Dark Energy
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Transcript of Dark Energy
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:
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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 solutionsThe 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