New Print on ‘Quantum Gravity meets DESI’

This page has a Chinese version.

A quick announcement: our latest paper from Prof. Yi-Fu Cai’s group and me is now online:

https://alphaxiv.org/abs/2504.07791

The core idea of this project was originally proposed by me, and Prof. Cai readily agreed with and supported it. Shortly after we began, an expository piece by Brandenberger appeared ([Rob2025]), which made me genuinely happy—it suggests that we are indeed moving along the right track.

Working with Prof. Cai’s group has been a great pleasure. I am quite satisfied that we were able to complete a PRD-level paper within about a week. The efficiency of cosmologists is truly remarkable; at the very least, we accomplished everything that could reasonably be done in one week.

Let me briefly explain the motivation. When I learned that the DESI 2025 results favor dynamical dark energy, I felt deeply uneasy. In the context of string phenomenology, the cosmological constant (\Lambda) is often viewed as the vacuum expectation value of a scalar field—namely a quintessence field. Going further, in the context of the Swampland Distance Conjecture, we are typically assumed to live on a flat moduli space of scalar fields ([OoguriVafa2006]). ([arXiv][1])

However, the latest DESI dark-energy analyses point to (at least) the following two empirical features:

(i) Dark energy appears to be “weakening.” More concretely, the equation-of-state parameter [ w \equiv \frac{P}{\rho} < 0 ] is inferred to be increasing. If we imagine dark energy as a kind of negative-pressure substance, this means the negative pressure is becoming less negative. In a certain sense, a “weakening” dark-energy sector may look compatible with some swampland expectations ([vafa2024])—but that expectation is usually about the magnitude of the cosmological constant. By contrast, a true cosmological constant—viewed as a vacuum expectation value—must have [ w = -1 ] exactly. On the other hand, if dark energy is slowly varying, that would suggest we may not be sitting anywhere on the vacuum moduli space of a scalar field, but rather rolling slowly down a potential slope.

(ii) Evidence for crossing the critical line (w=-1). Both the DESI collaboration’s (w_0w_a)CDM fits and Bayesian reconstructions by the China–Taiwan DESI collaboration (e.g. Gongbo Zhao and collaborators) report behavior consistent with crossing (w=-1). In some reconstructions, repeated crossings of (w=-1) are even indicated. This is commonly referred to as phantom crossing, or the Quintom scenario. ([arXiv][2])

Yet, in standard frameworks, the Quintom scenario faces at least the following difficulties:

(i) Ordinary matter fields cannot realize (w<-1), except by introducing a phantom field with a wrong-sign kinetic term. But phantom dark energy is unstable already at the classical level, not to mention its problematic quantization.

(ii) For an ideal fluid, (w<-1) typically implies violation of the Null Energy Condition (NEC). The NEC plays a foundational role in general relativity; without it, the singularity theorems lose their standard footing. If Nature truly allows NEC violation, we would have to revisit questions as extreme as whether primordial black holes (PBHs) and even wormholes could form.

(iii) Conventional dynamical dark-energy model building often starts from the minimal assumption of a single scalar degree of freedom. Yet Yi-Fu (2015) and earlier works emphasized a key point: a single scalar degree of freedom cannot realize the Quintom scenario. This in turn suggests that certain “naïve beliefs” in the string-phenomenology community, shaped by earlier (\Lambda)CDM-driven observations ([BoussoTASI2007]), may be on shaky ground. ([arXiv][3])

For these reasons, as a student in the theory community, I felt a strong sense of unease—and responsibility—when reading the DESI reports. As someone trained primarily in formal theory, I urgently needed cosmologists’ insight. This urgency is precisely what led to the rapid release of this preprint.

As the saying goes, “writing should carry the Way.” Through this paper, we aim to call for greater attention from formal theorists to experimental input—especially when observations confront us with genuine challenges and tensions (such as NEC issues and the Quintom/phantom-crossing behavior). Some problems are more serious precisely because they are more difficult, and they deserve to be faced head-on.

We chose to explore modified gravity because, compared with scalar-field dark energy, geometric effects of spacetime are not material fields; their effective dynamics can, in principle, exhibit NEC-violating behavior. Given the extremely short time window, existing modified-gravity frameworks were simply the best answers we could realistically provide.

In the acknowledgments, we note that Qin Xun, as a member of the broader collaboration, actively promoted and generously shared information about the DESI experiment, which helped me—coming from formal theory—stay alert to the newest movements in dark-energy observations. Dr. Ren Xin has deep expertise and extensive experience in modified gravity and guided us toward a modern understanding of geometric theories of gravity. On one occasion when I visited the Institute of Theoretical Physics for a seminar, Prof. Pi Shi told me that Prof. Shaojiang is very knowledgeable about dark energy; I then consulted him about DESI DR2. His broad command of both formal theory and cosmology, and his care for younger students, impressed me greatly. Dr. Zhizhen’s insights on string cosmology, and Yuhang’s knowledge of (f(Q)) and (f(T)) gravity, were also extremely helpful.

Among the coauthors, Chunyu was a crucial reason this paper could be finished so quickly: she led the choice and computations for the (f(T)) modified-gravity model, drafted related sections, and produced most of the figures. Dr. Dongdong participated throughout the project and provided substantial support and insights in phrasing, formatting, polishing, and supplementation; the paper’s striking title was also proposed by him, and I wish him every success in his academic job search. Prof. Emmanuel at the National Observatory of Athens is Prof. Cai’s “golden partner”; his rich experience led to incisive guidance and concrete revisions that made the exposition more concise and sharper. In addition, the discussion course “The Lotus and Swampland,” organized earlier this year at the Tsinghua Sanya International Mathematics Forum (TSIMF) by Dr. Fengjun and Prof. Babak, was profoundly enlightening and was one of the key factors that helped me grow from a learner of the landscape to someone capable of carrying a project independently.

Finally, I would like to express my deepest gratitude to Prof. Yi-Fu Cai. Without his initiation, care, and guidance, this paper would not have been completed.