Astronomy & Celestial Mechanics
the sky, computed
Concept

Phantom energy — where it appears

Dark energy with an equation-of-state parameter below −1, whose density grows as the universe expands. No simple scalar field behaves this way, and a phantom that persists ends the universe in a finite time.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Whether an event horizon exists at all, against one number. The comoving event horizon today — the distance a signal sent now will ever cover — against the equation of state of the dark energy, for a flat universe with the measured matter density. The curve runs away at w = −1/3 and does not exist above it: that is where the expansion stops accelerating, and in a universe that does not accelerate the integral ∫da/a²E diverges and every galaxy is eventually reachable, however far away. Below −1/3 the horizon is finite and shrinks as w falls, because a more negative equation of state makes the dark energy density grow with time rather than stay constant. At the cosmological constant's w = −1 the horizon is 16.7 billion light years against a particle horizon of 46.1, so 4.7 per cent of the volume now observable is still reachable. The band is the measured −1.03 ± 0.03. What the figure is for is the asymmetry in what the measurement still allows: two sigma toward zero puts the horizon at 17.5 Gly and two sigma the other way at 14.7, and the shape of the curve means that the closer the true value sits to −1/3 the more violently the answer moves. The reachable fraction is not a robust number in the way the particle horizon is.

Whether there is a horizon at all

An event horizon exists precisely when the expansion accelerates, and its size is not a smooth function of how much. The integral that defines it runs away as the equation of state approaches minus a third, so two sigma either way on a measured number are two very different futures.

cosmology · Horizons Three fits of the dark energy's equation of state, and the line they all cross. The equation of state w of the dark energy against redshift, for the three combined fits published with the second year of acoustic-scale data from the largest spectroscopic galaxy survey — the same galaxy and microwave-background data with three different supernova compilations — each written as w = w₀ + wₐ z/(1 + z). A cosmological constant is the horizontal line at −1. All three fits have w above −1 today (between −0.84 and −0.67) and below it in the past, and they cross it at redshift 0.35, 0.44, 0.41. Below −1 lies the phantom region, where a density grows as the universe expands; a single field with ordinary kinetic energy can be on either side of the line but cannot cross it. The preference for these fits over a constant is quoted at 2.8, 3.8 and 4.2 standard deviations, and the only thing that differs between the three is the supernovae.

A crossing that may belong to the fitting form

Allow the dark energy's equation of state to change and three independent fits say it has: above −1 today, below it before redshift half. The data hold w well at one redshift only, a line crossed from below is one no single field can cross, and a straight line in the scale factor fitted to a curved history crosses it anyway.

cosmology · Dark energy

Named alongside it

The objects these essays reach for when they reach for this one.

Cosmological constantDark energyEquation of stateAcoustic scaleBig ripComoving distanceConformal timeDe sitter spaceDeceleration parameterDegeneracy directionEvent horizonFigure of merit

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