Information: a temporal-spatial-entropic expanding universe

We introduce the concept of an informational spacetime, where entropy is promoted from a thermodynamic parameter to a fundamental coordinate on equal footing with space and time. Building upon the Advanced Manifold-Metric Pairs (AMMP) framework developed by Ntelis (2025), we construct the txyzS metric—a novel 5-dimensional temporal-spatial-entropic manifold that extends standard FLRW cosmology. In this framework, information becomes the fundamental substrate of reality: space encodes positional information, time encodes sequential information, and entropy encodes configurational information about microscopic arrangements. The universe is not made of ``stuff'' that possesses information; rather, the universe \textit{is} information. Our analysis demonstrates that the entropy dimension naturally generates an effective dynamical dark energy, producing observable deviations from standard $\Lambda$CDM cosmology. Positive values of the entropy Hubble parameter $H_{S,0}$ increase the expansion rate at high redshift (phantom-like behavior), while negative values decrease it (quintessence-like behavior). The model provides a geometric origin for a redshift-dependent equation of state without requiring an additional scalar field. Comparison with cosmic chronometers data yields a best-fit value $H_{S,0} = 1.385\ \text{km/s/Mpc}$, with $\Delta\chi^2 = 0.24$ relative to $\Lambda$CDM—fully consistent with current observations and offering new physics for future high-precision surveys. To enable this analysis, we have developed \texttt{EinsteinKPy2Tex}, an open-source Python package that automates the computation of quadratic curvature invariants and exports results to publication-ready \LaTeX. The entropy dimension, by unifying geometry, thermodynamics, and information, offers a new lens through which to view the nature of space, time, and the cosmos itself. The software is open-source under an MIT license and permanently archived on Zenodo (DOI: 10.5281/zenodo.20563701), with the latest version available at \url{https://github.com/lontelis/EinsteinKPy2Tex}.

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