Historical research guide · 0681 · 2022
Rapidly Descending Dark Energy and the End of Cosmic Expansion
Cosmin Andrei · Anna Ijjas · Paul J. Steinhardt
In one minute
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.
Connection
Chapter 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.
From the source
If 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
For 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
The 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
Detecting 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
The 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)
The 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
The way in
https://doi.org/10.1073/pnas.2200539119How 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