# Effects of Violation of Equivalence Principle on UHE Neutrinos at IceCube in 4 Flavour Scenario

## TL;DR

This paper investigates how tiny violations of the weak equivalence principle could influence ultra high energy neutrino detection at IceCube, using a 4-flavour model to identify potential gravity-induced oscillation effects.

## Contribution

It introduces a 4-flavour neutrino framework to analyze gravity-induced oscillations caused by weak equivalence principle violation at ultra high energies.

## Key findings

- Small VEP ($ extasciitilde 10^{-42}$) significantly alters muon yields from UHE neutrinos.
- Detection signatures differ with and without gravity-induced oscillations.
- Long baseline and high energies enhance sensitivity to tiny VEP effects.

## Abstract

If weak equivalence principle is violated then different types of neutrinos would couple differently with gravity and that may produce a gravity induced oscillation for the neutrinos of different flavour. We explore here the possibility that very small violation of the principle of weak equivalence (VEP) can be probed by ultra high energy neutrinos from distant astrophysical sources. The very long baseline length and the ultra high energies of such neutrinos could be helpful to probe very small VEP. We consider a 4-flavour neutrino scenario (3 active + 1 sterile) with both mass-flavour and gravity induced oscillations and compare the detection signatures for these neutrinos (muon tracks and shower events) with and without gravity induced oscillations at a kilometer scale detector such as IceCube. We find that even very small VEP ($\sim 10^{-42}$) can considerably affect the detected muon yield produced by UHE neutrinos from distant Gamma Ray Bursts (GRBs)