Why Is the Expansion of the Universe Speeding Up?

The core insight

Cosmic expansion is accelerating, driven by something with repulsive gravity — but nobody knows if it is an unchanging constant, a dynamical field, or a clue that general relativity itself breaks down on cosmic scales.

The question

State it plainly: what is the physical nature of the negative-pressure component — dark energy — that is causing the Friedmann equation-governed expansion of the universe to accelerate rather than decelerate?

That single sentence hides three genuinely distinct possibilities, and distinguishing them is the actual scientific problem.

The first possibility is that dark energy is the cosmological constant, Λ, exactly as Einstein first inserted it into his field equations in 1917 — not to explain acceleration, which nobody had observed yet, but to permit a static universe. In this picture, empty space itself possesses a fixed energy density that never dilutes as the universe expands, and this vacuum energy exerts a smooth, unchanging negative pressure. It is the simplest possible answer: one number, unchanging across cosmic history, unchanging across the sky.

The second possibility is that dark energy is a dynamical field, often generically called quintessence, whose energy density and pressure evolve with time (and possibly with position). Under this view, "dark energy" is a substance with its own equation of motion, much like the inflaton field thought to have driven the universe's earliest exponential expansion, or like a slowly rolling scalar field left over from some deeper high-energy theory. If this is right, the acceleration we see today might strengthen, weaken, or even reverse in the cosmic future.

The third possibility is more radical: there is no new substance at all. Instead, general relativity — spectacularly successful in the solar system, around black holes, and in the early universe — subtly fails at the scale of billions of light-years, and what we are misinterpreting as a mysterious energy component is actually the signature of modified gravity. In this view, dark energy is not a thing but a symptom, evidence that Einstein's field equations need an extension at the largest distances, just as Newtonian gravity needed extension near black holes and at high velocity.

What would an answer look like? Not a single number, but a function: the equation-of-state parameter w(a), which relates dark energy's pressure p to its density ρ via p = wρ, tracked as a function of the universe's scale factor a (essentially, cosmic time). A true cosmological constant demands w = −1, exactly, forever. Any convincing, statistically significant departure from w = −1, or any redshift-dependence w(z), would kill the simplest model and point toward dynamical dark energy or modified gravity. This is why the question is hard: the signal we are chasing is a small, slow deviation from a very well-measured baseline, buried in astrophysical noise, systematic calibration errors, and our incomplete understanding of gravity on the largest scales we can probe.

What we know

The story begins, as so much of modern cosmology does, with Hubble's law. In the late 1920s, Edwin Hubble found that galaxies recede from us with velocities proportional to their distance, v = H₀d. The universe is expanding — space itself stretching, carrying galaxies apart, and stretching the wavelength of the light they emit, which is why we call this stretching redshift. A photon that leaves a distant galaxy with some wavelength arrives at our telescopes redder, its wavelength dilated by the same factor the universe has expanded since it was emitted. Redshift is, in this sense, a direct fossil record of cosmic history: a light-echo timestamp.

Einstein's general relativity, applied to a homogeneous, isotropic universe, produces the Friedmann equations, which relate the expansion rate H(t) = ȧ/a to the energy content of the cosmos:

H² = (8πG/3)ρ − k/a² ,

where ρ is the total energy density (matter, radiation, and anything else), k describes spatial curvature, and a(t) is the scale factor tracking cosmic expansion. A companion "acceleration equation" governs ä, the second derivative of the scale factor:

ä/a = −(4πG/3)(ρ + 3p) .

This second equation is the crux of the whole mystery. Ordinary matter has positive pressure or none at all (p ≥ 0), and radiation has p = ρ/3 — both make the right-hand side negative, so ä < 0: gravity decelerates the expansion, exactly as intuition demands. But if some component has sufficiently negative pressure, specifically p < −ρ/3, the quantity (ρ + 3p) turns negative, and ä becomes positive. Expansion accelerates. This is not a loophole or an exotic addendum to general relativity; it is baked into the theory from the start. Einstein's equations have always permitted repulsive gravity, provided you can find a substance strange enough to supply it.

For most of the twentieth century, this was a theoretical curiosity, not an observational necessity — until distant exploding stars made it unavoidable.

<span class="wiki-link-missing">Type Ia supernovae</span> are the standard candles that let cosmologists measure not just how fast the universe is expanding today, but how the expansion rate has changed over billions of years. A Type Ia supernova occurs when a white dwarf star, accreting matter from a companion (or merging with another white dwarf), approaches the Chandrasekhar mass limit of about 1.4 solar masses and detonates in a runaway thermonuclear explosion. Because the trigger mass is nearly universal, these explosions reach nearly uniform peak luminosity — calibratable to a few percent using the well-known relationship between light-curve shape and brightness (the Phillips relation). Knowing their true luminosity, and measuring their apparent brightness, gives their distance via the inverse-square law. Measuring their redshift gives, in effect, when they exploded. Put many such standard candles at many redshifts on a single plot — the Hubble diagram — and you're mapping the entire expansion history of the universe.

That is exactly what the High-Z Supernova Search Team, led by Brian Schmidt and Adam Riess, and the Supernova Cosmology Project, led by Saul Perlmutter, did in the mid-1990s. Both groups expected to measure the deceleration parameter and pin down how much matter would eventually decide the universe's fate — whether it would collapse in a Big Crunch or expand forever. Both found supernovae systematically fainter, at fixed redshift, than a decelerating universe predicted. The simplest fit required roughly 70 percent of the universe's energy budget to be something with negative pressure — dark energy — and about 30 percent to be matter, most of it the unrelated but equally mysterious dark matter.

This was not evidence from supernovae alone for long. The pattern of hot and cold spots in the cosmic microwave background, first exquisitely mapped by the COBE and then WMAP and Planck satellites, encodes the universe's total energy density through the characteristic angular size of acoustic oscillations frozen into the plasma at recombination. That measurement independently demands a spatially flat universe (k ≈ 0) with a total density budget that only balances if roughly 68 percent is dark energy. Baryon acoustic oscillations — a subtler standard ruler imprinted in the clustering of galaxies, the relic scale of pre-recombination sound waves — corroborate the same picture from a third, largely independent direction. Three separate observational techniques, with different systematics, converge on the same answer. This convergence is why dark energy, however mysterious its identity, is not seriously in doubt as an empirical phenomenon.

In 1998, two teams of astronomers pointed their telescopes at the most distant stellar explosions they could find, expecting to measure how much the universe's expansion was slowing down. Gravity, after all, pulls things together — every galaxy tugging on every other should act as a brake on cosmic expansion. Instead, both teams found the opposite. The faraway supernovae were fainter than they should have been, which meant they were farther away than expected, which meant that somewhere across the past several billion years, the expansion of space had shifted into a higher gear. The universe was not just growing. It was accelerating.

That result, initially so strange that some researchers suspected a systematic error in dust or evolving supernova physics, has now been confirmed by more than two decades of independent evidence: finer supernova surveys, the cosmic microwave background, the large-scale clustering of galaxies, gravitational lensing maps. Something is pushing space apart, and it dominates the energy budget of the cosmos — roughly 68 percent of everything there is, by the standard reckoning. We have given this something a name, dark energy, and a placeholder in our equations. We have not the faintest consensus on what it actually is.

This is one of those rare scientific situations where the data are excellent and the theory is almost embarrassingly bare. We can measure the effect to a few percent precision. We cannot say whether it is a fixed feature of empty space, a field that evolves in time, or a symptom that our two-hundred-year-old law of gravity simply gives out at the largest scales the universe offers.

svg[The three cosmic actors and their pressure] cosmic time → scale factor a(t)

[Expansion history: matter dominance decelerates the scale factor early on; a negative-pressure component later takes over and the expansion curve bends upward — the signature actually measured in the supernova Hubble diagram.]

The essential theoretical point, again: whatever dark energy is, it must have equation-of-state parameter w close to −1 today, and its density must have been subdominant in the early universe (otherwise it would have suppressed structure formation and altered the cosmic microwave background in ways we do not see) but must have overtaken matter density roughly five to six billion years ago, precisely because matter density dilutes as a⁻³ while a true cosmological constant does not dilute at all. This "coincidence" — that we happen to live at the epoch when the two components are comparable — is itself an open puzzle, sometimes called the cosmic coincidence problem, nested inside the larger mystery.

Where it breaks down

The trouble is not that the data are inconsistent. The trouble is that the leading candidate explanation, the cosmological constant, is theoretically embarrassing on a scale almost without parallel in physics.

If dark energy is literally the energy of the vacuum — zero-point fluctuations of quantum fields, permeating all of space — then quantum field theory offers a way to estimate its magnitude. That estimate, using an ultraviolet cutoff at the Planck scale, exceeds the observed dark energy density by something like 120 orders of magnitude. Even more conservative estimates, cutting off at scales where we trust quantum field theory (say, the electroweak scale), still overshoot by tens of orders of magnitude. This is widely regarded as the worst quantitative prediction failure in the history of physics, and it constitutes its own frontier — the cosmological-constant-problem — distinct from, but tightly bound to, the question of dark energy's identity. Any theory that identifies dark energy with vacuum energy inherits this problem in full.

There is a second, subtler breakdown, one of interpretation rather than mere magnitude. All the leading evidence for dark energy — supernovae, the cosmic microwave background, baryon acoustic oscillations — infers its existence by assuming that general relativity, applied to a smoothed, homogeneous universe, correctly describes the expansion history. But the real universe is lumpy: galaxies, clusters, voids, filaments. A minority but persistent research program argues that the observed acceleration could be, at least partly, an artifact of how light propagates and how averages are taken through an inhomogeneous universe — backreaction from structure formation mimicking the effect of a repulsive component without any real dark energy at all. This idea has not overturned the standard picture (most careful calculations suggest the effect is far too small to explain the observed acceleration), but it has not been definitively closed off either, and it exposes an uncomfortable truth: the "smooth universe" assumption underlying the entire Friedmann-equation framework is an approximation, and we do not have complete control over its errors.

A third and more recent crack has opened directly in the data. In 2024 and 2025, results from the Dark Energy Spectroscopic Instrument (DESI), which measures baryon acoustic oscillations across millions of galaxies and quasars, reported hints — at roughly 2 to 4 sigma significance depending on which datasets are combined — that dark energy's equation of state may not be a constant −1 after all, but instead evolves with redshift: appearing slightly more negative than −1 (so-called "phantom" behavior) in the past and creeping toward −1 or above it today. This is far from a discovery; it depends on combining DESI with supernova compilations and the cosmic microwave background, and different supernova catalogs (Pantheon+, Union3, DES-SN5YR) pull the fit in somewhat different directions. But it is the first serious observational crack in the simple Λ picture in a quarter-century, and it has reenergized the entire field.

The contenders

The cosmological constant (ΛCDM). This is the reigning model, not because it is theoretically satisfying but because it is stunningly economical: one new parameter, w fixed at exactly −1, and it fits essentially every large-scale cosmological dataset we have to good precision. Its appeal is Occam's razor made quantitative. Its trouble is twofold: the vacuum-energy magnitude catastrophe described above, and the fact that a true constant offers no dynamical explanation for why it takes the coincidental value it does, or why acceleration began right around the epoch when complex structures — including us — were forming. Critics call this fine-tuning; defenders sometimes invoke anthropic reasoning (in a multiverse of differing vacuum energies, only those hospitable to galaxy formation would host observers to measure them), which is intellectually serious but famously difficult to test.

Quintessence and dynamical dark energy. Here dark energy is a scalar field, φ, rolling slowly down a potential V(φ), much as the inflaton is hypothesized to have done in the universe's first fraction of a second. Its equation of state w(a) need not equal −1; it can vary, cross −1 (so-called quintom models), or even dip below −1 temporarily (phantom-like behavior) without necessarily violating known energy conditions if multiple fields or non-canonical kinetic terms are involved. The appeal of quintessence is that it converts dark energy from a fixed embarrassment into a dynamical, in-principle-predictable process, potentially connected to particle physics — some models tie the quintessence field to axion-like particles, to the same machinery that may have driven inflation, or to string-theory moduli fields. Its trouble is that it trades one fine-tuning problem for another: the potential V(φ) must be extraordinarily flat to keep the field rolling slowly enough, over a timescale comparable to the age of the universe, without the usual radiative corrections that plague scalar field theories (the same technical naturalness problem that dogs the Higgs field, but worse). It also, so far, has no unique observational signature beyond "w is not exactly −1" — a huge space of models can produce nearly any w(a) trajectory, so a detection of evolving w confirms this general class without picking out a specific mechanism.

Modified gravity. Here the boldest move: throw out the idea that a new energy component exists at all, and instead modify the Einstein-Hilbert action itself. Popular constructions include f(R) gravity, where the Ricci scalar R in the gravitational action is replaced by some more general function f(R) chosen so that late-time acceleration emerges naturally from geometry rather than from a substance; braneworld models such as the Dvali–Gabadadze–Porrati (DGP) proposal, where gravity leaks into an extra dimension at large distances and weakens in a way that mimics acceleration; and more general "dark energy as modified gravity" frameworks such as Horndeski theories, the most general scalar-tensor theories with second-order equations of motion. The appeal here is conceptual economy of a different kind: no new fluid, no coincidence problem to explain independently — acceleration is simply gravity's true behavior at low curvature and large scale, analogous to how Mercury's perihelion precession revealed that Newtonian gravity itself, not some undiscovered planet, needed replacing.

The trouble with modified gravity is severe and specific: gravitational-wave astronomy delivered it a near-fatal blow in 2017. The neutron-star merger GW170817 was observed in gravitational waves by LIGO/Virgo and, 1.7 seconds later, in gamma rays by the Fermi and INTEGRAL satellites. That tiny time delay, after traveling some 130 million light-years, constrained the speed of gravitational waves to equal the speed of light to about one part in 10¹⁵. This single observation eliminated or severely fine-tuned an entire large class of modified-gravity dark-energy models (particularly many Horndeski-type theories that predicted a different gravitational-wave speed). Some modified-gravity models survive — those engineered to keep gravitational waves luminal — but the space of viable options shrank dramatically overnight, a rare case of a single, clean astrophysical coincidence killing off years of theoretical work.

Figure
Three explanations for the same acceleration
Cosmological constant w = −1, fixed forever vacuum energy of space ✗ 10¹²⁰ magnitude problem ✓ simplest fit to data Quintessence field w(a) evolves with time rolling scalar field, like φ ✗ needs ultra-flat potential ✓ dynamical, testable w(z) Modified gravity Einstein eqs. altered at cosmological scales ✗ GW170817 excludes much ✓ no new substance needed Same observable today: accelerating a(t), w ≈ −1 ± small error bars Discriminated only by precision w(z), growth-of-structure, and gravitational-wave tests — not by expansion rate alone

[All three contenders can reproduce today's expansion rate; only measurements of how w evolves, how structure grows, and how gravitational waves propagate can tell them apart.]

Beyond these three broad families sit more exotic minority proposals: unified dark fluids that try to make dark matter and dark energy two faces of a single substance (Chaplygin gas models); ideas that gravity is fundamentally entropic or emergent, so that acceleration reflects thermodynamics rather than a field (proposals associated with Erik Verlinde, among others, though these remain far from a complete, quantitatively predictive theory); and the inhomogeneity-and-backreaction proposals mentioned earlier. None of these currently matches the combined explanatory power of ΛCDM, but the field keeps them alive because ΛCDM's own theoretical foundations remain so shaky.

What would settle it

The observational program here is unusually clear, even if the answer is not yet in hand: measure w(a) — dark energy's equation of state as a function of cosmic time — to a precision fine enough to detect or rule out deviations from −1 at the percent level, across as much of cosmic history as possible.

Several major instruments are mid-campaign on exactly this task. DESI, operating at Kitt Peak since 2021, is building the largest three-dimensional map of galaxy and quasar positions ever made, using baryon acoustic oscillations as a standard ruler across redshifts from the present out past z = 2, precisely to track w(z) through the era when dark energy came to dominate. The European Space Agency's Euclid satellite, launched in 2023, and NASA's Nancy Grace Roman Space Telescope, expected to launch by the late 2020s, will map weak gravitational lensing — the subtle distortion of background galaxy shapes by intervening mass — across enormous swaths of sky, providing an independent handle not just on the expansion history but on the growth of cosmic structure, which is the key extra lever that can separate dark energy from modified gravity. This is the crucial diagnostic: a cosmological constant and certain modified-gravity theories can be tuned to produce an identical expansion history, H(z), while predicting different rates at which matter clumps into galaxies and clusters over time. Measuring both the geometry (via distances and redshifts) and the growth (via lensing and galaxy clustering) simultaneously is the only way to break this degeneracy.

The Vera C. Rubin Observatory, having begun science operations in 2025 with its Legacy Survey of Space and Time, will independently discover and characterize thousands of Type Ia supernovae per year, dramatically shrinking the statistical uncertainty on the supernova Hubble diagram and, crucially, allowing tighter control of systematic effects like dust extinction and supernova population evolution that have historically been the chief worry in this measurement.

Gravitational-wave astronomy offers a second, structurally different path. "Standard sirens" — merging neutron stars or black holes observed both in gravitational waves and (for neutron star mergers) electromagnetically — provide an absolute distance measurement without the calibration chain that supernovae require, because the gravitational waveform itself encodes luminosity distance through general relativity's prediction for how the signal's amplitude falls off. As detectors improve — LIGO, Virgo, KAGRA, and eventually the space-based LISA mission (targeted for the 2030s) and next-generation ground detectors like the Einstein Telescope and Cosmic Explorer — the number of standard sirens with redshift counterparts should grow from a handful to many hundreds, offering a Hubble-constant and dark-energy measurement built on entirely different physics and different systematics than supernovae. Independent confirmation from such a distinct method would be extraordinarily persuasive, in either direction.

There is also a theoretical route to settlement, less glamorous but no less important: a genuine understanding of the cosmological-constant problem itself, from quantum gravity or a deeper symmetry principle, could in principle predict a specific, calculable value or behavior for dark energy, rather than merely fitting one. No such calculation currently exists that is both rigorous and successful — string theory's landscape of vacua offers a framework for why a small positive value might be typical (or anthropically selected) but not a first-principles derivation of the observed number.

If the DESI-hinted evolving-w signal strengthens over the next few years — as more data accumulate through the mission's full run into the late 2020s, and as Euclid and Rubin data come online — that alone could constitute a genuine discovery: the first confirmed departure from the simplest cosmological constant since the initial 1998 acceleration discovery itself. Conversely, if w converges tightly back to −1 as statistics improve, that will sharpen, rather than solve, the theoretical crisis, because it will leave the vacuum-energy magnitude problem entirely unaddressed while closing off the dynamical alternatives that might have explained it away.

Why it matters

This is not an abstract argument among specialists. The answer to what dark energy is determines the future of everything. If dark energy is truly a constant, the ultimate-fate-of-the-universe is sealed: exponential expansion forever, galaxies beyond our Local Group receding faster than light can ever reach us, until in the unfathomably distant future even the cosmic microwave background redshifts beyond detectability and the observable universe shrinks, effectively, to a lonely island of gravitationally bound galaxies in an otherwise dark and empty cosmos — a scenario sometimes called cosmic heat death by isolation. If dark energy is dynamical and its density is increasing (phantom-like, w < −1), the future could be more violent still: a "Big Rip," in which even atoms and nuclei are eventually torn apart as the expansion rate diverges in finite time. If dark energy is instead a temporary phase — say, a quintessence field currently near, but not stuck at, a potential minimum — cosmic acceleration could someday weaken, or even one day reverse into renewed deceleration or collapse. These are not equally likely on current evidence, but they are not equally excluded either, and which one is true depends entirely on resolving the question this essay is about.

Beyond eschatology, dark energy sits at the unresolved junction between the two great theories of twentieth-century physics. Quantum field theory predicts vacuum energy; general relativity says that energy, whatever its source, must gravitate. Reconciling the wildly discrepant predictions of these two frameworks for the energy of empty space is arguably the sharpest, most quantitatively precise clash between quantum mechanics and gravity that we possess — sharper, in some ways, than the black-hole information paradox, because here we have an actual number to explain and we are off by 120 orders of magnitude. Any theory of quantum gravity that hopes to be taken seriously must eventually explain why the cosmological constant is small, but not zero — a demand that has already ruled out or heavily strained several once-promising approaches.

There's also a philosophical undertone worth naming honestly. Dark energy is, alongside the dark-matter-problem, the second of two "dark" components that together outweigh ordinary matter by more than five to one. We have built an extraordinarily successful cosmological model — one that predicts the cosmic microwave background's acoustic peaks, the abundance of light elements, the large-scale structure of galaxies, all to impressive precision — whose two dominant ingredients remain, in a strict sense, unidentified. Some scientists find this galling, evidence that we are still missing something conceptually fundamental. Others see it as the ordinary condition of a science at its frontier: Newton could describe planetary motion precisely without knowing what gravity was; perhaps we can describe the universe's expansion precisely, for now, without yet knowing what drives it.

The people chasing it

physicist[Albert Einstein|1879–1955|Introduced the cosmological constant Λ in 1917 to permit a static universe, later reportedly calling it his "biggest blunder" once Hubble's expansion was confirmed — though the term re-entered cosmology on far firmer footing eight decades later.]

Origins · 1 minSaul Perlmutter and how this was discovered
SP
Saul Perlmutter
b. 1959 · Led the Supernova Cosmology Project; shared the 2011 Nobel Prize in Physics for the discovery of accelerating expansion via distant Type Ia supernovae.

physicist[Brian Schmidt|b. 1967|Led the High-Z Supernova Search Team alongside Adam Riess; shared the 2011 Nobel Prize for the same discovery, reached independently and nearly simultaneously.]

Origins · 1 minAdam Riess and how this was discovered
AR
Adam Riess
b. 1969 · Lead author of the High-Z team's 1998 paper; has since led precision measurements of the local expansion rate that revealed the separate "Hubble tension," a related but distinct crack in the standard cosmological model.

Other figures loom large in the surrounding theoretical landscape: Steven Weinberg, who in 1987 offered an early anthropic argument for why the cosmological constant might be small, in a landscape of possible universes, years before acceleration was observed; Michael Turner, who helped popularize and name "dark energy" itself in the late 1990s; Paul Steinhardt and Robert Caldwell, among the theorists who developed quintessence models and explored phantom dark energy's exotic consequences; and the large collaborations — DESI, Euclid, the Dark Energy Survey, the Vera C. Rubin Observatory's LSST team — whose thousands of collective scientist-years now form the actual observational engine of the field.

history

  • 1917 — Einstein adds the cosmological constant to permit a static universe.
  • 1929 — Hubble establishes the expanding universe via galaxy redshifts.
  • 1998 — Two independent supernova teams discover accelerating expansion.
  • 2024 — DESI baryon acoustic oscillation results hint w may deviate from −1.

The open frontier

Stand back and the shape of the problem is almost paradoxical: we have never been more sure that cosmic acceleration is real, and never less sure what it is made of. A quarter-century of increasingly precise measurement has pinned the phenomenon down while leaving its cause almost as open as it was the week the 1998 papers appeared. That is the peculiar signature of a genuine frontier — not confusion from lack of data, but a razor-sharp anomaly that refuses to resolve into a single clean story despite excellent data.

What keeps this question alive, rather than settled by fiat toward the simplest model, is the sheer implausibility of that simplest model's theoretical foundations. A cosmological constant that fits every observation but is off by 120 orders of magnitude from any naive calculation is not obviously a triumph of Occam's razor; it may instead be a placeholder awaiting a mechanism, the way the phrase "luminiferous ether" was a placeholder before 1905. Equally, the recent hints of evolving w from DESI are tantalizing precisely because they are not yet decisive — strong enough to reopen serious theoretical work on quintessence and modified gravity, too weak to declare the constant dead.

What remains genuinely, currently unresolved:

  • Is dark energy's equation-of-state parameter w exactly −1, or does it evolve with cosmic time — and if it evolves, does it cross the "phantom divide" w = −1, a transition many single-field models cannot easily produce?
  • Can any theoretical framework explain, rather than merely accommodate, why the vacuum energy density is neither zero nor the roughly 120-orders-of-magnitude-larger value naive quantum field theory predicts?
  • Is the near-coincidence between matter density and dark energy density today — the fact that we happen to observe them as comparable — a clue to new physics, an anthropic selection effect, or simple happenstance?
  • Do gravitational-wave standard sirens, as their numbers grow through the 2030s, confirm the same expansion history as supernovae and baryon acoustic oscillations, or reveal a discrepancy that points toward modified gravity?
  • Is the observed acceleration partly an illusion of inhomogeneity and structure — a backreaction effect from analyzing a lumpy universe with equations built for a smooth one — rather than evidence for any new energy component at all?
  • What does the resolution imply for the universe's ultimate fate: endless cold expansion, a violent Big Rip, or some third path we have not yet imagined?

Ask the tutor: If the DESI hints of evolving dark energy hold up, what would that imply about the very early universe's inflationary era, given that both processes may be driven by similar rolling scalar fields?