Prospects for probing the dark energy via supernova distance measurements
Dragan Huterer · Michael S. Turner
Abstract and summary · read the original at the source
In one page
Written months after the supernova result that showed the expansion of the universe speeding up, Dragan Huterer and Michael Turner of Chicago and Fermilab ask the obvious next question: can the same supernovae tell us what the dark energy actually is? Their answer is a set of reconstruction equations. Measure how far away exploding stars are as a function of redshift, take the first and second derivatives of that curve, and out drops the pressure-to-density ratio of the dark component — and, if it is a rolling scalar field, the shape of the field’s potential energy curve itself. They then test the idea honestly, by simulating forty measurements out to redshift one, adding realistic noise, and rebuilding the potential a thousand times over. With two per cent distance errors the input curve comes back inside the confidence band, and every constant pressure law can be excluded. Beyond redshift about 0.8 the dark energy is too small a fraction of the total to leave a trace.
Why it matters hereChapters 2 and 13 turn on one number: what fills empty space, and whether it stays the same. This is the paper that turned that into a measurement plan rather than a philosophical question — it says exactly which curve to measure, how precisely, and what each answer would mean. It is also the ancestor of everything the site tracks under dark-energy evolution today. Read it beside the naturally relaxed vacuum-energy model at /library/stm-a322526415 and the DESI DR2 result at /library/stm-15541611e8, which is the modern version of the discrimination this paper designed.
What it claims
01Distance measurements to more than fifty Type Ia supernovae out to redshift about one show the expansion of the universe accelerating rather than slowing. Combined with a cosmic-background-radiation peak near multipole 200, which indicates a flat universe, and dynamical measurements giving a matter density near 0.4 of critical, this implies an unknown component with strongly negative pressure making up roughly two thirds of the critical density.Abstract; Section 1, Introduction
Settled physics02The three candidates for the dark component differ in one measurable quantity: the ratio of its pressure to its energy density. A cosmological constant, that is vacuum energy, gives exactly minus one; a frustrated network of topological defects of dimension N gives minus N over three; an evolving scalar field — quintessence — is the only one whose value can change with time and can take any value. Distinguishing them therefore reduces to measuring that ratio and asking whether it moves.Section 1, Introduction
Published and peer-reviewed03The authors derive the reconstruction equations. The potential energy curve of the scalar field, and the rate at which the field rolls, can both be written parametrically in terms of the coordinate distance to redshift z together with its first and second derivatives and the present matter density. Without assuming a scalar field at all, a companion equation returns the bulk pressure-to-density ratio as a function of redshift from the same measured curve.Section 2, Reconstruction Equations, Equations 8, 9 and 17
Published and peer-reviewed04Supernovae are the right probe for this and the microwave background is not, for a simple physical reason: the background radiation samples the universe at redshift about a thousand, when the ratio of dark-energy density to matter density was smaller than one part in a million, whereas supernovae sample the recent epoch, when the dark energy is just beginning to dominate and all of the scalar-field action is happening.Section 1, Introduction
Published and peer-reviewed05Monte-Carlo test of the method: forty simulated supernova distances out to redshift one, fitted with a fourth-order polynomial and reconstructed a thousand times. With two per cent luminosity-distance errors the input potential is recovered inside the ninety-five per cent confidence band, and for an exponential potential every constant pressure-to-density law can be excluded at better than 99.9 per cent confidence. The dominant error comes from taking a second derivative of noisy data, and a ten per cent uncertainty in the matter density barely changes the result.Section 3, Simulating Reconstruction, figs. 1 to 3
Published and peer-reviewed06The method has a horizon and a bottleneck, both named by the authors. Because the dark-energy fraction falls off steeply with redshift, reconstruction beyond about redshift 0.8 becomes extremely difficult and data above redshift one are of very limited value. What to watch is the reliability of the supernovae themselves — then ten to twenty per cent per object, from host-galaxy reddening, intrinsic scatter in the brightness–decline relation, possible evolution with redshift and differing progenitor composition. Ten supernovae per redshift bin, about five hundred in total, would bring the distance curve to three per cent.Section 3 closing paragraph; Section 4, Discussion
What to watch
The way in
https://arxiv.org/abs/astro-ph/9808133Posted to arXiv in 1998 under the pre-2004 assumed licence, which is not a Creative Commons licence, so only the abstract is reproduced here. Published as Physical Review D 60, 081301(R), 1999; report number FERMILAB-Pub-98/247-A.
How to cite it
Dragan Huterer, Michael S. Turner (1998) Prospects for probing the dark energy via supernova distance measurements. doi:10.1103/PhysRevD.60.081301
Where it sits in the curriculum