Carroll Particle: A Possible Candidate for Dark Matter

The contraction of the Poincar\'e algebra gives rise in two distinct frameworks: Galilean physics and Carrollian physics. While classical Galilean mechanics encompasses well-established relationships for momentum, energy, energy-momentum, and Newton's second law, the corresponding formulas in Carrollian mechanics has remain unknown. This study aims to uncover these formulas within the context of Carrollian mechanics and investigate the thermodynamics of an ideal gas under this framework. The findings reveal a deviation from Galilean mechanics and present a remarkable discovery: Carrollian matter generates an outward gravitational field, in stark contrast to the inward gravitational field observed in Galilean mechanics. Based on this surprising observation, along with additional supporting reasonings, we propose that Carroll particles may be potential candidates for dark matter and may simultaneously provide an explanation for dark energy.