The Biological Cosmological Constant ΛB: Exploratory Propensity, Dynamical Habitability And The Geometric Origin Of Life

[BioSystems via PubMed] The emergence of life represents a fundamental geometric phase transition in the state space of complex systems, rather than a mere sequence of chemical syntheses.

Building upon the framework of Biorelativity, we introduce ΛB, the biological cosmological constant, which quantifies the intrinsic exploratory propensity of a system, also conceived as the basal pressure driving the expansion of the eco-evolutionary manifold into the adjacent possible.

By mathematically formalising ΛB as proportional to the squared fractional expansion rate of the Fisher Information Volume, we provide a rigorous criterion to distinguish between chemical persistence (subcriticality) and genuine open-ended evolution. Furthermore, we demonstrate that macroevolutionary trajectories in the Phanerozoic record, traditionally debated through logistic and dynamic models, represent a multi-stage geometric evolution.

We argue that the biosphere transitioned from a high-volatility inflationary regime in the Cambrian to a geometrically stabilised, high-curvature state in the Meso-Cenozoic. In this mature regime, ΛB is counterbalanced by relational interaction curvature κbio to form an asymptotic Ricci soliton, maintained through continuous thermodynamic dissipation.

This geometric perspective offers a novel theoretical distinction between structural and dynamical habitability, reconceptualises lithopanspermia as the robust transport of dynamically subcritical systems and recasts the early Earth as a geometric amplifier where Gaian feedbacks tune geometric parameters to secure long-term dynamical habitability.

Ultimately, this synthesis suggests that extraterrestrial life-detection strategies should prioritise the search for thermodynamic and atmospheric signatures characteristic of dynamically expanding information spaces, including intermittent or patchy chemical anomalies indicative of aborted geometric expansions, providing a unifying mathematical foundation for understanding the evolutionary potential of planetary biospheres.