How to Make a Universe

There's a new paper How to Make a Universe by Bassani and Magueijo on the quantum cosmology arXiv that proposes a curious and clever new cosmology. They propose that the fundamental constants (\(c, G, \hbar, k_B, e\)) are not fixed numbers, but instead evolve through a process akin to natural selection. Unlike the cosmological natural selection proposed by Smolin, this paper doesn't require any kind of anthropic reasoning, multiverses, or black hole assumptions, instead if just presuppositionally requires a universe in which the physical laws are not fixed but evolve according to a deeper mathematical structure. And most interestingly an evolution of the laws of physics and matter creation/destruction are intertwined! I'm far far outside the field anymore, but I'm always interested in clever new ideas, so I thought I'd try to digest it for a lay audience.

Their core premise is trying to understand the origin of the universe, not as a singular event meticulously preordained, but as the outcome of a process akin to natural selection, with selection happening on the fundamental laws of physics themselves. Essentially order arising from chaos, as many pre-scientific theories have proposed. They challenge the conventional view of immutable laws and constants, proposing a dynamic environment where variations in these parameters play a crucial role in shaping the cosmos we observe. The paper marries extensions of unimodular gravity with absorbing Markov chains, to paint a picture of a universe sculpted by chaos and selection.

At the heart of their model lies the idea that the "laws" of physics are not fixed entities from the beginning, but rather evolve through a period of extreme variability. This "higgledy-piggledy" phase, reminiscent of Wheeler's vision of a chaotic cosmic start, allows for the exploration of a vast space of possible physical realities. The paper explores ways to link the degree of the "lawlessness" to matter generation, in what can be seen as an implementation of Noether's theorem. They suggest this variability is not entirely random; it is driven by a deterministic process (the mechanism isn't specified) that favors certain configurations over others.

The authors introduce the distinction between local and global variables. Local variables, such as the position and momentum of particles, describe the properties of spacetime at a given point. Global variables, on the other hand, characterize the universe as a whole. These global variables, representing fundamental constants like the gravitational constant or the cosmological constant, are treated as intensive quantities. They introduce a "preferred foliation" of spacetime, which provides a "matrix" for the evolution and possible freezing of constants.

A essential part of their model is the reinterpretation of "time." The authors propose that time is canonically dual to the constants of nature. Inspired by phenomenological fluid clocks (based on isentropic fluids), time becomes a "chemical potential" of fundamental constants: that is, the time dual to a certain constant (e.g., Newton's constant) dictates the rate at which the constant can change. This analogy allows them to connect variations in fundamental constants to matter creation or destruction. The rate of flow of the time dual to a constant is determined by the chemical potential of that constant. This means the violation of energy conservation is directly linked to the interaction between a matter parameter and a gravity clock (or vice versa). This provides a theoretical basis for the creation of matter in the early universe.

The other core idea in their model is the separation of matter and gravity within the chaotic early universe. While intuitively we might assume that no such distinction exists in a state of complete chaos, the authors postulate that even a modest level of separation can provide an evolutionary advantage. This requirement translates into the existence of separate local and global variables for matter and gravity, leading to a separation of the Hamiltonian into matter and gravity components.

The separation leads to a deterministic mechanism of evolution where constants of nature can evolve with time and, consequently, can lead to a change in the mass-energy of the Universe. The equation they derive for the time evolution of matter depends on the Poisson bracket between matter and gravity parts of the Hamiltonian.

The key concept in their model is the role of diffeomorphism invariance. Diffeomorphism invariance is the expression of general covariance (the laws of physics are independent of the coordinate system). The authors propose that diffeomorphism invariance emerges as a natural outcome of the selection process. By requiring the algebra of the constraints to follow the Dirac hypersurface deformation algebra in the absence of global interactions, they ensure that their framework respects this fundamental symmetry. This ultimately explains how gravity is always present, whereas matter can be optional. The upshot is that nearly diffeomorphism-invariant states are favoured as the end product of the evolutionary process.

The authors then introduce a stochastic element, inspired by the random mutations that drive biological evolution. They model these mutations using an absorbing Markov chain, where states represent different configurations of the universe with varying physical constants. The absorbing state represents a stable configuration where evolution ceases, and the laws of physics become fixed (i.e. constants become truly constant). The use of an absorbing Markov chain implies that, once the absorbing state is reached, it can no longer be left, meaning the "constants" of Nature really become constant.

Within this Markov chain, the constants of nature can jump from state to state, either becoming a function of an a variable, or converging to an a variable. This random distribution has no biases to one or other side and the chance to keep positive gains of mass creation requires a local Hamiltonian with a clear separation of matter and gravity.

The combination of the deterministic process and stochastic mutations provides a theoretical framework for cosmic natural selection. Universes with configurations conducive to matter creation and stability are favored, while those that lead to annihilation or instability are eliminated. Universes containing clear separation between matter and gravity are favoured by the evolution along the Markov chain, as are those with nearly-diffeomorphism symmetry, which is also an absorbing state.

I'm far outisde my depth as to speak to the validity or falsifiability of this model, but it's a very clever formalism that at the very least is interesting and novel. The idea that we live in a universe where random mutations in physical constants were guided by a deterministic environment which favored stable matter-rich configurations and ultimately led to the nearly diffeomorphism-invariant cosmos we observe.