Neutrino Interactions Framework May Resolve Cosmological Puzzles and Improve Future Analyses

Neutrino self-interactions represent a compelling avenue for resolving inconsistencies within the standard cosmological model and alleviating existing tensions. Ivan Pérez-Castro, Josue De-Santiago, and Gabriela Garcia-Arroyo, working in collaboration with Jorge Venzor from Tecnol ogico de Monterrey, Escuela de Ingenier ıa y Ciencias, and Abdel Pérez-Lorenzana from Departamento de F ısica, Centro de Investigaci on y de Estudios Avanzados del Instituto Polit ecnico Nacional, present a new framework for calculating the neutrino-neutrino collision term within the Boltzmann hierarchy. Their approach uniquely incorporates both neutrino and mediator masses as free parameters, distinguishing between Dirac-like neutrinos and two neutrino mass eigenstates, and originates from a collaborative effort spanning the Departamento de F ısica at the Centro de Investigaci on y de Estudios Avanzados del Instituto Polit ecnico Nacional, the Instituto de Ciencias F ısicas at Universidad Nacional Aut onoma de M exico, and Tecnol ogico de Monterrey. This research is significant because it provides a robust tool for analysing future observations should neutrino self-interaction signals emerge, and importantly demonstrates a smooth transition between light and heavy mediator approximations as the Universe cools, refining the validity of current heavy mediator paradigms.

Scientists are developing a new framework to model neutrino self-interactions, potentially resolving tensions within standard cosmological models and opening avenues for understanding anomalies in neutrino physics. This work introduces a method for calculating how neutrinos collide with each other, incorporating both the mass of the neutrinos and the hypothetical particles that mediate their interactions as adjustable parameters.

The research distinguishes between different types of neutrinos, Dirac and Majorana, and accounts for the possibility that neutrinos have varying masses, a crucial detail often overlooked in previous studies. This advancement provides a powerful tool for analysing future data, should evidence of neutrino self-interaction be detected, and promises to refine our understanding of the universe’s fundamental constituents.

Remarkably, the calculations demonstrate a seamless transition between approximations used for light and heavy mediator particles as the universe cools, simplifying complex cosmological modelling. This eliminates the need for approximations at high redshifts, when the universe was hotter and denser, allowing for more accurate testing of the heavy mediator paradigm.

The research builds upon previous work establishing the Boltzmann hierarchy of self-interacting neutrinos, recognising that simplified treatments, such as modelling interactions as viscosity, fail to capture the full complexity of the phenomenon. While the study focuses on interactions mediated by scalar particles, the underlying framework is adaptable to a wider range of neutrino self-interactions and even to scenarios involving warm dark matter, expanding its potential applications.

This study addresses a critical gap by incorporating neutrino mass, a fundamental parameter in modern cosmology, into the calculations. The core achievement lies in constructing a systematic framework capable of computing the collision term, a measure of how often particles interact, across a broad range of temperatures and mediator masses, answering key questions about the impact of neutrino type and mass on these interactions.

The team’s approach offers a more general description of the collision term, valid for any heavy scalar mediator, and provides a means to assess the validity of existing approximations. Furthermore, the framework allows for calculating thermal corrections for light mediators without relying on further simplifying assumptions, offering a more robust and accurate model of neutrino behaviour in the early universe. This theoretical advancement is poised to facilitate the interpretation of future data and refine our understanding of the role neutrinos play in the cosmos.

Relativistic Boltzmann equation treatment of neutrino self-interactions in expanding spacetime

A detailed calculation of the neutrino-neutrino collision term within the Boltzmann hierarchy underpins this work, incorporating both neutrino and mediator masses as free parameters. To achieve this, researchers formulated the relativistic Boltzmann equation, a cornerstone of kinetic theory describing the evolution of particle distribution functions, and adapted it to a cosmological context characterised by a Friedmann, Lemaıtre, Robertson, Walker (FLRW) background spacetime.

This necessitated careful consideration of coordinate choices, specifically employing both the conformal Newtonian and synchronous gauges to accurately represent scalar perturbations of the spacetime metric. The choice of gauge dictated how momenta and energies were transformed to account for the expanding universe and gravitational potentials, ensuring a consistent description of particle trajectories.

The study meticulously separated the momenta of particles into magnitude and direction, allowing for a simplified form of the Boltzmann equation applicable to a homogeneous and isotropic universe. This simplification, combined with the use of conformal time, facilitated the analysis of collision terms, which represent the rate of particle interactions.

Crucially, the research focused on 2→2 scattering processes, where two particles collide and transform into two others, and the collision term was formulated to account for both local momenta and scattering amplitudes. The framework was designed to resolve ambiguities in the formulation of the collision term, paying particular attention to the distribution function, background terms, particle degrees of freedom, and the conventions used for calculating scattering amplitudes.

This approach moves beyond standard approximations by explicitly calculating the collision term without relying on relaxation time approximations, particularly for scenarios involving light mediators. By focusing on scalar mediators, the research establishes a versatile framework adaptable to a wider range of neutrino self-interactions and potentially to warm dark matter scenarios, providing a robust tool for analysing future NSI signal detections.

Neutrino self-interaction modelling incorporating mediator mass and Dirac-Majoraja distinctions

Calculations reveal a smooth transition between the light and heavy mediator approximations as the Universe cools, demonstrating a continuous shift in the dominant interaction regime. This detailed approach allows for a comprehensive analysis of neutrino self-interactions, accounting for fundamental particle properties often simplified in previous models.

The research incorporates both Dirac-like and Majorana neutrinos, distinguishing between two neutrino mass eigenstates within the Boltzmann hierarchy framework. The study constructs a novel framework to obtain the neutrino collision term, incorporating both neutrino and mediator masses as free parameters. This flexibility enables exploration of a broader range of potential interaction scenarios, moving beyond fixed mass assumptions.

By systematically deriving the collision term from the most general case, the work addresses key questions regarding the impact of neutrino mass and the distinction between Dirac and Majorana particles on self-interaction dynamics. The framework presented is not limited to a specific mediator mass, offering a versatile tool for future cosmological analyses.

Furthermore, the research provides a means to compute thermal corrections for the light mediator case without relying on the standard relaxation time approximation. This advancement allows for a more accurate assessment of interactions when the mediator mass is significantly smaller than the neutrino temperature. The ability to accurately model interactions across a wide range of mediator masses and cosmological conditions represents a significant step forward in understanding neutrino self-interactions and their potential role in resolving cosmological tensions. This methodology can also be adapted to explore warm dark matter self-interaction scenarios, broadening its applicability beyond neutrino physics.

The Bigger Picture

Scientists have long grappled with subtle discrepancies in our standard cosmological model, tensions that hint at physics beyond our current understanding. This work offers a significant step forward in addressing these issues by providing a refined method for calculating how neutrinos interact with each other. The difficulty lies in accurately modelling these ‘neutrino self-interactions’ within the complex environment of the early universe, a period crucial for shaping the cosmos we observe today.

Previous approaches often relied on approximations that broke down under certain conditions, limiting their precision and scope. This new framework elegantly sidesteps those limitations, offering a robust calculation applicable across a wider range of energies and cosmic epochs. It is not merely a technical improvement; it unlocks the potential to rigorously test theoretical models proposing neutrino self-interactions as solutions to cosmological puzzles, including the persistent Hubble tension, the disagreement between different measurements of the universe’s expansion rate.

The ability to accurately model these interactions is vital as upcoming astronomical surveys promise to deliver increasingly precise data, potentially revealing the elusive signature of these interactions. However, the framework, while versatile, currently focuses on interactions mediated by a specific type of particle. Extending it to encompass other interaction types and exploring its implications for scenarios like self-interacting dark matter remain open challenges. Future work will undoubtedly focus on refining these calculations further and, crucially, on comparing the theoretical predictions with the wealth of observational data expected in the coming years, finally determining whether neutrinos truly hold a key to unlocking the mysteries of the universe.