[Paper Review] A Diffraction Grating for the Cosmic Neutrino Background and Dark Matter

Asimina Arvanitaki, Savas Dimopoulos|arXiv (Cornell University)|Mar 8, 2023

Astrophysics and Cosmic Phenomena6 citations

TL;DR

This paper proposes a macroscopic sea urchin-like diffraction grating structure, 1–100 meters in size, that enhances the local cosmic neutrino background (CνB) asymmetry by up to ~10^6 times via phase grating effects, generating a force ~10^3 times stronger than Earth's neutrino reflection. The design also enables efficient diffraction of QCD axion dark matter, producing a gradient force up to 100 times stronger than from CνB alone.

ABSTRACT

We propose structures of size between $\sim 1$ meter to 100 meters that drastically alter the local distribution of the Cosmic Neutrino Background ($CνB$). These structures have a shape reminiscent of a sea urchin: They consist of rods of width $w$ and length $L \gg w$ periodically arranged on the surface of sphere of radius $R\sim L$. Such a structure functions as a diffraction phase grating and produces a region around its center where the fractional neutrino-antineutrino asymmetry is $\sim kδ_νL$, where $k$ is the neutrino momentum, and $δ_ν$ the deviation of the neutrino index of refraction from unity. The asymmetry has a gradient set by the rod width. We find that the local neutrino asymmetry can be enhanced by $\mathcal{O}( ext{few} imes 10^6)$ relative to the naive Standard Model expectation, for reasonably sized structures. This results in a force $\mathcal{O}(10^3)$ times bigger than the one we recently pointed out due to the neutrinos' reflection on the surface of the Earth. While in this paper we do not propose a concrete detection setup, we estimate that the $\mathcal{O}(G_F)$ force on a test mass can be close to the Standard Quantum Limit of a torsion balance or a low frequency harmonic oscillator. Finally, we show that this $C νB$ diffractor can be used as a Dark Matter diffractor. For example, the QCD axion Dark Matter with decay constant $f_a$ around $10^9$ GeV can be sufficiently diffracted to produce a gradient force that is up to $\mathcal{O}(10^2)$ times larger than the one from the $C νB$. This is the first setup of this kind and the simplicity of our design suggests that there could be significant improvements that escape us.

Motivation & Objective

• To explore macroscopic structures that can significantly alter the local distribution of the Cosmic Neutrino Background (CνB).
• To design a phase grating structure capable of amplifying neutrino-antineutrino asymmetry gradients for enhanced detectable forces.
• To demonstrate that such a structure can also act as a diffractor for QCD axion dark matter, enhancing its interaction forces.
• To identify a novel, simple setup that could surpass existing force sensitivities in precision tests of neutrino and dark matter interactions.

Proposed method

• Design a spherical structure with periodically arranged rods of width w and length L ≫ w, where R ≈ L is the sphere's radius.
• Model the system as a diffraction phase grating that modulates the neutrino index of refraction, creating a spatially varying asymmetry in the CνB.
• Use the gradient of the rod width to set the spatial scale of the neutrino asymmetry, leading to a force proportional to the gradient of the refractive index deviation δν.
• Derive the force enhancement factor as O(few × 10^6) relative to the Standard Model expectation for neutrino asymmetry.
• Extend the model to show that the same structure can diffract QCD axion dark matter, producing a gradient force up to O(10^2) times stronger than from CνB alone.
• Estimate the force on a test mass to be near the Standard Quantum Limit for torsion balances or low-frequency harmonic oscillators.

Experimental results

Research questions

• RQ1 Can a macroscopic, structured object significantly enhance the local neutrino-antineutrino asymmetry in the Cosmic Neutrino Background?
• RQ2 What is the maximum force amplification achievable via such a diffraction grating structure compared to natural neutrino scattering on Earth?
• RQ3 Can the same structure efficiently diffract QCD axion dark matter, and how does the resulting force compare to that from the CνB?
• RQ4 What is the force magnitude on a test mass, and how close is it to the Standard Quantum Limit in precision measurement devices?

Key findings

• The proposed structure enhances the local CνB neutrino-antineutrino asymmetry by a factor of approximately 10^6 compared to the naive Standard Model expectation.
• The resulting force on a test mass is enhanced by a factor of about 10^3 compared to the force from neutrino reflection on Earth.
• The force on a test mass reaches the order of magnitude of the Standard Quantum Limit for torsion balances or low-frequency harmonic oscillators.
• The same structure can diffract QCD axion dark matter, producing a gradient force up to 100 times stronger than the force from the CνB alone.
• The design is simple and suggests potential for further improvements beyond current estimates.