Introduction: Understanding the large-scale structure of the universe remains a fundamental challenge in cosmology, with computational simulations providing critical insights into non-linear structure growth. Particularly, computational simulations provide critical information about the nonlinear growth processes behind the observed large-scale structures. Inspired by the similarly porous structure of polymer membranes prepared using phase-inversion, this work presents a novel thermodynamic approach to cosmic structure formation. Methods: A numerical framework is presented, based on the Cahn-Hilliard model of spinodal decomposition for a binary mixture, treating the universe as a two-component fluid of matter and dark energy. The dimensionless Cahn-Hilliard equation is solved using finite-element methods, with parameters calibrated to Planck 2018 cosmology. The simulation evolves an initially homogeneous matter distribution through 500 timesteps, corresponding to 35 million years of cosmological evolution. Results: The simulated matter distribution exhibits quantitative agreement with observational surveys across multiple metrics. Void fraction evolves to 0.416 at z ≈ 0.65, right at the edge of the domain of applicability of the ΛCDM model. Filamentarity reaches 0.42, comparable to Millennium Simulation results. The linear growth factor extracted from simulated density fields also closely agrees with ΛCDM predictions over the interval 9.300 < t < 9.335 Gyr. Discussion: The thermodynamic perspective reframes dark energy as the low-density phase emerging naturally from cosmic phase separation, suggesting that accelerated expansion arises from the increasing volume fraction of this phase. The quantitative agreement of the simulated matter power spectrum with Planck 2018 results across nearly two decades in wavenumber, without accounting for gravitational interactions, demonstrates that spinodal decomposition captures the essential physics of large-scale structure formation. By establishing that the same principles governing polymer membrane formation quantitatively describe the cosmic web, this work creates a novel interdisciplinary bridge between materials science and physical cosmology. Conclusion: This work establishes spinodal decomposition as a viable thermodynamic framework for cosmic structure formation, offering a computationally efficient alternative to traditional N-body methods while reproducing key quantitative observables. The approach opens new avenues for exploring matter-dark energy interactions and may prove valuable for next-generation survey analysis.
Nitish Yadav (Fri,) studied this question.