robert caldwell- dark energy cosmology
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Dark Energy Cosmology
INPE Winter School
September 12-16, 2005
Robert Caldwell
Dartmouth College
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Gravity? a provocative list
cosmic acceleration
Pioneer anomaly
Anderson et al, PRL 81 (1998) 2858
dark energy
galaxy rotation curves
dark matter
Krasinsky & Brumberg, Cel. Mech. & Dyn. Astro. 90 (2004) 267
drift of Astronomical Unit
drift of Moon from Earth
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Tests of Gravity
• Test bodies fall with the same acceleration independently of
internal structure or composition (WEP: weak equivalence principle)
• The outcome of any local, non-gravitational experiment is
independent of velocity of the freely falling reference frame in which
it is performed (LLI: local Lorentz invariance)
• The outcome of any local, non-gravitational experiment is
independent of where or when in the universe it is performed (LPI:
local position invariance)
Einstein Equivalence Principle
Will, gr-qc/0504086
Einstein’s General Relativity is
the standard model of gravitation
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Tests of Gravity
PPN Parameters
γ: (=1 in GR) How much curvature is produced by unit rest mass
β: (=1 in GR) The amount of non-linearity in gravitational superposition
Time delay of signals from Cassini spacecraft
Bertotti et al, Nature 425 (2003) 374
Lunar laser rangingWilliams et al, PRL 93 (2004) 261101
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Tests of Gravity
local acceleration of bodies of different compositionEot-Wash: Baessler et al, PRL 83 (1999) 3585
Lunar laser rangingWilliams et al, PRL 93 (2004) 261101
Nordtvedt effect: observations of the acceleration of bodieswith different gravitational binding energies tests the Strong
Equivalence Principle
Mass definitions:
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Tests of Gravitational Coupling
Oklo (Gabon) natural fission reaction, 2 Gyrs ago
EEP: non-gravitational phenomena independent of cosmic evolution
Peik et al, PRL 93 (2004) 170801
Fischer et al, PRL 92 (2004) 230802
Laboratory Measurements
Serendipitous Result
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Tests of Gravitational Coupling
First limit from quasar spectraBahcall & Salpeter, ApJ 142 (1965) L1677
EEP: non-gravitational phenomena independent of cosmic evolution
Astrophysical Observations
First limit on ΔαSavedoff, Nature 176 (1956) 688
Webb et al, PRL 87 (2001) 091301
Srianand et al, PRL 92 (2004) 121302
…more published limits
possible systematics in baseline lab measurements
Ivanchik et al, A&A 440 (2005) 45
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Dark Energy
There are numerous other proposed models of dark energy.
Artistic view of a universe filled by a turbulent sea of dark energy
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Dark Energy Ideas
Dark Energy - Matter Coupling Amendola et al, ApJ 583 (2003) L53
Dark Energy Solid Bucher & Spergel, PRD 60 (1999) 043505Chaplygin Gas Kamenshchik et al, PLB 511 (2001) 265
Bulk Pressure of Particle Creation Zimdahl, PRD 61 (2000) 083511
Quantum Effects of a Scalar Field Parker & Vanzella, PRD 69 (2004) 104009
…
Dark Energy & Gravity: Non-Minimal Coupling
Scalar-Tensor Models
Modifications of Einstein Gravity
GR as an attractor of S-T Theories:
Damour & Nordtvedt, PRL 70 (1993) 2217Perrotta et al, PRD 61 (2000) 023507
Bartolo et al, PRD 61 (2000) 023518
…
Carroll et al, PRD 70 (2004) 043528
…
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Dark Energy & Gravity
Modification of Einstein Gravity
Metric Variation of the Action
Palatini Variation of the Action
The scalar field is non-dynamical. Instead, it is a derived quantity
which depends on the local matter density and the potential.
Olmo, gr-qc/0505135,6
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Dark Energy & Gravity
Modification of Einstein Gravity also modifies Newtonian Gravity!
Constraints on Newtonian potential…
Gravitational Constant, G…
Plus considerations of cosmic acceleration…
…tight restrictions on the form of the gravitational Lagrangian
Olmo, gr-qc/0505135,6
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Dark Energy
The influence of dark energy on the cosmic expansion slows the
growth of inhomogeneities in the dark matter and baryons.
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Dark Energy
The influence of dark energy on the cosmic expansion leads to the
integrated Sachs-Wolfe effect in the cosmic microwave background
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Dark Energy
BOOMERANG, MAXIMA, TOCO
The influence of dark energy on the cosmic expansion modifies the
distance to the CMB last scattering surface
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Dark Energy
Huey et al, PRL 59 (1999) 063005
Dark energy models with the same
and all other parameters held
fixed have nearly identical CMB
anisotropy spectra.
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Dark Energy
evaluate classical tests of cosmology to constrain “w”
Aldering et al, astro-ph/0507426
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Dark Energy
evaluate classical tests of cosmology to constrain “w”
Because dark energy kicks in at late
times, find the greatest sensitivity at
late times.
Huterer & Turner, PRD 64 (2001) 123527
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Dark Energy
forecasting
Kim et al, MNRAS 347 (2004) 909
SNAP : SuperNova Acceleration Probe snap.lbl.gov
1. select theoretical model
2. calculate F for proposed experiment3. use eigensystem to project limits
recipe
Tegmark et al, astro-ph/9805117
Dodelson, “Modern Cosmology”, Ch 11
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Dark Energy
Forecasting: H,q
2-D eigensystem:
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Dark Energy: Constant Equation-of-State
Caldwell & Doran, PRD 69 (2004) 103517
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Dark Energy
Test for super-acceleration phase
Was w<-1 in the past?
Kaplinghat & Bridle, PRD 71 (2005) 123003
Fit a constant w to data
(true w need not be constant)
If w<-1 is found
then w < -1,or Ω m is wrong
For fixed Ωm , more negative
w means more distant objects
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Dark Energy
What are the fundamental bounds on w?
Weak:
Dominant:
Null:
Timelike/Strong:
Hawking & Ellis, 1973
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Singuarities
What is a singularity? A place where the curvature blows up!
Excluded from the spacetime manifold…
The Big Bang and Black Hole singularities are not part of the spacetime.
Role of Energy Conditions: useful for identifying the forms of (realistic) matterwhich permit the proof of singularity theorems.
New type of singularity: Sudden Future Singularity
Barrow CQG 21 (2004) L79; PLB 180 (1987) 335
Davies, Ann. Inst. Henri Poincare 49 (1988) 297
Big Rip: violates null or dominant energy condition with w < -1
A spacelike singularity as the
curvature diverges in finite time
RC, Kamionkowski, Weinberg, PRL 91 (2003) 071301
Unnecessary to violate strong energy condition!
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Dark Energy
How to achieve w<-1?
negative kinetic energy requires special considerations
Or it signals a breakdown of gravity? Dark matter?
Or it simply means we are mis-interpreting the data!
Hsu et al, PLB 597 (2004) 270
Cline et al, PRD 70 (2004) 043543Carroll et al, PRD 68 (2003) 023509;
PRD 71 (2005) 023525
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Phantom!
positive energy density
increases with time!
!"#
>$+
%=
+
m
w
mm
mmm
t t wt t wa
t t t t at a
)33/(2
3/2
]/)1[(
)()(
Dark Energy:
Universe ends catastrophically in a finite time!
Horizon radius shrinks to a point: every particle is torn away and isolated
Force equation for a
gravitationally-bound particle
Perivolaropoulos, PRD 70 (2004) 123529
Caldwell et al, PRL 91 (2003) 071301
Objects on smaller and smaller scales will be ripped apart.
Caldwell, PLB 545 (2002) 23
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Dr. Egon Spengler: There's something very important I forgot to tell you.Dr. Peter Venkman: What?Dr. Egon Spengler: Don't cross the streams.Dr. Peter Venkman: Why?Dr. Egon Spengler: It would be bad.Dr. Peter Venkman: I'm fuzzy on the whole good/bad thing. What do you
mean "bad"?Dr. Egon Spengler: Try to imagine all life as you know it stopping
instantaneously and every molecule in your bodyexploding at the speed of light.
Dr. Raymond Stantz: Total protonic reversal.Dr. Peter Venkman: That's bad. Okay. Alright, important safety tip,
thanks Egon.
Ghostbusters (1984).
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Charting the ΛCDM Spacetime Tamara Davis, astro-ph/0402278
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Conformal Diagrams: Mapping Infinity
Hawking & Ellis, 1973
Chiba et al, CQG 22 (2005) 3745
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Looking Ahead…
New ways to sense the dark energy
Distances, Evolution, Cross-Correlation
New ways to test gravity
Cluster Lensing, 1/r in the laboratory
New ideas from theory, clues from experiment
Dark Energy Survey decam.fnal.gov
Dark Matter Telescope www.dmtelescope.org
SNAP snap.lbl.gov
…
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Roadmap for Cosmology:New Physics in Light of Dark Energy
Robert CaldwellDartmouth College
September 2005