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

Dark Energy Evidence Low redshift cosmic geometry

Dark Energy Evidence Large Scale Structure Percival et al. MNRAS Galaxy distribution favours a low matter Universe; CMB acoustic peak locations indicate a flat cosmic geometry Evidence for 70 % of the critical energy density in the vacuum

Vacuum Energy: a Mystery For Physics The Planck mass is GeV; a natural scale for the vacuum energy density would be  » GeV 4 Instead, present observations indicate a vacuum energy density comparable to the critical one:  » h 2 GeV 4  » 10 8 GeV 4 Particle physics takes the Standar Model form at the mass scale of the electroweak vector bosons: ? ? ? ? ?

for Physics for Physics Why  so small with respect to any particle physics scale Why comparable to the cosmological matter density today Two Two

Dark Energy Models Trans Planckian: energy stored in perturbation modesTrans Planckian: energy stored in perturbation modes on super-horizon scales (Mersini et al., PRD , 2001) Spacetime microstructure: self-adjusting spacetime capableSpacetime microstructure: self-adjusting spacetime capable to absorbe vacuum energy (Padmanabhan, gr-qc/ ) Matter-Energy Transition: dark matter converts to dark energy atMatter-Energy Transition: dark matter converts to dark energy at low redshifts (astro-ph/ ) Brane worlds: brane tension (Shani & Sthanov astro-ph/ );Brane worlds: brane tension (Shani & Sthanov astro-ph/ ); cyclic-ekpyrotic cosmic vacuum (Steinhardt &Tutok hep-th/ ) Quintessence: tracking scalar fields (Steinhardt, Wang & Zlatev, PRD59, , 1999; Ratra & Peebles, Wetterich...) Extended Quintessence: non-minimal coupling to Gravity (Uzan Chiba, Perrotta, Baccigalupi, Matarrese, PRD61, , 2000 Coupled Quintessence: coupling with dark matter (Amendola, Pietroni...)

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

Quintessence Cosmilogy Background Evolution: Perturbation Evolution: (synchronous gauge)

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

Why are Tracking Solutions Important? Avoid Fine-Tuning in the Early Universe!

Unlike the Cosmological Constant... Quintessence fluctuates! (Newtonian gauge)

Dark Energy CMB constraints & Extended Theory

Effects on the CMB Projection Projection Integrated Sachs-Wolfe Integrated Sachs-Wolfe

Effects on the CMB Projection: ISW (Bardeen 1980):

Quintessence & CMB Advantages: well understood geometrical features of high amplitude, well above the sensitivity of MAP & Planck Disdvantages: CMB degeneracy (Efstathiou 2001); in particular, the projecttion is degenerate with a positive spatial curvature

Quintessence & CMB: simulations Hubble constant fixed, no spatial curvature: h=0.65,  K =0 Cosmological abundances: ·  b · 0.04 (step 0.02), 0.4 ·   · 0.8, step 0.02,  CDM =1-   -  b Quintessence equation of state: · w  · –0.6 (step 0.03), w  =-1 Cosmological Perturbations: 0.90 · n s · 1.10 (step 0.02), 0 · R · 0.5 (step 0.05), n T =-R/6/8 Gaussian, adiabatic initial conditions

Quintessence & CMB: data BOOMERanG: 19 points, 76 · l · 1025 MAXIMA: 13 points, 36 · l · 1235 DASI: 13 points, 36 · l · 1235 COBE: 24 points, 2 · l · 25 Gaussian likelihood assumed, calibration uncertainty included

Quintessence & CMB: early results Balbi et al. 2001

Quintessence & CMB: results Baccigalupi et al. 2002

Quintessence & CMB: w ,   Baccigalupi et al. 2002

Quintessence & CMB: results

Is there a projection on the CMB?  CDM vs. QCDM

Quintessence & CMB: conslusions In flat cosmologies, h fixed, CMB data show a mild preference for a time varying dark energy: 0.6 ·   · 0.8, -1 · w  · –0.6 (2  )   = , w  = (1  )

Extended Quintessence Formulate Quintessence theory in Generalized General Relativity: Presently explored classes: with in analogy with Extended Inflation models

Why non-minimal coupling? The theory has to be extended, the simplest model does not work The theory has to be extended, the simplest model does not work Extend the theory to the Gravitational sector Extend the theory to the Gravitational sector Can Dark Energy be the signature of a modification of General Relativity? Can Dark Energy be the signature of a modification of General Relativity?

Extended Cosmic Expansion

Scalar-Tensor Cosmological Perturbations h  metric trace & traceless perturbation  p: total density & pressure perturbation  total velocity & shear perturbation

Varying G encoded in fluid propertes (Hwang 1991) Perrotta et al. 2000

Tracking Extended Quintessence Extended Quintessence admits tracking solutions The early time behavior differs from ordinary GR because of R; at early times: R-boost

Tracking Extended Quintessence: R-boost shrinks to

for the R-boost solution is Tracking Extended Quintessence: R-boost

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

Changing Gravity Changing CMB Baccigalupi et al. 2000

Extended Quintessence & CMB: ISW if F=1/8  G +  2,  C l /C l ' 96  G  for  >0 + for  >0 * for  <0

Extended Quintessence & CMB: Projection if F=1/8  G +  2,  l/l '  G  0 2

Gravitational Dragging

Gravitational Dragging: Background   scales as the dominant component

Gravitational Dragging: Perturbations In the matter dominated era: Dark energy sound speed (Hu 1998):

Dark Energy Clustering Redshift behavior of  k 2 =4  k 3 (  /  ) k 2 Perrotta & Baccigalupi 2002

Extended Quintessence: Conclusions Extended Quintessence admits tracking solutions The Ricci scalar causes an initial enhancement of the field dynamics, the R-boost Gravitational Dragging: the dark energy density scales as the dominant component Gravitational Dragging: dark energy density perturbations track the matter ones ) it participates to structure formation (!) ISW:  C l /C l ' 12(1-G/G dec ) Projection:  l/l ' (1-G/G dec )/8

Dark Energy Evidence