robert caldwell- dark energy cosmology

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Dark Energy Cosmology

INPE Winter School

September 12-16, 2005

Robert Caldwell

Dartmouth College



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



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



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



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:



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



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



Dark Energy

There are numerous other proposed models of dark energy.

Artistic view of a universe filled by a turbulent sea of dark energy



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

…



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



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



Dark Energy

The influence of dark energy on the cosmic expansion slows the

growth of inhomogeneities in the dark matter and baryons.



Dark Energy

The influence of dark energy on the cosmic expansion leads to the

integrated Sachs-Wolfe effect in the cosmic microwave background



Dark Energy

BOOMERANG, MAXIMA, TOCO

The influence of dark energy on the cosmic expansion modifies the

distance to the CMB last scattering surface



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.



Dark Energy

evaluate classical tests of cosmology to constrain “w”

Aldering et al, astro-ph/0507426



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



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



Dark Energy

Forecasting: H,q

2-D eigensystem:



Dark Energy: Constant Equation-of-State

Caldwell & Doran, PRD 69 (2004) 103517



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



Dark Energy

What are the fundamental bounds on w?

Weak:

Dominant:

Null:

Timelike/Strong:

Hawking & Ellis, 1973



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!



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



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



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).



Charting the ΛCDM Spacetime Tamara Davis, astro-ph/0402278



Conformal Diagrams: Mapping Infinity

Hawking & Ellis, 1973

Chiba et al, CQG 22 (2005) 3745



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

…



Roadmap for Cosmology:New Physics in Light of Dark Energy

Robert CaldwellDartmouth College

September 2005

robert caldwell- dark energy cosmology

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