Relativistic diffusing particles, entropy and varying cosmological constants

The universe is often imagined as a grand stage where matter and energy perform a cosmic dance, governed by the rigid laws of gravity. In the standard view of this performance, the rules are set in stone: the strength of gravity, the amount of matter, and the mysterious force driving the universe's expansion are treated as fixed constants. However, a new perspective suggests that the stage itself might be shifting, and the actors might be interacting with an invisible medium that changes the script as the show progresses. This idea challenges the long-held belief that the total energy and momentum of the cosmos are perfectly conserved, meaning they never change or leak away. Instead, it proposes that particles moving through the universe might be diffusing, or spreading out, in a way that subtly alters the fundamental constants of nature, such as the gravitational pull and the rate of expansion.

This concept is central to a recent study by physicist Z. Haba, which explores a model where the universe is filled with a gas of particles that are not just moving, but actively diffusing through an unseen background. In this scenario, the particles are not isolated; they interact with a medium that is not directly observed, much like a drop of ink spreading through water. As these particles diffuse, they lose or gain energy in a way that breaks the traditional rule of energy conservation. To keep the mathematical description of the universe consistent, the study suggests that the "constants" of nature, specifically the strength of gravity and the cosmological term (which drives the expansion of space), must vary over time to compensate for this energy exchange. The research does not claim to have measured these changes directly but rather constructs a theoretical framework where such variations are a natural consequence of particle diffusion.

The paper begins by revisiting the equations that describe how matter shapes the geometry of space and time. In the standard model, these equations assume that the total energy and momentum of the universe remain constant. Haba's work modifies this by introducing a term that accounts for the flow of heat and viscosity, similar to how a fluid resists motion. When particles diffuse, they create a situation where the energy-momentum tensor, which represents the density and flow of matter, is no longer conserved. To balance the equations, the study posits that the Newtonian gravitational constant and the cosmological term must change in response. This creates a dynamic relationship where the diffusion of particles drives the evolution of the universe's expansion and the strength of gravity itself.

To test these ideas, the author models a gas of massive particles moving in an expanding universe. The study finds that as time passes, these massive particles behave more and more like massless particles, such as light. The model calculates how the energy density and temperature of this gas change as the universe expands. A key finding is that the temperature of the gas does not simply drop as the universe stretches; instead, the diffusion process adds energy back into the system, causing the temperature to eventually stabilize or even grow linearly over very long periods, depending on how fast the universe is expanding. This behavior is distinct from the standard model, where the temperature of a gas would simply cool down as space stretches.

The study also delves into the thermodynamics of this diffusing gas, linking the microscopic behavior of particles to the macroscopic concept of entropy, which is a measure of disorder. The research demonstrates that the increase in entropy caused by the diffusion of particles is directly related to the variation of the cosmological term. In a surprising connection, the study suggests that the logarithm of the gravitational constant is approximately equal to the entropy of the gas. This implies that as the universe becomes more disordered through diffusion, the strength of gravity and the rate of expansion adjust in a precise, calculable way. The author shows that this relationship holds true whether the particles are massive or massless, providing a unified picture of how diffusion influences cosmic evolution.

One of the most concrete results of the paper is the solution to the equations describing a universe filled with massless diffusing particles. The study finds that under certain conditions, the universe could evolve into a state known as "coasting cosmology," where the universe expands at a constant speed rather than accelerating or decelerating. This is a specific, mathematically exact solution that emerges naturally from the diffusion equations. The research also explores an exponential expansion, similar to the rapid growth seen in the early universe, and shows that the diffusion process leads to a stable, equilibrium state where the particles settle into a predictable distribution. These solutions are not just abstract mathematical exercises; they offer specific predictions for how the density of matter and the value of the cosmological constant would change over time.

The paper explicitly rules out the idea that the standard model of cosmology, with its fixed constants and conserved energy, can fully explain the behavior of a diffusing medium. It argues that if particles are indeed diffusing, then the assumption of constant gravitational strength and a fixed cosmological term is insufficient. The study does not claim to have proven that the universe is currently in this diffusing state, but it establishes that if such a process is occurring, it would leave a distinct signature in the way the universe expands and how gravity behaves. The findings suggest that the "dark energy" often invoked to explain the universe's acceleration might not be a separate entity, but rather a consequence of the non-conservation of energy in a diffusing system.

In the final analysis, the work provides a detailed map of how a universe governed by diffusing particles would look. It connects the microscopic motion of individual particles to the grand scale of cosmic expansion, showing that the two are inextricably linked. The study concludes that the variation of fundamental constants is not an arbitrary addition to the theory but a necessary consequence of the diffusion process. By deriving the entropy of the gas from both thermodynamic principles and the microscopic distribution of particles, the author confirms that the two approaches yield the same result, reinforcing the validity of the model. The paper leaves the reader with a clear picture of a universe where the rules are not static, but evolve in tandem with the very matter that fills it, driven by the simple, relentless process of diffusion.