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Dark Energy Cosmology. Robert Caldwell Dartmouth College. INPE Winter School September 12-16, 2005. galaxy rotation curves. dark matter. Pioneer anomaly. Anderson et al, PRL 81 (1998) 2858. drift of Astronomical Unit. Krasinsky & Brumberg, Cel. Mech. & Dyn. Astro. 90 (2004) 267.

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dark energy cosmology

Dark Energy Cosmology

Robert Caldwell

Dartmouth College

INPE Winter School

September 12-16, 2005


galaxy rotation curves

dark matter

Pioneer anomaly

Anderson et al, PRL 81 (1998) 2858

drift of Astronomical Unit

Krasinsky & Brumberg, Cel. Mech. & Dyn. Astro. 90 (2004) 267

drift of Moon from Earth


a provocative list

cosmic acceleration

dark energy


Tests of Gravity

Einstein Equivalence Principle

  • 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)

Will, gr-qc/0504086

Einstein’s General Relativity is the standard model of gravitation


Tests of Gravity

PPN Parameters

: (=1 in GR) The amount of non-linearity in gravitational superposition

: (=1 in GR) How much curvature is produced by unit rest mass

Lunar laser ranging

Williams et al, PRL 93 (2004) 261101

Time delay of signals from Cassini spacecraft

Bertotti et al, Nature 425 (2003) 374


Tests of Gravity

local acceleration of bodies of different composition

Eot-Wash: Baessler et al, PRL 83 (1999) 3585

Lunar laser ranging

Williams et al, PRL 93 (2004) 261101

Nordtvedt effect: observations of the acceleration of bodies with different gravitational binding energies tests the Strong Equivalence Principle

Mass definitions:


Tests of Gravitational Coupling

EEP: non-gravitational phenomena independent of cosmic evolution

Serendipitous Result

Oklo (Gabon) natural fission reaction, 2 Gyrs ago

Laboratory Measurements

Peik et al, PRL 93 (2004) 170801

Fischer et al, PRL 92 (2004) 230802


Tests of Gravitational Coupling

EEP: non-gravitational phenomena independent of cosmic evolution

Astrophysical Observations

First limit on 

Savedoff, Nature 176 (1956) 688

First limit from quasar spectra

Bahcall & Salpeter, ApJ 142 (1965) L1677

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) 043505

Chaplygin 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

GR as an attractor of S-T Theories:

Damour & Nordtvedt, PRL 70 (1993) 2217

Perrotta et al, PRD 61 (2000) 023507

Bartolo et al, PRD 61 (2000) 023518

Modifications of Einstein Gravity

Carroll et al, PRD 70 (2004) 043528


Dark Energy & Gravity

Modification of Einstein Gravity

Olmo, gr-qc/0505135,6

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.


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

The influence of dark energy on the cosmic expansion modifies the distance to the CMB last scattering surface



Dark Energy

Dark energy models with the same

and all other parameters held fixed have nearly identical CMB anisotropy spectra.

Huey et al, PRL 59 (1999) 063005


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


SNAP: SuperNova Acceleration Probe


Kim et al, MNRAS 347 (2004) 909


select theoretical model

calculate F for proposed experiment

use eigensystem to project limits

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?

Fit a constant w to data

(true w need not be constant)

For fixed m , more negative w means more distant objects

If w<-1 is found

then w < -1,

or m is wrong

Kaplinghat & Bridle, PRD 71 (2005) 123003


Dark Energy

What are the fundamental bounds on w?





Hawking & Ellis, 1973



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) matter which permit the proof of singularity theorems.

New type of singularity: Sudden Future Singularity

A spacelike singularity as the curvature diverges in finite time

Barrow CQG 21 (2004) L79; PLB 180 (1987) 335

Davies, Ann. Inst. Henri Poincare 49 (1988) 297

Unnecessary to violate strong energy condition!

Big Rip: violates null or dominant energy condition with w < -1

RC, Kamionkowski, Weinberg, PRL 91 (2003) 071301


Dark Energy

How to achieve w<-1?

requires special considerations

negative kinetic energy

Hsu et al, PLB 597 (2004) 270

Cline et al, PRD 70 (2004) 043543

Carroll et al, PRD 68 (2003) 023509;

PRD 71 (2005) 023525

Or it signals a breakdown of gravity? Dark matter?

Or it simply means we are mis-interpreting the data!



Dark Energy:

positive energy density increases with time!

Universe ends catastrophically in a finite time!

Caldwell, PLB 545 (2002) 23

Horizon radius shrinks to a point: every particle is torn away and isolated

Force equation for a gravitationally-bound particle

Caldwell et al, PRL 91 (2003) 071301

Perivolaropoulos, PRD 70 (2004) 123529

Objects on smaller and smaller scales will be ripped apart.


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 body

exploding 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 CDM 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

Roadmap for Cosmology:New Physics in Light of Dark Energy

Robert Caldwell

Dartmouth College

September 2005