11 papers
Ascertaining Learning: Generative AI, the Proxy Problem, and Cognitive Competence in University Mathematics
Bob Osano
For decades, university mathematics assessed executable procedure, computing and reproducing standard proofs, as a proxy for the understanding it cared about, because procedure was…
Beyond the equation of state: a second-order diagnostic for dynamical dark energy
Bob Osano
The first-order continuity equations determine the evolution of the energy densities but depend only on the instantaneous value of the dark-energy equation-of-state parameter. Diff…
Kinetic Theory of Cosmological Magnetogenesis at Second Order: A New Density-Gradient Source and Comparison with the Harrison Mechanism
Bob Osano
We derive and compare three mechanisms of cosmological magnetogenesis: the Thomson-scattering velocity-difference mechanism of Takahashi et al.\ (2005), a new density-gradient sour…
Non-Perturbative Bounds on Cosmological Backreaction, the Non-Linear Scale, and Gauge-Invariant Mutual Information from the Matter Power Spectrum
Bob Osano
We apply the mesoscopic coarse-graining framework of~\cite{OsanoMeso,OsanoExtensivity,OsanoPerturbation} to three problems in Cosmological Perturbation Theory and the backreaction…
The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure
Bob Osano
We develop a mesoscopic formulation of equilibrium statistical mechanics based on coarse-grained occupation-number sectors of one-particle phase space. A mesoscopic partition funct…
Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function
Bob Osano
We develop a systematic perturbation theory for the Helmholtz free energy of a classical -body system within the mesoscopic framework of~\cite{OsanoMeso,OsanoExtensivity}. The c…
Entropy additivity from exponential decay of correlations: a coarse-grained operator approach
Bob Osano
Thermodynamic extensivity is commonly introduced as a postulate -- the homogeneity of degree one in thermodynamic potentials. We provide a constructive derivation of this property…
Interacting Dark Sector: An Isobaric Approximation
Bob Osano
What if the dark sector is not a static entity but rather a dynamic entity with interactive components of the universe? This intriguing hypothesis raises important questions regard…
Matter-Dark Energy Transition: A Dynamical Systems Approach
Bob Osano
In this study, we deviate from the traditional examination of the evolving universe through the scale factor and instead consider a parameter $\chiME$, defined by the ratio of two…
Dark Energy: A Dynamical Systems Approach to the Reconstruction of the Equation of State
Bob Osano
This correspondence delves into the application of dynamical systems methodologies within the context of cosmology, specifically addressing a preliminary strategy for determining t…
Dynamics of the transitions epochs in cosmological evolution
Bob Osano
We study two transition periods in cosmology: radiation-to-matter and matter-to-dark energy. In each case, we define a new parameter given by the ratios of the two energy densi…