Coupled Quintessence

2000Luca AmendolaFrontier4 primary sources, 4 established Reviewed October 17, 2026

Quintessence coupled directly to matter, so the field and matter exchange energy and matter feels an extra, fifth force.

Scene · placeholder

3D visualisation in development

Visualisation · Dark Energy Candidates

dark energy: The unknown component driving the accelerating expansion of the universe, making up about 68 percent of its energy.
scalar field: A field with one value at each point in space, like a temperature map. The inflaton is one example.
dark matter: A form of matter that interacts gravitationally but emits no light, making up about 27 percent of the universe.
Hubble tension: The 5-sigma disagreement between the local-distance-ladder measurement of the present-day Hubble constant (around 73 km/s/Mpc) and the value inferred from the cosmic microwave background under standard cosmology (around 67 km/s/Mpc).
cosmic microwave background: The faint, uniform glow of light released about 380,000 years after the Big Bang, when the universe first became transparent.
cosmological constant: A constant energy density of empty space. In general relativity, it drives the accelerated expansion of the universe. Often written as Lambda.

§1 · The claim, in one sentence

Coupled quintessence links the dark energy field directly to matter, so the two exchange energy, dark matter in many versions feels a fifth force, and dark energy stays present through the matter era.

§2 · Why it might be true

Plain quintessence treats dark energy as a scalar field that touches the rest of the universe only through gravity. Amendola argued in 2000 that such a field should couple directly to matter, unless an unknown symmetry forbids it.

He worked out the simplest case, an exponential potential with a linear coupling to matter. The coupling lets energy pass between the field and matter, which changes how both evolve.

The main new feature appears during the matter era. There the field holds a finite and almost constant energy density, an epoch Amendola called the phi-matter-dominated epoch.

In later coupled dark energy models, dark matter particles feel a fifth force on top of gravity. Its strength is set by the same coupling constant.

The family stance

Dark energy may not be a constant. If its equation of state differs from -1, or changes with time, a cosmological constant cannot be the whole story and a dynamical component, most naturally a scalar field, is required. The case that the universe accelerates is overwhelming; the case for any one physical model of what drives it is not.

§2.5 · Evidence

Amendola's starting point was that a light scalar field is expected to couple to matter unless some unknown symmetry prevents it.
Pettorino (2013) found a peak for a nonzero coupling in Planck data combined with BAO, 2.2 sigma away from zero.
Adding Hubble Space Telescope measurements of the expansion rate raised that preference to about 3.6 sigma, driven mostly by the Hubble tension.
A broader class of interacting dark energy models, related to but not the same as Amendola's, shows a preference for interaction in Planck plus DESI 2024 data (Giarè et al. 2024). Such preferences depend on the data sets and the parametrization.

§3 · What you'd need to test it

During matter domination the field keeps a small, nearly constant share of the total energy density, unlike uncoupled quintessence, which quickly becomes negligible.
The cosmic microwave background spectrum tilts at large angles, and its acoustic peaks shift position and change height.
In Amendola's original model, matter clumps less on scales of about 8 Mpc/h today than in uncoupled models; the size and sign of the effect depend on the coupling chosen.
Dark matter particles attract each other more strongly than gravity alone predicts, through a fifth force set by the coupling.

§4 · Where it breaks

Already in 2000, the data limited the dimensionless coupling to at most 0.1, so any effect on cosmic history must be small.
Pettorino notes that the Planck plus Hubble Space Telescope preference comes mostly from the Hubble tension and may reflect systematics in one data set.
When Planck is combined with BAO, supernova, and lensing data, interacting dark energy is fully consistent with a cosmological constant and shows no compelling coupling (Di Valentino et al. 2017).

Go deeper

Amendola (2000) used an exponential potential and a linear coupling, a model conformally equivalent to Brans-Dicke Lagrangians with a power-law potential. The coupling produces the phi-matter-dominated epoch (phiMDE), during which the field's energy density stays finite and almost constant. This tilts the CMB multipole spectrum at large angles, shifts and rescales the acoustic peaks, and lowers the present 8 Mpc/h density variance. Data at the time bounded the dimensionless coupling at |beta| <= 0.1.

In the coupled dark energy formulation tested by Pettorino (2013), dark matter feels a fifth force larger than gravity by a factor 2 beta^2, giving an effective gravitational constant G_eff = G(1 + 2 beta^2). Planck with WMAP polarization and BAO gave beta = 0.036 ± 0.016, and Planck with WMAP polarization and HST gave beta = 0.066 ± 0.018.

Phenomenological interacting dark energy models parameterize the energy exchange with a rate xi. Di Valentino, Melchiorri, and Mena (2017) found that such an interaction can ease the H0 tension, most effectively when the dark energy equation of state is free and phantom-like. Giarè et al. (2024) found that Planck plus DESI BAO prefer xi = -0.32 (+0.18, -0.14) and give H0 = 70.8 km/s/Mpc, reducing the tension with SH0ES to below about 1.3 sigma. The Early Dark Energy variant in the Hubble Tension Solutions family approaches the same tension from the early universe.

▸§5 · Who built it, and when(4 sources, 4 established)

Variants in this family

Compare variants

0votes

Currently #1 in this family · #2 in Ch.5

Up next

Spotted an error? Have a source to add?

Prefer email?

You can also send a prefilled email with the variant URL already filled in.