Dark Energy Dark Energy The first Surprise in The first Surprise in the era the era of precision of precision cosmology?cosmology?

Dark Energy Evidence Dark Energy Evidence

Low Low redshiftredshiftcosmic cosmic geometry geometry

Dark Energy Evidence Dark Energy Evidence Large Scale Large Scale Structure Structure

Percival et al. MNRAS 327 Percival et al. MNRAS 327 1297 20011297 2001

Galaxy Galaxy distribution distribution favours a favours a low matter low matter Universe; Universe; CMB CMB acoustic acoustic peak peak locations locations indicate a indicate a flat cosmic flat cosmic geometrygeometry

Evidence Evidence for 70 % for 70 % of the of the critical critical energy energy density in density in the vacuumthe vacuum

Vacuum Energy: Vacuum Energy: a Mystery For Physics a Mystery For Physics

The Planck mass is 10The Planck mass is 101919 GeV; a natural scale for the GeV; a natural scale for the vacuum energy density vacuum energy density would bewould be

»» 10 107676 GeV GeV44

Instead, present observations Instead, present observations indicate a vacuum energy indicate a vacuum energy density comparable to the density comparable to the critical one: critical one:

»» 10 10-49-49 h h22GeVGeV44

»» 10 1088 GeV GeV44

Particle physics takes the Particle physics takes the Standar Model form at the Standar Model form at the mass scale of the mass scale of the electroweak vector bosons:electroweak vector bosons:

?

?

??

?

for Physics for Physics

Why Why so small so small with respect to with respect to

any particle any particle physics scalephysics scale

Why Why comparable comparable

to the to the cosmological cosmological

matter matter density todaydensity today

Two Two

Dark Energy Models Dark Energy Models • Trans PlanckianTrans Planckian: : energy stored in perturbation modes energy stored in perturbation modes on super-horizon scales (Mersini et al., PRD64 043508, 2001)on super-horizon scales (Mersini et al., PRD64 043508, 2001)• Spacetime microstructureSpacetime microstructure: self-adjusting spacetime capable : self-adjusting spacetime capable to absorbe vacuum energy (Padmanabhan, gr-qc/0204020)to absorbe vacuum energy (Padmanabhan, gr-qc/0204020)• Matter-Energy TransitionMatter-Energy Transition: dark matter converts to dark energy at: dark matter converts to dark energy atlow redshifts (astro-ph/0203383)low redshifts (astro-ph/0203383)• Brane worldsBrane worlds: brane tension (Shani & Sthanov astro-ph/0202346);: brane tension (Shani & Sthanov astro-ph/0202346);cyclic-ekpyrotic cosmic vacuum (Steinhardt &Tutok hep-th/0111098)cyclic-ekpyrotic cosmic vacuum (Steinhardt &Tutok hep-th/0111098)

• Quintessence: tracking scalar fields (Steinhardt, Wang & Zlatev, PRD59, 123504, 1999; Ratra & Peebles, Wetterich ...)• Extended Quintessence: non-minimal coupling to Gravity (Uzan Chiba, Perrotta, Baccigalupi, Matarrese, PRD61, 023507, 2000• Coupled Quintessence: coupling with dark matter (Amendola, Pietroni...)

Quintessence Quintessence The Quintessence scalar field The Quintessence scalar field slowly rolls down its slowly rolls down its potential V(potential V(), becoming ), becoming dominant at low redshift, flat dominant at low redshift, flat enough to mimick the enough to mimick the behavior of a Cosmological behavior of a Cosmological Constant. Constant.

Quintessence Cosmilogy Quintessence Cosmilogy Background Evolution:Background Evolution:

Perturbation Evolution:Perturbation Evolution:

(synchronous gauge)(synchronous gauge)

Quintessence Tracking Solutions Quintessence Tracking Solutions For interesting forms of For interesting forms of potentials, attractor trajectories potentials, attractor trajectories have the following property: have the following property:

Inverse power law potential: Inverse power law potential:

Why are Tracking Why are Tracking Solutions Important? Solutions Important?

Avoid Fine-Tuning in Avoid Fine-Tuning in the Early Universe!the Early Universe!

Unlike the Unlike the Cosmological Cosmological Constant... Constant... Quintessence fluctuates! Quintessence fluctuates!

(Newtonian gauge) (Newtonian gauge)

Dark EnergyDark EnergyCMB CMB constraints & constraints & Extended Extended TheoryTheory

Effects on the CMB Effects on the CMB • ProjectionProjection• Integrated Sachs-WolfeIntegrated Sachs-Wolfe

Effects on the CMB Effects on the CMB Projection:Projection:

ISW (Bardeen 1980): ISW (Bardeen 1980):

Quintessence & CMB Quintessence & CMB AdvantagesAdvantages: well understood : well understood geometrical features of high geometrical features of high amplitude, well above the sensitivity amplitude, well above the sensitivity of MAP & Planckof MAP & Planck

DisdvantagesDisdvantages: CMB degeneracy : CMB degeneracy (Efstathiou 2001); in particular, the (Efstathiou 2001); in particular, the projecttion is degenerate with a projecttion is degenerate with a positive spatial curvature positive spatial curvature

Quintessence & CMB: simulations Quintessence & CMB: simulations Hubble constant fixed, no spatial curvature: h=0.65,Hubble constant fixed, no spatial curvature: h=0.65,KK=0 =0

Cosmological abundances: 0.016Cosmological abundances: 0.016··bb·· 0.04 (step 0.02), 0.4 0.04 (step 0.02), 0.4····

0.8, step 0.02, 0.8, step 0.02, CDMCDM=1-=1---bb

Quintessence equation of state: -0.96Quintessence equation of state: -0.96·· w w·· –0.6 (step 0.03), w –0.6 (step 0.03), w=-1=-1

Cosmological Perturbations: 0.90Cosmological Perturbations: 0.90·· n nss·· 1.10 1.10

(step 0.02), 0(step 0.02), 0·· R R·· 0.5 (step 0.05), n 0.5 (step 0.05), nTT=-R/6/8=-R/6/8

Gaussian, adiabatic initial conditionsGaussian, adiabatic initial conditions

Quintessence & CMB: data Quintessence & CMB: data

BOOMERanG: 19 points, 76BOOMERanG: 19 points, 76·· l l·· 1025 1025

MAXIMA: 13 points, 36MAXIMA: 13 points, 36·· l l·· 1235 1235

DASI: 13 points, 36DASI: 13 points, 36·· l l·· 1235 1235

COBE: 24 points, 2COBE: 24 points, 2·· l l·· 25 25

Gaussian likelihood assumed, Gaussian likelihood assumed, calibration uncertainty includedcalibration uncertainty included

Quintessence & CMB: early results Quintessence & CMB: early results

Balbi et al. 2001Balbi et al. 2001

Quintessence & CMB: results Quintessence & CMB: results

Baccigalupi et al. 2002Baccigalupi et al. 2002

Quintessence & CMB: wQuintessence & CMB: w,,

Baccigalupi et al. 2002Baccigalupi et al. 2002

Quintessence & CMB: results Quintessence & CMB: results

Is there a projection on the CMB? Is there a projection on the CMB?

CDM vs. QCDMCDM vs. QCDM

Quintessence & CMB: conslusions Quintessence & CMB: conslusions In flat cosmologies, h fixed, CMB In flat cosmologies, h fixed, CMB data show a mild preference for a data show a mild preference for a time varying dark energy: time varying dark energy:

0.60.6···· 0.8, -1 0.8, -1·· w w·· –0.6 (2 –0.6 (2 ) )

=0.71=0.71-0.04-0.04+0.05+0.05, w, w=-0.82=-0.82-0.11-0.11

+0.14+0.14 (1 (1 ) )

Extended Quintessence Extended Quintessence

Formulate Quintessence theory in Generalized Formulate Quintessence theory in Generalized General Relativity:General Relativity:

Presently explored classes:Presently explored classes:

withwith

in analogy with Extended Inflation modelsin analogy with Extended Inflation models

Why non-minimal coupling? Why non-minimal coupling? • The theory has to be The theory has to be extended, the simplest extended, the simplest model does not workmodel does not work• Extend the theory to Extend the theory to the Gravitational sector the Gravitational sector

• Can Dark Energy be the Can Dark Energy be the signature of a signature of a modification of General modification of General Relativity? Relativity?

Extended Cosmic Expansion Extended Cosmic Expansion

Scalar-Tensor Cosmological Perturbations Scalar-Tensor Cosmological Perturbations

hhmetric trace & traceless perturbationmetric trace & traceless perturbation

p: total density & pressure perturbationp: total density & pressure perturbation

total velocity & shear perturbationtotal velocity & shear perturbation

Varying G encoded in fluid Varying G encoded in fluid propertes (Hwang 1991)propertes (Hwang 1991)

Perrotta et al. 2000 Perrotta et al. 2000

Tracking Extended Quintessence Tracking Extended Quintessence Extended Quintessence admits tracking solutionsExtended Quintessence admits tracking solutions

The early time behavior The early time behavior differs from ordinary GR differs from ordinary GR because of R; at early times: because of R; at early times:

R-boostR-boost

Tracking Extended Quintessence: R-boost Tracking Extended Quintessence: R-boost

shrinks toshrinks to

for for

the R-boost solution is the R-boost solution is

Tracking Extended Quintessence: R-boost Tracking Extended Quintessence: R-boost

Tracking Extended Quintessence: R-boost Tracking Extended Quintessence: R-boost

The R-boost ends when the energy density equals the potential

Changing Gravity Changing CMB Changing Gravity Changing CMB

Baccigalupi et al. 2000 Baccigalupi et al. 2000

Extended Quintessence & CMB: ISW Extended Quintessence & CMB: ISW

if F=1/8if F=1/8 G + G +22 , , C Cll/C/Cll'' 96 96 G G0022

++ for for >0 >0

** for for <0 <0

Extended Quintessence & CMB: Projection Extended Quintessence & CMB: Projection

if F=1/8if F=1/8 G + G +22 , , l/ll/l'' G G0022

Gravitational Dragging Gravitational Dragging

Gravitational Dragging: Background Gravitational Dragging: Background

scales as the dominant scales as the dominant

component component

Gravitational Dragging: Perturbations Gravitational Dragging: Perturbations

In the matter dominated era: In the matter dominated era:

Dark energy sound Dark energy sound speed (Hu 1998): speed (Hu 1998):

Dark Energy Clustering Dark Energy Clustering Redshift behavior of Redshift behavior of kk

22=4=4 k k33(( / /))kk22

Perrotta & Baccigalupi 2002 Perrotta & Baccigalupi 2002

Extended Quintessence: Conclusions Extended Quintessence: Conclusions Extended Quintessence admits tracking solutionsExtended Quintessence admits tracking solutions

The Ricci scalar causes an initial enhancement The Ricci scalar causes an initial enhancement of the field dynamics, the R-boostof the field dynamics, the R-boost

Gravitational Dragging: the dark energy Gravitational Dragging: the dark energy density scales as the dominant componentdensity scales as the dominant component

Gravitational Dragging: dark energy density Gravitational Dragging: dark energy density perturbations track the matter ones perturbations track the matter ones )) it participates to it participates to structure formation (!)structure formation (!)

ISW: ISW: C Cll/C/Cll'' 12(1-G/G 12(1-G/Gdecdec))

Projection: Projection: l/ll/l'' (1-G/G (1-G/Gdecdec)/8 )/8

Dark Energy Evidence Dark Energy Evidence