structure formation in dark energy cosmology la magia, april 2005
TRANSCRIPT
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Structure formation in dark energy cosmology
La Magia, April 2005
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outline
• Quintessence scheme • Cosmological expansion rate• Cosmological perturbations • Cosmic microwave background • Gravitational lensing • Non-linear structure formation• Quintessence, dark matter and gravity• Conclusion
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Quintessence scheme
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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
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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
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Cosmological expansion
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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
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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
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Cosmological perturbations
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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)
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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)
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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
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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)
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Cosmic microwave background
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Projection
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Integrated sachs-wolfe
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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
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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
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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…
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Gravitational lensing
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Weak lensing in dark energy cosmology
• Probing intermediate redshifts only• Collecting effects from modified geometry and
perturbations • Details in Acquaviva et al. 2004
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Breaking the projection degeneracy
Dark energy records in lensed CMB, Acquaviva and Baccigalupi, 2005, in preparation
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Breaking the projection degeneracy
Dark energy records in lensed CMB, Acquaviva and Baccigalupi, 2005, in preparation
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CMB three-point correlation function from lensing
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CMB bispectrum
l1
l2
l3
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CMB bispectrum
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Lensing chronology
Giovi et al. 2003, PhD thesis
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CMB three-point statistics and dark energy
Giovi et al. 2003, 2005, PhD thesis
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CMB three-point statistics and dark energy
Giovi et al. 2003, 2005, PhD thesis
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Non-linear structure formation
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Galaxy clusters
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Matthias Bartelmann
Massimo Meneghetti
Klaus Dolag
Carlo Baccigalupi
Viviana Acquaviva
Francesca Perrotta
Lauro Moscardini
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Matthias Bartelmann
Massimo Meneghetti
Klaus Dolag
Carlo Baccigalupi
Viviana Acquaviva
Francesca Perrotta
Lauro Moscardini
Heidelberg
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Matthias Bartelmann
Massimo Meneghetti
Klaus Dolag
Carlo Baccigalupi
Viviana Acquaviva
Francesca Perrotta
Lauro Moscardini
MPA, Garching
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Matthias Bartelmann
Massimo Meneghetti
Klaus Dolag
Carlo Baccigalupi
Viviana Acquaviva
Francesca Perrotta
Lauro Moscardini
SISSA, Trieste
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Matthias Bartelmann
Massimo Meneghetti
Klaus Dolag
Carlo Baccigalupi
Viviana Acquaviva
Francesca Perrotta
Lauro Moscardini
Bologna
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Dark energy records in galaxy cluster concentrations
Klypin et al. 2003, Maccio et al. 2003, Dolag et al. 2004, …
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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
Maccio 2004, Meneghetti et al. 2004
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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
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Quintessence, dark matter and gravity
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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)
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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
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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)
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Weird dark energy dynamics
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Weird dark energy dynamics
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Weird dark energy dynamics
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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)
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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, …
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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
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Conclusion: minimally coupled Quintessence
• Linear perturbation behavior rather well understood
• Non-linear perturbation behavior still poorly known (only clusters, nothing on larger scales, mergers, …)
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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
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Conclusion
• Constraints from observables including the present are polluted 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
• The promise of lensing