaplygin gas: dark matter and energy described by a single gas having variable : dark matter and energy described by a single gas having variable
equation of state (Den et al. 2003, Carturan & Finelli 2003)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)
Quintessence Field Quintessence Field
!! (t)+(t)+(t,x), U((t,x), U())
vs. vs.
Background energy density: dynamical, Background energy density: dynamical, tt22/2+U(/2+U())
Background pressure: dynamical, Background pressure: dynamical, tt22/2-U(/2-U())
Fluctuations, Fluctuations, (t,x)(t,x)
Background energy density: Background energy density: =constant=constant
Background energy density: p=-constantBackground energy density: p=-constant
No fluctuationsNo fluctuations
Constant equation of state, w=p/Constant equation of state, w=p/
Dynamical equation of state, w=p/Dynamical equation of state, w=p/
Quintessence Field Quintessence Field
!! (t)+(t)+(t,x), U((t,x), U())U(U())// (Ratra & Peebles 1988)(Ratra & Peebles 1988)
U(U())// cos cos (Coble et al. 1997)(Coble et al. 1997)
U(U())// exp exp (Wetterich 1988)(Wetterich 1988)
……
U(U())// exp(exp(22)(Brax & Martin 2000))(Brax & Martin 2000)
w today w today
WMAP+ACBAR+CBI+2dF+LyWMAP+ACBAR+CBI+2dF+Ly
Spergel et al. 2003Spergel et al. 2003
w < -0.8 w < -0.8 (2(2 ) )
Effects on the CMB Power Spectrum Effects on the CMB Power Spectrum • ProjectionProjection• Integrated Sachs-WolfeIntegrated Sachs-Wolfe
Dark Energy & CMB power spectrumDark Energy & CMB power spectrum
• Balbi et al. 2001, Baccigalupi et al. Balbi et al. 2001, Baccigalupi et al. 2002:evidence for w2002:evidence for w'' –0.8, h fixed and –0.8, h fixed and =1 =1 • Efstathiou 2002: tensor degeneracy for Efstathiou 2002: tensor degeneracy for cosmological parameterscosmological parameters•Bean & Melchiorri 2002: degeneracy with hBean & Melchiorri 2002: degeneracy with h•Balbi et al. 2003: degeneracy with Balbi et al. 2003: degeneracy with
A CMBfast plug-in for scalar field dark energyA CMBfast plug-in for scalar field dark energy
DEDEfastfast
Features:Features:Quintessence evolution in ordinary and scalar-tensor cosmologyQuintessence evolution in ordinary and scalar-tensor cosmology
SUGRA and RP tracking trajectoriesSUGRA and RP tracking trajectories
Scalar field fluctuationsScalar field fluctuations
User specifies User specifies QQ, w, w00, and the scenario to obtain the right trajectory, and the scenario to obtain the right trajectory
Dark Energy & CMB power spectrumDark Energy & CMB power spectrum
Dark Energy & CMB: beyond CDark Energy & CMB: beyond Cl l s s
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
CMB bispectrum CMB bispectrum
BBllm m
l`l`m`m`
l``l``m``m``=a=almlm a al`m`l`m` a al``m``l``m``
aalmlm==ss ( ( )Y )Ylmlm(( )d )d
BBl l`l``l l`l``==m m` m``m m` m`` ( (mmllm`m`
l`l`m``m``
l``l``) a) almlm a al`m`l`m` a al``m``l``m``
ll
l`l`l``l``
(( ) ) ´́ T(T( )/T )/T
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >=0>=0
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >> 0 0
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
<B<Bl l`l``l l`l``>=[(2l+1)(2l`+1)(2l``+1)/16>=[(2l+1)(2l`+1)(2l``+1)/16]]1/21/2((00ll00
l`l`0``0``
l``l``) ) ¢¢
¢ ¢ [l(l+1)- l`(l`+1)+ l``(l``+1) ][l(l+1)- l`(l`+1)+ l``(l``+1) ] CCl l Q(l``)Q(l``) +Perm. +Perm.
Q(l)=Q(l)=ss00dec dec D(z) F(z) D(z) F(z)
dzdz
D(z)=[r(zD(z)=[r(zdecdec)-r(z)]/r(z)-r(z)]/r(zdecdec)r(z))r(z)33
F(z)=dPF(z)=dP/dz|/dz|k=l/r(z)k=l/r(z)
PP=(3=(3m0 m0 /2)/2)22(H(H00/ck)/ck)44P(k,z)(1+z)P(k,z)(1+z)22 P(k,z)=AkP(k,z)=AknnT(k,z)T(k,z)22
(( ) = ) =lsslss((++)+)+ISW ISW '' lsslss(()+)+rrlsslss(())¢¢
ISWISW(( )=2 )=2ss00decdecdr ddr d (r, (r, )/d )/d
=2=2ss00decdecdr[(r-rdr[(r-rdecdec)/r)/rdecdecr]r]r,r,))
Hu & White 1997, Bartelmann & Schneider 2001, Hu & White 1997, Bartelmann & Schneider 2001, Komatsu & Spergel 2001, Verde & Spergel 2002Komatsu & Spergel 2001, Verde & Spergel 2002
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
ll-1-1
=2=2 /k=r(z /k=r(z33)/l)/l
=r(z=r(z22)/l)/l
=r(z=r(z11)/l)/l
r(zr(z11))
r(zr(z22))
r(zr(z33))
zz11
zz22
zz33
zzrr
CMB bispectrum line of sight chronology CMB bispectrum line of sight chronology
ll-1-1
horizon crossing, horizon crossing, decaying linearly, dQ/dz>0 decaying linearly, dQ/dz>0
zz!1!1 :super-horizon scales in a flat :super-horizon scales in a flat CDM universe, dPCDM universe, dP/d/d =0, dQ/dz =0, dQ/dz!! 0 0
zzrr
Non-linearity, Non-linearity, grows, dQ/dz<0 grows, dQ/dz<0
zz!! 0, 0, vanishes, dQ/dz vanishes, dQ/dz!! 0 0
onset of acceleration, change in cosmic onset of acceleration, change in cosmic equation of state, equation of state, decaying linearly, dQ/dz>0 decaying linearly, dQ/dz>0
CMB bispectrum line of sight distributionCMB bispectrum line of sight distribution
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy Quintessence reference modelsQuintessence reference models
SUGRASUGRA
RPRP
CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
Ma et al. Ma et al. 1999, 1999,
Smith et Smith et al. 2003al. 2003
CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy
Giovi et al. 2003, PRD in press, astro-ph/0308118 Giovi et al. 2003, PRD in press, astro-ph/0308118
CMB bispectrum & Structure Formation CMB bispectrum & Structure Formation
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >=0>=0
< B< Bllm m
l`l`m`m`
l``l``m`` m`` >> 0 0
Giovi, Liguori et al. 2004, in preparation Giovi, Liguori et al. 2004, in preparation
=2=2ss00decdecdr[(r-rdr[(r-rdecdec)/r)/rdecdecr]r]r,r,))
N-body in Dark Energy Cosmology N-body in Dark Energy Cosmology
Dolag et al. 2003, A&A submitted, see also Klypin et Dolag et al. 2003, A&A submitted, see also Klypin et al. 2003, Linder & Jenkins 2003al. 2003, Linder & Jenkins 2003
N-body in Dark Energy Cosmology N-body in Dark Energy Cosmology
Dolag et al. 2003, A&A submittedDolag et al. 2003, A&A submitted
GADGET (Springel et al. 2001)GADGET (Springel et al. 2001)
initial box: 512initial box: 51233 particles, particles, side = 479hside = 479h-1-1MM , , 88 today today
fixed to 0.9fixed to 0.9
Dark energy in background Dark energy in background expansion, linear growth rateexpansion, linear growth rate
Haloes fitted with NFWHaloes fitted with NFW
N-body in Dark Energy Cosmology N-body in Dark Energy Cosmology
Dolag et al. 2003, A&A submittedDolag et al. 2003, A&A submitted
Quintessence reference modelsQuintessence reference models
N-body in Dark Energy Cosmology N-body in Dark Energy Cosmology
Dolag et al. 2003, A&A submittedDolag et al. 2003, A&A submitted
tttt+2H+2Htt –4 –4 G G =0, D =0, D++(z)=(z)=(z)/(z)/00
N-body in Dark Energy Cosmology N-body in Dark Energy Cosmology
Dolag et al. 2003, A&A submittedDolag et al. 2003, A&A submitted
c(M,z)=cc(M,z)=c0 0 /(1+z)(M/10/(1+z)(M/101414hhMM))
N-body in Dark Energy Cosmology N-body in Dark Energy Cosmology
Dolag et al. 2003, A&A submittedDolag et al. 2003, A&A submitted
c(M,z)=[cc(M,z)=[c0 0 /(1+z)](M/10/(1+z)](M/101414hhMM))
is cis c0 0 dependent on the dark energy dynamics?dependent on the dark energy dynamics?
can such dependence be predicted?can such dependence be predicted?
cc0 0 !! c c00 CDM CDM ¢¢ D D++(z(zcollcoll) / D) / D++
CDM CDM(z(zcollcoll))
Dark Energy in Generalized Cosmologies Dark Energy in Generalized Cosmologies
L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-
--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]
Dark Energy in Generalized Cosmologies Dark Energy in Generalized Cosmologies
L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-
--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]
QuintessenceQuintessence
Dark Energy in Generalized Cosmologies Dark Energy in Generalized Cosmologies
L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-
--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]
Extended QuintessenceExtended Quintessence
Dark Energy in Generalized Cosmologies Dark Energy in Generalized Cosmologies
L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-
--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]
Coupled QuintessenceCoupled Quintessence
Dark Energy in Generalized Cosmologies Dark Energy in Generalized Cosmologies
L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-
--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]
k-essencek-essence
Dark Energy in Generalized Cosmologies Dark Energy in Generalized Cosmologies
L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-
--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]
New GravityNew Gravity
Bravely facing the Coincidence Bravely facing the Coincidence
What happens at that epoch?What happens at that epoch?
Cosmic acceleration is a recent occurrence, say z of order unity …Cosmic acceleration is a recent occurrence, say z of order unity …
funny physics: the formation of funny physics: the formation of cosmological clumps affects the cosmological clumps affects the cosmological vacuum statecosmological vacuum state
matter over-densities move the matter over-densities move the dark energy field out of the dark energy field out of the potential minimum potential minimum
Extended Quintessence & New Gravity Extended Quintessence & New Gravity HH2 2 = (8= (8 G/3)[ G/3)[ + stuff ] + stuff ]
stuff = (1/8stuff = (1/8 GF)[ GF)[(1-8(1-8 G F) + G F) +tt22/2+(RF-f)/2+V-3HF/2+(RF-f)/2+V-3HFtt]]
HHtt = - 4 = - 4 G[ G[ + p + stuff ] + p + stuff ]
stuff = (1/8stuff = (1/8 GF)[( GF)[(p)(1-8p)(1-8 G F) + G F) +tt22+F+Ftttt-HF-HFtt]]
non-minimal coupling: f=Fnon-minimal coupling: f=F¢¢ R R
new gravity: f(R)new gravity: f(R) R/8 R/8 G G
Hwang 1991, generalized cosmologiesHwang 1991, generalized cosmologies
F=F= f / f / R R
Extended Quintessence Extended Quintessence
kk22=4=4 k k33(( / /))kk
22
Perrotta, Baccigalupi, Matarrese, PRD 2000, Perrotta, Baccigalupi, Matarrese, PRD 2000, Baccigalupi, Matarrese, Perrotta, PRD 2000 Baccigalupi, Matarrese, Perrotta, PRD 2000
mm
cc22eff, eff, 11
GG== T T
Perrotta, Baccigalupi 2002Perrotta, Baccigalupi 2002
GG== T TPerrotta et al. 2003, PRD submittedPerrotta et al. 2003, PRD submitted
Non-linear Clustering in Extended Quintessence Non-linear Clustering in Extended Quintessence
GG== T T ds2=a2[(-1+2)d2+(1-2)ijdxidxj]
r2 = (1/2F)[a2m+a2 U+r 2( F)+|r( |2/2]
r2=(1/2F)[a2m-2a2 U-r 2( F)]
r2() =a2 U-(dF/d /2F)[a2m+4a2 U+3r 2( F)+|r( |2/2]-a2 (dF/d )R
Perrotta et al. 2003, PRD submittedPerrotta et al. 2003, PRD submitted
Non-linear Clustering in Extended Quintessence Non-linear Clustering in Extended Quintessence
GG== T T ds2=a2[(-1+2)d2+(1-2)ijdxidxj]
r2 = (1/2F)[a2m+a2 U+r 2( F)+|r( |2/2]
r2=(1/2F)[a2m-2a2 U-r 2( F)]
r2() =a2 U-(dF/d /2F)[a2m+4a2 U+3r 2( F)+|r( |2/2]-a2 (dF/d )R
Perrotta et al. PRD 2004Perrotta et al. PRD 2004
Continua…Continua…• CMB & bispectrum,*observability*, vary CMB & bispectrum,*observability*, vary
cosmological parameters, non-linearity, …cosmological parameters, non-linearity, …• N-body, gain statistics, check N-body, gain statistics, check
concentration dependence on w(z), concentration dependence on w(z), *lensing*…*lensing*…
•Generalized cosmologies, are *dark Generalized cosmologies, are *dark haloes* affected? If so, check with N-haloes* affected? If so, check with N-body, …body, …
Dark Energy Dark Energy
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