Cosmological structure formation and dark energy

Carlo Baccigalupi

Madrid, November 15, 2005

Cosmological Constant Problem Cosmological Constant Problem

GGµµνν=8=8ππTTνν

Cosmological Constant Problem Cosmological Constant Problem

GGνν+ + ggνν=8=8ππTTνν ++VVggνν

Geometry Geometry

Quantum VacuumQuantum Vacuum

Cosmological Constant Problem Cosmological Constant Problem

||-V|/M-V|/M44PlanckPlanck ≈≈1010-123-123

::

V:V:

for Physics for Physics

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

any particle any particle physics scalephysics scaleWhy Why

comparable comparable to the to the

cosmological cosmological matter matter

density todaydensity today

Two Two

outline

• Quintessence scheme • Cosmological expansion rate• Cosmological perturbations • Cosmic microwave background • Gravitational lensing • Non-linear structure formation• Quintessence, dark matter and gravity• Conclusion

Quintessence scheme

The Quintessence: a minimal generalization of

• setting up a phenomenology of the impact of vacuum energy in cosmology

• Predicting observable signatures if the acceleration is not due to a constant into the Einstein equations

Quintessence tracking solutions

• Classical trajectories for the Quintessence field converging to the present energy density from a large set of initial conditions

• The field may (Wetterich 1988) or may not (Ratra-Peebles 1998) scale as the dominant component

• Dark energy abundance today still severely tuned

Where are we now? Where are we now?

-1.1 -1.1 ≤≤ ‹‹ww››zz ≤≤ -0.9 -0.9

Present constraints from CMB and Present constraints from CMB and LSS on the redshift average of the LSS on the redshift average of the equation of state: equation of state:

Quest to be continued, the study of the Quest to be continued, the study of the dark energy is one of the core topics of dark energy is one of the core topics of the Beyond Einstein (NASA) and the Beyond Einstein (NASA) and Cosmic Vision (ESA) programs for the Cosmic Vision (ESA) programs for the next decades…next decades…

Cosmological expansion

Cosmological expansion rate

• For a fixed value today, H is larger if w > -1 in the past

• The comoving distance at a given redshift gets contracted

• The redshift dependence of w is washed out by two redshift integrals

Cosmological expansion rate

• For a fixed value today, H-1 is larger if w > -1 in the past

• The comoving distance at a given redshift gets contracted

• The redshift dependence of w is washed out by two redshift integrals

Cosmological perturbations

Effects on cosmological perturbations

• Modified geometry affects the growth of linear perturbations

• The dark energy possesses fluctuations which are dragged on large scales by the background evolution (Brax & Martin 2000)

Effects on cosmological perturbations

• Modified geometry affects the growth of linear perturbations

• The dark energy possesses fluctuations which are dragged on large scales by the background evolution (Brax & Martin 2000)

Effects from modified geometry

• For w greater than -1, the cosmological friction gets enhanced for a fixed H0

• This affects the linear density perturbations growth and the dynamics of the gravitational potentials on all scales in linear regime

Effects from quintessence perturbations

• A minimally coupled quintessence field is light, m»(d2V/d2)1/2» H-1

• Fluctuations live on horizon and super-horizon scales

• Excess power visible on small wavenumbers in the density power spectrum (Ma et al. 1999)

Cosmic microwave background

Projection

Integrated sachs-wolfe

Effects at decoupling

• If the dark energy tracks the dominant component at a few percent level, the physics at decoupling is affected at a measurable level (early quintessence, see Caldwell et al. 2005 and references therein)

• The equivalence epoch is shifted• The dark energy sound speed enters into the

acoustic oscillations

Constraining dark energy with primary CMB anisotropies

• Main effect from the shift of acoustic peaks due to the variation of distances

• The constraining power is limited by the projection degeneracy

Constraining dark energy with primary CMB anisotropies

• Assume flatness, fix H, gravitational waves in single field inflation

• Fit with B98, COBE, MAXIMA, DASI, get some preference for a dynamical dark energy (Baccigalupi et al. 2002)

• Mind degeneracies • Is WMAP tot=1.02±0.02

a similar indication? • Probably not…

Gravitational lensing

CMB lensing from structure formation

Main predictions of CMB lensing

Main predictions of CMB lensing

Main predictions of CMB lensing

Non-Gaussianity

The promise of CMB lensing

z

z ≈ 1

The promise of CMB lensing

z

z ≈ 1

acceleration

Weak lensing in dark energy cosmology

• Probing intermediate redshifts only• Collecting effects from modified geometry and

perturbations • Details in Acquaviva et al. 2004

Breaking the projection degeneracy

Dark energy records in lensed CMB, Acquaviva and Baccigalupi, 2005

Breaking the projection degeneracy

Dark energy records in lensed CMB, Acquaviva and Baccigalupi, 2005

Probing dark energy with CMB B modes from lensing

• B modes are lensing dominated at arcminute scales

• The lensing picks up power at the onset of acceleration only

• Cosmic variance is not simply Gaussian

• Near future probes: EBEx, Quad, Clover, …

CMB three-point correlation function from lensing

CMB bispectrum

l1

l2

l3

CMB bispectrum

Lensing chronology

Giovi et al. 2003, PhD thesis

CMB three-point statistics and dark energy

Giovi et al. 2003, 2005, PhD thesis

CMB three-point statistics and dark energy

Giovi et al. 2003, 2005, PhD thesis

Non-linear structure formation

Galaxy clusters

Matthias Bartelmann

Massimo Meneghetti

Klaus Dolag

Carlo Baccigalupi

Viviana Acquaviva

Francesca Perrotta

Lauro Moscardini

Matthias Bartelmann

Massimo Meneghetti

Klaus Dolag

Carlo Baccigalupi

Viviana Acquaviva

Francesca Perrotta

Lauro Moscardini

Heidelberg

Matthias Bartelmann

Massimo Meneghetti

Klaus Dolag

Carlo Baccigalupi

Viviana Acquaviva

Francesca Perrotta

Lauro Moscardini

MPA, Garching

Matthias Bartelmann

Massimo Meneghetti

Klaus Dolag

Carlo Baccigalupi

Viviana Acquaviva

Francesca Perrotta

Lauro Moscardini

SISSA, Trieste

Matthias Bartelmann

Massimo Meneghetti

Klaus Dolag

Carlo Baccigalupi

Viviana Acquaviva

Francesca Perrotta

Lauro Moscardini

Bologna

Dark energy records in galaxy cluster concentrations

Dolag et al. 2004

Strong lensing arc statistics

• Numerical ray tracing machines integrate null geodesics across structures out of N-body codes

• Internal parameters of structures may be constrained through the lensing pattern

Meneghetti et al. 2004

Strong lensing arc statistics

• A w > -1 dynamics in the dark energy makes the linear growth rate of perturbations behaving in the middle between an open and a CDM universe

• The number of giant arcs is a cosmological probe, which favours an open universe (Bartelmann 1999)

Meneghetti et al. 2004

Quintessence, dark matter and gravity

Coupled quintessence

• Coupling with baryons severely constrained by standard model physics

• Dark matter coupling realized with exchange in the energy density (Amendola 2000), variable masses for dark matter particles (Matarrese et al. 2003)

Extended quintessence

• Relating gravity and dark energy through an explicit coupling with the Ricci scalar

• Severely constrained on solar system scales

• Cosmological bounds improving with incoming data

Why weird cosmologies for the dark energy?

• Is it a new component or the signature of a modification in known physics?

• Coincidence unsolved• The couplings with dark matter or gravity may

induce new attractor mechanism driving the dark energy density to the present abundance from a large set of initial conditions (Bartolo and Pietroni 2000, Tocchini-Valentini and Amendola 2000, Matarrese et al. 2004)

Weird dark energy dynamics

Weird dark energy dynamics

Weird dark energy dynamics

Saving the Quintessence from fine-tuning…again

• Early universe attractors even for a cosmological constant behavior today (Matarrese et al. 2004)

• Examples: attraction to general relativity (Bartolo and Pietroni 1999), the R-boost (Baccigalupi et al. 2000, Pettorino et al. 2005)

• Consequences for the dark matter relic abundance (Catena et al. 2005)

Perturbation behavior in weird cosmologies

• Affecting geometry and perturbation growth rate• The mutual interaction between dark energy and

other components may drastically change the behavior of dark energy evolution and perturbations

• Spacetime variation of the gravitational constant, variable dark matter masses, scalar fields in galaxies, …

Perrotta and Baccigalupi 2002, Wetterich 2002, Maccio et al. 2003, Perrotta et al. 2004, Amendola 2004, …

Gravitational dragging

• Power injection on the dark energy density from other components

• Dark energy density fluctuations may be dragged to non-linearity by structure formation itself (Perrotta and Baccigalupi 2002)

• Non-linear structure formation in these scenarios largely unknown

T[ ]

;=Q ,

T[ ]

;= Q

Conclusion: minimally coupled Quintessence

• Linear perturbation behavior rather well understood

• Non-linear perturbation behavior still poorly known (only clusters, nothing on larger scales, mergers, …)

Conclusion: non-minimally coupled Quintessence

• Linear perturbation behavior still unclear (spacetime variations of constants, …)

• Possibility of gravitational dragging, dark energy density perturbations still present on sub-horizon scales

• Dark energy in dark haloes, major modification to N-body codes

Conclusion

• Constraints from the dark energy considered so far are dominated by the present cosmological constant like behavior

• Need to isolate observables which cut out the present in order to study the onset of cosmic acceleration, where models may still differ

• The CMB lensing possesses promising features in this respect