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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


GG++gg==88TT++VVgg

Geometry Geometry

Quantum VacuumQuantum Vacuum


||-V|/M-V|/M22PlanckPlanck .. 10 10-123-123

::

V:V:


||-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


<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


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


CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy Quintessence reference modelsQuintessence reference models

SUGRASUGRA

RPRP

CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy


Ma et al. Ma et al. 1999, 1999,

Smith et Smith et al. 2003al. 2003

CMB bispectrum & Dark Energy CMB bispectrum & Dark Energy



< 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


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



Quintessence reference modelsQuintessence reference models



tttt+2H+2Htt –4 –4 G G =0, D =0, D++(z)=(z)=(z)/(z)/00



c(M,z)=cc(M,z)=c0 0 /(1+z)(M/10/(1+z)(M/101414hhMM))



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)])]


L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-

--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]

QuintessenceQuintessence


L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-

--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]

Extended QuintessenceExtended Quintessence


L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-

--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]

Coupled QuintessenceCoupled Quintessence


L=f(L=f( ,R)/2-[ ,R)/2-[(()/2])/2];;;;-U(-U( )- )-

--kk[[;;;;+V(+V(kk)+W()+W(,,kk)])]

k-essencek-essence


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, …

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