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Dark Energy Cosmology. Robert Caldwell Dartmouth College. INPE Winter School September 12-16, 2005. Cosmic Evolution. Cosmic Acceleration. observations of type 1a supernovae indicate our universe is accelerating. RC, Physics World, May 2005 data: Riess et al, ApJ 607 (2004) 665.

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dark energy cosmology

Dark Energy Cosmology

Robert Caldwell

Dartmouth College

INPE Winter School

September 12-16, 2005


Cosmic Acceleration

observations of type 1a supernovae indicate our universe is accelerating

RC, Physics World, May 2005

data: Riess et al, ApJ 607 (2004) 665


Cosmic Acceleration

observations of type 1a supernovae indicate our universe is accelerating

universe contains m, k, 

k=0 (CMB)

basic picture

spatially-flat RW spacetime

acceleration due to :

Riess et al, ApJ 607 (2004) 665


Cosmological Constant

“The Cosmological Constant and the Theory of Elementary Particles”

Zel’dovich, Sov. Phys. Uspekhi 11 (1968) 381

“The genie () has been let out of the bottle….”

“A new field of activity arises, namely the determination of ”

The quantum vacuum energy of scalar particles resembles a cosmological constant

Problem: IR phenomenon has UV divergence


Casimir Effect

sketch of basic calculation

oscillator energy

energy density

with boundaries

change due to plates

pressure difference

uniform stress-energy between the plates

Milton, 2001


Casimir Effect: Measurements

Lamoreaux, PRL 78 (1997) 5

Mohideen & Roy, PRL 81 (1998) 4549

Bressi et al, PRL 88 (2002) 041804


Casimir Effect

Vacuum Energy is not Immutable

Casimir Effect in a Weak Gravitational Field

Energy density carried in vacuum fields distorts in response to a weak gravitational field

Caldwell, astro-ph/0209312


Cosmological Constant

Are unattached vacuum loops real? Do they gravitate?

Casimir Effect: a real manifestation of fluctuations of the QED vacuum

Quantum vacuum contributes to inertia

Jaekel, Lambricht, Reynaud, New Astron. Rev. 46 (2002) 727

Casimir effect without the vacuum

Jaffe, PRD 72 (2005) 021301


Constant Problems

Numerous sources of an effective  in physics beyond SM

Everywhere you look in QFT (even standard model)

Symmetry-breaking vacuum energy (Higgs-like fields)

Supergravity 3-form (may be quantized)

Ways to get rid of it

Cancellation (unstable to dynamics)

Supersymmetry (broken)

Euclidean QG (probabilistic)

Weinberg, Rev Mod Phys 61 (1989) 1

Any physics content? There must be fluctuations!

Ghost Condensation…

Arkan-Hamed et al, JHEP 0405 (2004) 074


Action Principle

Einstein 1919

Anderson & Finkelstein, Am J. Phys. 39 (1971) 901

van der Bij and van Dam, Physica 116A (1982) 307

Unimodular gravity

a theory of (linear quantum) gravitation …

subject to symmetries satisfying -det(g)=1


nearly equivalent formulation of Einstein’s GR


Action Principle: Multiplication

Linde, PLB 200 (1988) 272

  • Two spacetimes, x & y
  • Identical matter content
  • Antipodal symmetry:
  • Result: zero vacuum and trace-free GR

quantum effects?

observable consequences?


Action Principle: Subtraction

Kaplan & Sundrum, hep-th/0505265

  • One spacetime
  • Identical matter content
  • Energy parity symmetry
  • Result: zero vacuum but there are ghosts

“ghost sector” must be underpopulated

classically stable, but QG instability

Slow instability with QG cutoff:  ~ 10-3 eV

observable consequence:

~30 breakdown of

gravitational potential


Cosmological Constant: a bookmark

Regard  as a placeholder until observation, experiment, and theory can determine the underlying physical laws behind the dark energy phenomenon.

Astrophysical phenomena not sensitive to the dark energy:

use  as a simple, economical model

Cosmological phenomena sensitive to the dark energy:

Question observations / experiments

Test theoretical foundation

Search for conflicts with baseline 

What are the alternatives?


Dark Energy

What is it?

The cosmological constant?

A new particle / field?

A new aspect of gravitation?

A misinterpretation of observations?

Astrophysical confusion?


Lives of the Cosmological Constant

1917 Einstein, deSitter

1968 Zel’dovich

History: Kragh, “Cosmology & Controversy”


 + dark matter or baryonic models

Numerous authors investigated the cosmological consequences of an additional smooth, time-varying component of the cosmic fluid.

Kinematic Tests of Exotic, Flat Cosmological Models

Charlton & Turner, ApJ 313 (1987) 495

Cosmology with a Time-Variable Cosmological “Constant”

Peebles & Ratra, ApJ 325 (1988) L17


Dark Energy

close the system of equations

evaluate classical tests of cosmology to constrain “w”


Dark Energy

w: equation-of-state controls the slope of the dark energy curve

past: in the simplest model, the dark energy does not play a significant role in cosmic evolution before z~2

present: the time-evolution of w determines the time-evolution of the dark energy

future: unknown without a reliable model of the dark energy


Dark Energy

The dark energy phenomena could be due to a new, very-light scalar field.


Why a scalar field?

This is arguably the simplest method of introducing new physics within the well-tested framework of quantum physics.

Due to the similarity of the dark energy phenomena with inflation, it seems plausible that a similar mechanism is responsible.

Scalar fields, while not necessarily fundamental, are ubiquitous in theories beyond the standard model of particle physics.


Dark Energy

The scalar field is a pioneer,

sent out to explore new worlds of physics!

  • Waves, Optics
  • Electrodynamics
  • Quantum Mechanics
  • Scalar QED
  • Field Theory
  • Symmetry Breaking
  • Dilatons, Moduli
  • Nordstrom’s Scalar Gravity
  • Kaluza-Klein Unification
  • Dirac and Jordan’s Cosmology
  • Scalar-Tensor Gravity
  • Inflaton
  • Quintessence

Gravity and the Tenacious Scalar Field

Carl Brans, gr-qc/9705069