The universe is known to be expanding at an accelerating rate. Physicists typically attribute this acceleration to dark energy, a mysterious component of the universe that exerts negative pressure, causing space to expand faster. Dark energy is thought to have become the predominant influence on the universe’s evolution around 3–4 billion years ago, at the beginning of what is known as the dark energy era.
Researchers at the University of Notre Dame and Fudan University recently showed that fluctuations in the cosmic microwave background (CMB), small variations in the radiation left over from the Big Bang, could be used to probe phase transitions during the dark energy era.
Using this theoretical approach, outlined in a paper published in Physical Review Letters, Seth Koren, Yuhsin Tsai and Runqing Wang examined a hypothetical first-order phase transition (FOPT) occurring after dark energy became predominant and placed limits on how much vacuum energy it could have released. A FOPT is a sudden change from one physical state to another that unfolds through the formation of bubbles and releases energy.
“As we continue to find null results on interactions of dark sector particles with Standard Model particles—including, importantly, dark matter—we must take more seriously the possibility that these sectors may only interact with us gravitationally,” Koren told Phys.org.
“This ‘nightmare case’ is harder to probe, but it doesn’t mean the dark sector is invisible. Our best hope is to look for the cosmological footprint of the dynamics of dark sectors, where the gravitational coupling with our sector may result in observable effects on our particles.”
In its early history, the universe underwent profound changes, including the electroweak and quantum chromodynamics (QCD) phase transitions. The researchers considered whether a hidden part of the universe could have undergone a similar phase transition more recently.
“This is a good place to start testing how well we can see purely gravitational dark sector effects,” said Koren.
“While science fiction often portrays vacuum decay as an instantaneous, apocalyptic catastrophe, our work highlights that a phase transition in a secluded dark sector would be a silent cosmic event, entirely imperceptible in our daily lives. To observe or constrain such an event, we must carefully look at precise cosmological measurements to check for subtle changes in the spectrum of photons from the CMB.”
Using CMB data to probe recent phase transitions
If the hypothetical phase transition considered by the researchers had occurred uniformly throughout the universe, the energy involved could only be constrained to around 10% of the total dark energy using observations of the universe’s expansion. Yet if it occurred unevenly, with bubbles of the new state forming and spreading across space, astronomers could place tighter limits on the energy it released.
“We show that we can use the cosmic microwave background as a backlight to probe these inhomogeneities by considering how the CMB photons coming to us from various directions would be redshifted anisotropically,” said Koren. “This anisotropic effect can be discovered or constrained by experiments that probe the microwave sky, such as the Planck observatory. Finally, another motivation for our study comes from quantum gravity and ideas about the ‘Swampland.'”
Some physicists who specialize in string theory, the idea that the smallest building blocks in the universe are tiny vibrating strings as opposed to point-like particles, have proposed that the universe cannot expand forever. They have suggested that it will eventually stop expanding, start contracting and ultimately collapse in a ‘big crunch.’
“If this switch occurs via a phase transition, then it is possible it has happened already and the universe’s expansion could be decelerating right now,” said the authors. “Our study probes this possibility, so that we can place a lower limit on the lifetime of the universe using cosmological data. Thankfully we are no more than halfway through the lifetime of the universe!”
One of the simplest ways to investigate a possible cosmological event is to examine how it may have affected the universe as a whole. Astronomers can do this by averaging cosmological observations collected from different directions across the sky.
This approach would reveal whether the hypothetical phase transition changed the universe’s overall expansion rate. Yet it would only probe transitions involving around 10% or more of the total dark energy.
“A phase transition will convert some of the dark energy into other degrees of freedom, such as dark matter or massless dark particles (‘dark radiation’), and this will change the rate of the expansion of space as a function of time, as parametrized by the changing Hubble parameter H(t),” said Koren. “However, we can only probe this homogeneous Hubble rate at the O(10%) level.”
The advanced telescopes available today allow astrophysicists to study not just how the universe as a whole changed over time, but also how its properties vary across the sky. Looking for these variations could help place tighter limits on a FOPT that occurred unevenly throughout the universe.
“In our study, we use the CMB photons as a backlight to probe the inhomogeneous variation of the cosmic energy during the period after a phase transition,” said Koren. “FOPTs proceed through bubble nucleation, just like when you boil water, and so the phase transition occurs at earlier or later times in different places. This means CMB photons coming from different directions will enter the region of true vacuum earlier or later, and consequently be redshifted more or less.”
Essentially, Koren, Tsai and Wang mathematically calculated how an uneven phase transition would alter the wavelengths of CMB photons by different amounts, depending on the direction from which they reached Earth. They then used the absence of detectable variations matching these predictions in existing CMB observations to place tight limits on the hypothetical phase transition.
“By mathematically modeling this anisotropic redshifting, we turned the CMB into an ultra-sensitive detector, giving us far tighter constraints than simply measuring the universe’s average expansion,” explained the team.
New constraints on dark energy phase transitions
According to the researchers, this is the first paper to use astronomical observations to constrain how dramatically the dark sector could have changed during the universe’s recent history.
“By utilizing CMB anisotropies rather than just background expansion, we found that the dark sector has remained incredibly stable during the era of dark energy domination,” said Koren. “If any violent phase transition did occur, we showed it could have only involved a tiny fraction of the total dark energy—less than 1%. This means we can learn about an important, understudied possibility: that the universe has already undergone a phase transition that changes its asymptotic behavior from expanding to contracting.”
The team’s calculations also offer insight that could be tied in with string theory. Specifically, they suggest that even if the universe already underwent a FOPT marking a shift from expansion to contraction, as proposed by some string theorists, it would not collapse for at least another 14 billion years, at least for transitions with β/H★ ≤ 500 (i.e., transitions with an inverse duration relative to the cosmic expansion rate, β/H★, that is no greater than approximately 500). This is to be compared with the stronger conclusion that less than 1% of the dark energy was involved, which applies only for β/H★ ≤ 25.
“With some fortuitous timing, after this research project was already underway, the Dark Energy Spectroscopic Instrument reported hints of late-time changes in the behavior of dark energy at z ∼ 0.5. A FOPT in the dark sector acts as a change in the behavior of dark energy, as some dark energy is converted into other forms such as dark matter or dark radiation,” added Koren.
“Our preliminary investigations along with Sai Chaitanya Tadepalli using these DESI data indicate that a cosmological history with a FOPT may present an improvement over ΛCDM. Unlike more exotic theories that require radical departures from known physics, a dark sector phase transition is an elegant, well-understood mechanism that naturally fits these new observations. We hope to put out a completed analysis soon.”
As part of their future studies, Koren, Tsai and Wang also plan to examine a hypothetical FOPT in a hidden sector that interacts weakly with known matter, instead of only affecting it through gravity. Such a transition may be accompanied by other effects that could be observed using existing telescopes and astronomical instruments.
“A further interesting direction is to consider a FOPT in a sector that is not entirely dark but has some portal connection to Standard Model matter through photons or Higgses or neutrinos,” explained Koren. “This will provide additional rich observational signatures past that for the solely gravitational case.”
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Publication details
Seth Koren et al, Boiling After the Dust Settles: Constraining First-Order Phase Transitions During Dark Energy Domination, Physical Review Letters (2026). DOI: 10.1103/1vyz-xdkb.
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Setting limits on phase transitions in the dark energy era (2026, August 25)
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