Aleksander Kubański — Independent Research

Research Programs

This site presents two distinct but methodologically related research programs: one in dark-sector cosmology and one in deterministic information storage in nonlinear systems.

Regime-Limited Dynamical Systems, interacting dark-sector dynamics, late-time cosmic stability, and paired expansion-growth signatures.

A three-part program by Maria Kubańska and Aleksander Kubański, progressing from a minimal bistable cell to coupled cascades and a continuum field.

Research Program I

Dark-Sector Feedback and Late-Time Cosmic Stability

An attractor-based program for interacting dark-sector dynamics, Regime-Limited Dynamical Systems, and late-time cosmological stability.

Core Hypothesis

The two dominant components of our universe, dark energy and dark matter, are not independent. Dark energy is a dynamical field that evolves over cosmic time, rather than a fixed cosmological constant. This field interacts with dark matter through a weak coupling that remains dormant in the early universe but activates when the matter fraction drops below a critical threshold. Once activated, the coupling creates a feedback loop: the field responds to the declining matter density, and that response alters the rate at which matter continues to decline. The system possesses a stable attractor, a long-term regime toward which it evolves from a wide range of initial conditions. The value we measure as the cosmological constant is the observable face of this regime, not a fundamental number.

Book

Why the Universe Will Not Destroy Itself: A Journey into Dark Energy, Dark Matter, and Cosmic Stability is a popular-science companion to this research, developing the same hypothesis for a general audience.

Figure 1

The Cosmic Trajectory

The solid curve traces the evolution of the matter fraction under the attractor hypothesis. The dashed curve shows ΛCDM. Four key moments: onset of acceleration, coupling threshold, present epoch, late-time attractor.

Key Testable Signature

The strongest consequence of this hypothesis is not a single isolated anomaly, but a paired observational signature. If the dark sector is regulated by a late-time attractor, then a deviation in dark-energy behavior should appear together with a correlated suppression of cosmic structure growth.

In other words, the relevant signal is the joint appearance of two effects: a late-time change in the expansion history and a simultaneous weakening of matter clustering. The hypothesis is therefore testable because the two effects must appear together, not separately.

Figure 2

The Paired Signature

Panel A: dark-energy equation of state dips below −1. Panel B: simultaneous suppression of structure growth. Both effects governed by the same coupling constant.

Figure 3

The Attractor is Robust

Fourteen universes with very different initial matter fractions converge to the same late-time band within a few cosmic e-folds.

Research Interests

• Dark matter / dark energy interaction
• Cosmic stability and attractor models
• Thermodynamic regulation of the universe
• Observational cosmology: DESI, Euclid, Rubin

Selected Works — RLDS Series

The RLDS series develops a five-part research program on Regime-Limited Dynamical Systems and Dark-Sector Attractor Cosmology.

Mathematical prototype for singular one-dimensional autonomous systems with a stable global attractor.

Canonical RLDS framework and reduction criteria for singular ODEs.

Numerical derivation of the paired dark-sector signature linking dark-energy dynamics and suppression of structure growth.

Consequences of dark-sector attractor closure for acceleration, matter density, and phantom-like behavior.

Representative descent from interacting dark-sector field theory to the effective RLDS attractor description.

Research Program II

Deterministic Phase Memory

Foundational research program by Maria Kubańska and Aleksander Kubański

Deterministic Phase Memory develops a mathematical framework for information storage in bistable nonlinear dynamical systems across three scales: a minimal local cell, a finite cascade of coupled cells, and a spatially distributed continuum field.

Formalizes phase memory in a minimal two-dimensional bistable system, including explicit switching thresholds, stability, basin structure, and hysteresis.

Extends the elementary cell to coupled cascades, with explicit stability bounds, quantitative addressability, transient confinement, and bidirectional-coupling analysis.

Extends the framework to a reaction-diffusion continuum in which spatial domains and domain walls carry information, connecting the single-cell and cascade scales to a field description.

All three works are open preprints on Zenodo and are also linked to the authors' ORCID records.

Software

RLDS-MAT is a scientific Python toolkit for the analysis and certification of Regime-Limited Dynamical Systems. It implements the mathematical framework developed in RLDS I–II, including threshold computation, auxiliary-function geometry classification, equilibrium detection, stability analysis, command-line tools, reports, and plots.

The package is designed as a computational companion to the RLDS paper series, allowing external models to be tested against the RLDS reduction criteria.

RLDS-PAIRED is a Python SDK for paired dark-sector signature analysis within the Regime-Limited Dynamical Systems (RLDS) framework.

The package includes source code, examples, tests, citation metadata, and Zenodo-ready metadata for reproducible scientific use.

Profiles

Contact

Email: aleksander@kubanski.pro