Dark Energy’s Limits: A New Approach Through Particle Physics

Author: Denis Avetisyan

Researchers are leveraging connections between low-energy effective theories and underlying high-energy physics to establish fundamental constraints on dark energy models.

Positivity bounds, as defined by equation <span class="katex-eq" data-katex-display="false">(10)</span>, constrain the parameter space of <span class="katex-eq" data-katex-display="false">{\alpha_B}</span> and <span class="katex-eq" data-katex-display="false">{c_T}</span>, effectively shifting posterior distributions from orange intervals to narrower, purple ones when implemented as a prior. — Positivity bounds, as defined by equation $(10)$ , constrain the parameter space of ${\alpha_B}$ and ${c_T}$ , effectively shifting posterior distributions from orange intervals to narrower, purple ones when implemented as a prior.

The study demonstrates how positivity bounds derived from the UV/EFT correspondence can significantly refine the viable parameter space for effective field theory descriptions of dark energy.

Despite successes in cosmological modeling, the connection between low-energy observations and fundamental high-energy physics remains a significant challenge. This work, ‘Amplitude constraints on dark energy’, explores this link via the UV/EFT correspondence, leveraging scattering amplitudes to relate effective field theory parameters to underlying ultraviolet completions. By imposing positivity bounds-constraints arising from fundamental principles of causality and unitarity-we establish limits on viable dark energy models. Could these amplitude-based constraints offer a novel pathway to probe the nature of dark energy and validate theoretical predictions at high energies?

The Limits of Predictability

While remarkably successful in predicting gravitational phenomena across vast cosmic distances, General Relativity encounters significant challenges when applied to the Universe’s most extreme environments. Observations of galactic rotation curves and the accelerating expansion of the Universe suggest the presence of dark matter and dark energy – components not accounted for within the theory’s original framework. Furthermore, attempts to reconcile General Relativity with quantum mechanics, particularly in the singularity at the heart of black holes or at the very beginning of the Universe, consistently yield mathematical inconsistencies and infinities. These breakdowns indicate that General Relativity, despite its proven accuracy in many scenarios, is likely an effective theory – a highly accurate approximation that breaks down at energy scales approaching the Planck scale, necessitating a more fundamental description of gravity to fully capture the Universe’s behavior at its most extreme limits. $E = mc^2$

Despite its extraordinary predictive power, the Standard Model of particle physics is acknowledged to be an incomplete description of reality. While accurately detailing known fundamental particles and their interactions – encompassing electromagnetism, the weak nuclear force, and the strong nuclear force – it fails to incorporate gravity, leaving a significant gap in a complete understanding of the universe. Furthermore, the model necessitates the existence of dark matter and dark energy to explain observed cosmological phenomena, yet provides no inherent particles or mechanisms to account for these pervasive components. Neutrino masses, also not predicted by the original Standard Model, were later accommodated through modifications, highlighting its initial limitations. These unresolved issues suggest the existence of physics beyond the Standard Model, motivating ongoing research into supersymmetry, string theory, and other theoretical frameworks seeking a more comprehensive and unified description of the fundamental constituents and forces governing the cosmos.

Acknowledging the inherent incompleteness of both General Relativity and the Standard Model, contemporary cosmological research is increasingly adopting Effective Field Theory (EFT) as a pragmatic and powerful tool. Rather than seeking a single, all-encompassing “theory of everything,” EFT embraces approximation, focusing on describing physical phenomena at specific energy scales without requiring complete knowledge of underlying physics at vastly higher energies. This approach allows physicists to model complex cosmological processes – such as inflation or dark energy – using a limited set of parameters, effectively encapsulating unknown high-energy effects within these parameters. By systematically including higher-order corrections, EFT provides a framework for testing theoretical predictions against observational data, even in regimes where fundamental theories break down, and offers a path towards uncovering new physics through precision measurements and the identification of deviations from expected behavior. The strategy prioritizes predictive power and testability, even if it means sacrificing a complete, fundamental understanding of the universe’s deepest secrets.

Bridging the Scales: From Ultraviolet to Effective

The UV/EFT correspondence establishes a systematic relationship between the degrees of freedom and dynamics described by a full, high-energy theory (UV completion) and the effective parameters appearing in a low-energy Effective Field Theory (EFT). This framework allows for the calculation of low-energy observables – those measurable at accessible energy scales – based on assumptions about the underlying UV physics. Specifically, the UV/EFT correspondence facilitates the determination of Wilson coefficients in the EFT, which encapsulate the effects of high-energy dynamics integrated out of the low-energy description. This connection is not a one-to-one mapping, as multiple UV completions can yield the same EFT, but it provides a calculable link between theoretical models and experimental measurements, enabling tests of high-energy physics through precision low-energy data.

The calculation of 2→2 scattering amplitudes, rigorously constrained by Poincaré invariance, serves as the fundamental bridge between ultraviolet (UV) completions and the parameter space of low-energy Effective Field Theories (EFTs). Poincaré invariance ensures Lorentz covariance and translational symmetry, dictating the allowed form of interaction terms and reducing the number of independent parameters needing determination. By computing these amplitudes in the UV theory and then matching them to the corresponding EFT operators via techniques like operator product expansion, one can establish precise relationships between high-energy scales and low-energy coefficients. This matching procedure allows for the determination of Wilson coefficients, which encapsulate the effects of the UV physics at lower energies, and provides a method for systematically exploring the consequences of different UV scenarios within the EFT framework.

By treating low-energy coefficients within an Effective Field Theory (EFT) as measurable proxies for unknown high-energy physics, researchers can constrain the parameter space of potential ultraviolet (UV) completions. Specifically, incorporating bounds derived from UV consistency conditions as prior distributions within global fit analyses has demonstrated the potential to improve precision by a factor of three compared to unconstrained fits. This methodology allows for statistically rigorous exploration of the implications of physics beyond the Standard Model, leveraging measurable low-energy data to indirectly probe high-energy scales and refine theoretical models. The improvement in precision arises from the reduction in parameter degeneracy achieved through the imposition of physically motivated priors based on UV behavior.

The Guardians of Consistency: Causality and Unitarity

Positivity bounds on Low-Energy Effective Theory (EFT) coefficients arise from the requirement that physical processes respect fundamental principles of causality and unitarity. Causality dictates that effects cannot precede their causes, and unitarity ensures probability conservation in quantum mechanics. These principles, when applied to the scattering amplitudes described by the EFT, lead to constraints on the allowed values of EFT coefficients. Specifically, these coefficients-which parameterize the low-energy behavior of a more complete, high-energy theory-must satisfy inequalities derived from the condition that the amplitudes remain positive-definite, reflecting the probabilistic nature of quantum events and preventing violations of fundamental physical laws. These bounds are not merely theoretical curiosities; they represent testable predictions and offer a means to constrain the parameter space of any proposed EFT.

Positivity bounds derived from causality and unitarity provide a rigorous method for validating Effective Field Theories (EFTs). Any proposed EFT contains a set of parameters which describe the low-energy behavior of a more complete, underlying theory. These bounds establish relationships between these parameters; parameter ranges that violate these relationships are therefore inconsistent with the fundamental principles of causality and unitarity, and can be definitively excluded. This constitutes a powerful consistency check, as it allows for the systematic reduction of the parameter space of any EFT and provides evidence, albeit indirect, for the underlying physics it approximates. Failure to satisfy these bounds indicates the EFT is not a valid low-energy description of a physical system.

Analysis of causality and unitarity constraints yields specific relationships between the Low-Energy Effective Theory (EFT) coefficients α_B and c_T. These calculations result in the following inequalities: $\alpha_B c_T^2 < 2(c_T^2 - 1)$ and $\alpha_B c_T^2 < 2(c_T^2 - 1)(2c_T^2 + 1)$ . These bounds define allowable ranges for the parameter space of the EFT, and any proposed values for α_B and c_T must satisfy both conditions to remain consistent with fundamental principles.

Dark Energy Through an Effective Lens

Horndeski theory represents a sophisticated attempt to model dark energy within the well-established framework of effective field theory. This approach doesn’t posit a single, specific dark energy component, but instead describes it through the most general scalar field theory with second-order field equations, allowing for a diverse range of behaviors consistent with cosmological observations. By focusing on the effective description, the theory sidesteps the need to know the fundamental ultraviolet completion – the underlying physics at extremely high energies – and instead concentrates on predicting the large-scale behavior of the Universe. This flexibility allows Horndeski theory to explore various scenarios for dark energy, from a simple cosmological constant to more complex, evolving fields that drive the accelerated expansion, offering a powerful tool for testing different cosmological models against observational data and potentially unraveling the mystery of dark energy’s influence on the cosmos.

The Horndeski theory posits that the accelerating expansion of the Universe isn’t driven by a simple cosmological constant, but rather by a dynamic scalar field – a field that permeates all of space and changes over time. Crucially, this field isn’t just any scalar field; its behavior is dictated by specific symmetries. Shift symmetry, for example, ensures the field’s value at any given point is essentially arbitrary, only its change having physical meaning. More complex is Galileon symmetry, which allows for non-standard interactions within the field itself, leading to interesting effects on gravity and potentially explaining why the expansion is accelerating at the observed rate. These symmetries aren’t merely mathematical conveniences; they constrain the possible forms of the scalar field’s interactions, offering a limited, and therefore testable, set of models for dark energy and providing a framework to differentiate it from other explanations like a static cosmological constant. The theory elegantly suggests that the universe’s expansion is not a property of space itself, but a consequence of the evolving dynamics of this fundamental field.

Horndeski theory proposes a compelling solution to the mystery of dark energy by integrating the fundamental concepts of a metric – describing the geometry of spacetime – and a cosmological constant, representing the energy density of empty space. This combination allows the theory to dynamically model the accelerating expansion of the universe, aligning with observational data gathered from distant supernovae and the cosmic microwave background. Unlike simpler models, Horndeski theory doesn’t require dark energy to be a static property of space; instead, it posits a scalar field whose interactions, governed by specific symmetries, drive the expansion. This framework provides a potentially viable explanation for the observed ΛCDM model, offering a pathway to understanding the forces behind the universe’s accelerated growth and addressing the long-standing puzzle of dark energy’s nature.

Toward a Unified Understanding

Current investigations are heavily focused on strengthening the UV/EFT correspondence, a critical link between the high-energy dynamics of ultraviolet (UV) complete theories and the low-energy effective field theories (EFTs) used to describe observable phenomena. A central aspect of this refinement involves meticulously calculating UV matrix elements – quantities that encapsulate the fundamental interactions at extremely high energies – and determining precisely how these elements dictate the values of coefficients within low-energy EFTs. This process isn’t merely a mathematical exercise; understanding this relationship allows physicists to predict the behavior of systems at accessible energies based on underlying, currently unobservable, high-energy physics. Researchers are employing increasingly sophisticated techniques to map these UV contributions to EFT parameters, aiming to establish a predictive framework where cosmological observations can, in turn, constrain the possible forms of the underlying UV theory – effectively peering into the very fabric of reality at energy scales far beyond current experimental reach.

Current investigations into dark energy are increasingly reliant on the precision of scattering amplitude calculations and the application of positivity bounds. These theoretical tools allow physicists to explore the consistency of effective field theories used to describe dark energy with the underlying principles of quantum gravity. By demanding that scattering amplitudes adhere to positivity constraints – stemming from the requirement of causality and unitarity – researchers can place stringent limits on the possible forms of low-energy effective actions. Improved calculations, incorporating higher-order corrections and leveraging advanced mathematical techniques, promise to refine these constraints, effectively narrowing the range of viable dark energy models and potentially revealing connections to more fundamental ultraviolet completions. This approach not only tests the validity of existing models but also guides the search for new physics beyond the Standard Model, offering a pathway to understand the accelerating expansion of the Universe through the lens of fundamental particle interactions.

The convergence of high-energy physics and cosmological observation represents a powerful, reciprocal pathway toward unraveling the Universe’s deepest mysteries. Researchers are increasingly focused on establishing a dialogue between the extreme energy scales probed by particle colliders and the large-scale structure revealed by astronomical surveys. This isn’t merely a matter of applying particle physics models to cosmology; instead, it’s an iterative process where cosmological data refines theoretical frameworks, guiding the search for physics beyond the Standard Model. Precision measurements of cosmic microwave background fluctuations, dark energy distributions, and gravitational waves provide stringent tests for ultraviolet (UV) completions of effective field theories (EFTs), while advancements in theoretical calculations, such as scattering amplitudes and positivity bounds, offer increasingly accurate predictions to compare with observational data. This synergistic approach holds the potential to not only constrain the parameters of existing models, but also to uncover entirely new phenomena and fundamentally reshape understanding of spacetime, dark matter, and the origins of the cosmos.

The pursuit of understanding dark energy, as detailed in the study, necessitates a rigorous examination of theoretical frameworks. It demands stripping away extraneous complexity to reveal fundamental constraints. Marie Curie observed, “Nothing in life is to be feared, it is only to be understood.” This sentiment resonates deeply with the paper’s methodology; by applying the UV/EFT correspondence and deriving positivity bounds, the authors aren’t simply adding layers to existing models, but rather, systematically removing inconsistencies and refining the permissible parameter space. The focus on causality and unitarity serves not to complicate the picture, but to clarify the boundaries of viable dark energy theories, embodying a similar spirit of focused inquiry.

The Road Ahead

The correspondence established between low-energy effective descriptions and ultraviolet completeness, while promising, merely shifts the burden of explanation. The positivity bounds derived are not revelations of fundamental physics, but rather statements of self-consistency. They define regions of parameter space allowed by the demands of causality and unitarity-a significant constraint, certainly, but one that highlights the extent of what remains unknown. The true test lies not in satisfying these bounds, but in identifying the underlying high-energy dynamics that saturate them.

Current work implicitly accepts the EFT as a faithful representation, a simplification. However, the very act of integrating out high-energy degrees of freedom introduces a level of abstraction that may obscure crucial physics. Future investigations must grapple with the limitations of this approach, exploring the sensitivity of results to higher-order corrections and the potential for non-local effects. The question isn’t simply whether dark energy models can be constrained, but whether the EFT framework itself is adequate to the task.

Ultimately, the pursuit of ultraviolet completions for dark energy, guided by these amplitude-based constraints, is a sculpting process. The bounds themselves are merely the chipping away of the impossible, leaving only the faint suggestion of the form hidden within. The true form, the fundamental theory, remains to be revealed – and may demand a radical departure from current assumptions.

Original article: https://arxiv.org/pdf/2512.25047.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/