[Paper Review] Extending cosmological natural selection

Gordon McCabe|arXiv (Cornell University)|Oct 5, 2006

Cosmology and Gravitation Theories19 references3 citations

TL;DR

This paper extends Lee Smolin's cosmological natural selection hypothesis by proposing that the emergence of quantum relativistic universes itself results from a stochastic process called 'cosmogenic drift,' which evolves mathematical structures toward stable, rigid forms. The theory explains the prior existence of a quantum relativistic universe as a natural outcome of this drift, enabling natural selection to subsequently operate on a population of reproducing universes.

ABSTRACT

The purpose of this paper is to propose an extension to Lee Smolin's hypothesis that our own universe belongs to a population of universes evolving by natural selection. Smolin's hypothesis explains why the parameters of physics possess the values we observe them to possess, but depends upon the contingent fact that the universe is a quantum relativistic universe. It is proposed that the prior existence of a quantum relativistic universe can itself be explained by postulating that a process of cosmogenic drift evolves universes towards stable ('rigid') mathematical structures.

Motivation & Objective

• To address the contingency of why our universe has the specific physical parameters it does, which cannot be derived from first principles.
• To explain why a quantum relativistic universe—necessary for Smolin's cosmological natural selection—exists in the first place.
• To propose a mechanism (cosmogenic drift) that explains the prior emergence of quantum relativistic universes as a natural outcome of stochastic evolution toward stable mathematical structures.
• To unify the origin of the physical universe with the framework of natural selection by postulating a pre-selection stochastic process.
• To provide a deeper explanatory foundation for multiverse theories by grounding the existence of life-permitting universes in a process of cosmogenic drift toward rigidity.

Proposed method

• Proposes a stochastic process called 'cosmogenic drift' that evolves mathematical structures toward stable, rigid forms, with quantum relativistic universes as attractors.
• Models the evolution of universes as a Markov process with transition probabilities defined by a function $ G(x,x';t) $, determining the time evolution of the probability distribution $ \rho(x,t) $.
• Applies the Fokker-Planck equation to describe the time evolution of the probability distribution, incorporating both diffusion and drift terms: $ \partial\rho/\partial t = D\nabla^2\rho - \nu\nabla\rho $.
• Considers both simple Brownian motion and geometric Brownian motion with drift, with the latter preferred if parameters must remain non-negative.
• Uses the path-space probability measure $ p(\gamma) = T(x_{n-1},x_n)\cdots T(x_0,x_1)\rho(x_0,0) $ to define the likelihood of evolutionary trajectories.
• Argues that any such stochastic process, given infinite time, will eventually evolve toward a quantum relativistic universe, which then becomes the stable starting point for natural selection.

Experimental results

Research questions

• RQ1 Why does a quantum relativistic universe exist, given that its parameters are contingent and not theoretically derivable?
• RQ2 Can the emergence of a quantum relativistic universe be explained as a natural outcome of a deeper stochastic process?
• RQ3 What type of stochastic process—simple diffusion or diffusion with drift—best explains the evolution toward stable, rigid mathematical structures?
• RQ4 How does cosmogenic drift provide a pre-selection mechanism that enables cosmological natural selection to operate?
• RQ5 Can the stochastic process governing parameter variation in the multiverse be derived from quantum gravity, or is it independent?

Key findings

• Cosmogenic drift, a stochastic process evolving mathematical structures toward stable, rigid forms, can explain the prior existence of a quantum relativistic universe.
• Quantum relativistic universes emerge as attractors of this drift process, regardless of the initial distribution, due to their structural stability.
• The Fokker-Planck equation with drift terms $ \partial\rho/\partial t = D\nabla^2\rho - \nu\nabla\rho $ governs the time evolution of the probability distribution over universes.
• Geometric Brownian motion with drift is a plausible model for parameter variation, especially if non-negative parameters are required.
• The process is insensitive to the specific form of the probability distribution (e.g., normal or lognormal), as long as it evolves toward stable structures.
• Once a quantum relativistic universe is reached, natural selection can begin, with black hole formation triggering the reproduction of new universes, as in Smolin's original hypothesis.