Rapidly Descending Dark Energy and the End of Cosmic Expansion
Cosmin Andrei · Anna Ijjas · Paul J. Steinhardt
Abstract and summary · read the original at the source
In one page
Cosmin Andrei, Anna Ijjas and Paul Steinhardt ask a question the standard picture never has to face: if dark energy is not a constant but a field slowly rolling downhill, when does the acceleration stop? In the textbook model dark energy is Einstein’s cosmological constant and the universe accelerates for ever. Replace the constant with quintessence — a scalar field descending a potential that keeps falling and eventually passes below zero — and general relativity forces a sequence instead: acceleration ends, expansion halts, and the universe passes into a gentle contraction. Every handover is smooth, so observers would live through all three. The authors then work out the soonest this could begin without straining any parameter, and the answer is close to home: with the steepest potential still consistent with the supernova data to within two standard deviations, acceleration could end about a tenth of a Hubble time from now and expansion itself about a quarter — billions of years, not the eternity a constant implies. Today’s measurements cannot yet separate the two futures.
Why it matters hereChapter 2 turns on what dark energy actually is, and this paper is the clearest statement of what changes if it is a rolling field rather than a fixed constant: the universe acquires an expiry date for its own expansion. Chapter 13 needs the whole picture to hang together, and here the same field that drives today’s acceleration also supplies the slow contraction a cyclic cosmology requires. Read it alongside the DESI baryon-acoustic-oscillation result on this site at /library/stm-15541611e8 and Shlivko and Steinhardt’s reading of the dark-energy constraints at /library/stm-2d66d437f4.
What it claims
01If dark energy is quintessence — a scalar field evolving down a potential that decreases monotonically and passes sufficiently below zero — then Einstein’s equations dictate a series of smooth transitions rather than endless acceleration: the potential energy falls below the kinetic energy and acceleration gives way to decelerated expansion, then the total energy density and with it the Hubble rate reach zero and expansion turns into slow contraction. Unlike the alternative in which a metastable vacuum decays by nucleating a bubble, every stage here is slow and smooth enough that observers survive to witness it.Introduction and ’The Q-SC-CDM model’, Equations 1 to 5
What to watch02For the family of potentials studied — a positive exponential term dominating today minus a negative exponential term that takes over later — the steepest form compatible with current observations to within two standard deviations has a scale of about 1.7 reduced Planck masses, and in the worked example the end of accelerated expansion arrives 0.1 Hubble times from now and the end of expansion 0.27 Hubble times, where one Hubble time is about 14 billion years. Steeper potentials bring both dates nearer still.’A worked example’ and ’Results and Discussion’, Equation 6; Figures 1, 2 and 4
Published and peer-reviewed03The model reproduces what is already measured: the predicted luminosity-redshift relation fits the supernova catalogue compiled from the Pantheon dataset to within two standard deviations, and going backwards in time its Hubble curve runs nearly parallel to the best-fit cosmological-constant model, so present observations do not distinguish the two. The authors note that because the past evolution is so similar, the model neither eases nor worsens the disagreement between the measured expansion rates.Figure 3 and Figure 2(a); the parenthetical remark on the expansion-rate problem
Published and peer-reviewed04Detecting the approach of these transitions is hard for a structural reason: the cosmic microwave background, baryon acoustic oscillations and distant supernovae all report light emitted long ago, whereas the turn to deceleration and contraction may occupy only a small fraction of a Hubble time. The generic route named by the authors is a better measurement of the total cosmic equation of state and above all of its rate of change — in their worked example the relevant quantity has already passed its maximum and begun to decrease as the field’s kinetic energy grows, and further observable effects would follow from how the field couples to other matter.’Results and Discussion’, third paragraph, citing references 15 to 18
What to watch05The scenario supplies exactly what a cyclic cosmology needs. Slow contraction — a scale factor going as the inverse Hubble rate raised to a power below one third, and 0.02 in the worked example — is what makes the universe homogeneous, isotropic and spatially flat and sets up the nearly scale-invariant spectrum of density perturbations; it would last of order a billion years before a non-singular classical bounce begins a new expanding phase that reheats far above the electroweak scale. In such a universe the question of why dark energy came to dominate just as galaxies and planets formed looks less mysterious, because that interval is the longest and the largest in volume.’Results and Discussion’, paragraphs on cyclic cosmology, citing Ijjas and Steinhardt 2019 (reference 19)
What to watch06The same ending is reached from quantum gravity. The swampland conjectures allow only the possibility considered here — dark energy as a quintessence field with a monotonically decreasing potential — and set an upper bound on how long the current acceleration can last of about 2.4 trillion years, roughly 160 Hubble times; the lower bound derived in this paper from observational constraints is consistent with it. Three independent lines of reasoning point the same way: the end of expansion could come surprisingly soon.’Results and Discussion’, final two paragraphs, citing references 9, 22, 23 and 24
What to watch
Read it · abstract
Abstract
If dark energy is a form of quintessence driven by a scalar field φ evolving down a monotonically decreasing potential V(φ) that passes sufficiently below zero, the universe is destined to undergo a series of smooth transitions. The currently observed accelerated expansion will cease; soon thereafter, expansion will come to end altogether; and the universe will pass into a phase of slow contraction. In this paper, we consider how short the remaining period of expansion can be given current observational constraints on dark energy. We also discuss how this scenario fits naturally with cyclic cosmologies and recent conjectures about quantum gravity.
Cosmin Andrei and Paul J. Steinhardt, Department of Physics, Princeton University; Anna Ijjas, Center for Cosmology and Particle Physics, Department of Physics, New York University. Published as Proceedings of the National Academy of Sciences 119 (15), e2200539119 (2022); preprint arXiv:2201.07704v2.
(Abstract only — see the rights note above for why the full text is not reproduced here. The complete paper, with the Q-SC-CDM potential and its parameters, the Friedmann and scalar-field equations governing the transitions, the Hubble-rate and equation-of-state histories, the supernova fit and the minimum time intervals plotted against the steepness of the potential, is at the source. The DESI baryon-acoustic-oscillation measurements are on this site at /library/stm-15541611e8, and Shlivko and Steinhardt’s assessment of the dark-energy constraints at /library/stm-2d66d437f4.)
The way in
https://doi.org/10.1073/pnas.2200539119LICENCE. Published as Proceedings of the National Academy of Sciences 119 (15), e2200539119, 12 April 2022; the version of record carries Creative Commons Attribution-NonCommercial-NoDerivatives 4.0, confirmed on the Crossref record and in Europe PMC (PMC9169868). That licence permits verbatim redistribution but not the cleaned, partly reformatted rendering this site makes of a full text, so the page holds the summary, the claims and the authors’ own abstract and sends the reader to the source. The preprint, arXiv:2201.07704v2 of 15 March 2022, carries the arXiv.org perpetual non-exclusive distribution licence and no Creative Commons statement. The claims below are read from that preprint text.
How to cite it
Cosmin Andrei, Anna Ijjas, Paul J. Steinhardt (2022) Rapidly Descending Dark Energy and the End of Cosmic Expansion. doi:10.1073/pnas.2200539119
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