Dark Energy the Easy Way?

Eric V. Linder

Direct Detection of Dark Energy on Solar System Orbits

The energy density of a physical dark energy will have no detectable direct effect on motions within the solar system. The dark energy density, summed over the solar system volume, amounts to an energy equivalent to that of only three hours of sunlight (at 1 AU). Only if dark energy changes the structure of gravity on solar system scales might it be directly detectable through solar system motions.

Direct Detection of Hubble Expansion in the Solar System

Effects of the Hubble expansion (not even the acceleration, just the expansion itself) enter as perturbations about the background in order (HR)^2, where R is the scale of the system. So for the solar system, with R=10^13 cm, the effects are of order (10^13/10^28)^2=10^-30, undetectable.

Detection of Dynamic Scalar Field through Varying Constants of Nature

If dark energy is not minimally coupled, but couples to fields other than gravity (or to gravity nonminimally), it will violate the Equivalence Principle. These couplings can cause variations in the fine structure constant of electromagnetism, Newton's constant, the proton to electron mass ratio, etc. Unfortunately, without a fundamental theory we cannot calculate how they would vary - and in particular how the variations interact with each other. So while there might be a role for laboratory and accelerator (and cosmological variation) experiments in exploring dark energy from this perspective, it is difficult to predict how observables would actually be affected, and of course stringent limits exist already on such variations. But any variation of basic constants would of great interest and excitement.

Direct Detection of Cosmic Acceleration

Cosmological redshift arises from the change of the cosmic scale factor over time - the expansion. If the expansion rate is not itself constant, i.e. it accelerates (or decelerates), then the redshift of an object also changes over time. The drift with observer time is dz/dt_o=H_0(1+z)-H(z), so the time scale for this redshift shift or drift is of order the Hubble time. Sandage discussed this in 1962 and it was considered for general equation of state universes by Linder in 1991.

Some interesting things to note: even a steady state universe exhibits a redshift drift; redshifts do not necessarily measure only the cosmological expansion, but include any other (exotic) effects on the photon four-momentum; and just as peculiar velocities upset measurement of cosmological redshifts, peculiar accelerations even at quite low levels confuse the sensitive measurements needed for redshift drift measurement. In particular this last effect makes direct detection of acceleration problematic, even with a decade long baseline and near term technology.

For more detailed discussion of direct acceleration, see Sections 3.5.2 and 3.5.3 of Linder's First Principles of Cosmology (Addison Wesley, 1997) and its additional web discussion.

Thus, these alternative possibilities to cosmological expansion and growth measurements for exploring the nature of dark energy do not appear to be likely to be fruitful, and no easier!