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Bob Osano

Publications and source records attributed to Bob Osano.

At least 19 recordsLinked to original sources
arXiv2026

Beyond the equation of state: a second-order diagnostic for dynamical dark energy

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. Differentiating these equations with respect to e-fold time introduces the term $\omega'_{\rm DE}$ explicitly, providing a second-order probe of dark-energy dynamics. Consequently, while information about the evolution of the equation of state is encoded in the full dynamical solution, it is not explicit in the first-order continuity equations evaluated at a given epoch. The second-order formulation, therefore, provides a complementary description in which the local evolution of the equation of state appears directly through the curvature of the density trajectory. For a two-fluid interacting dark-sector model with linear coupling $Q_{AB}=\alpha\rho_AH$, the resulting second-order equation defines a curvature diagnostic, $\mathcal{C}=\rho_{DE}''/\rho_{DE}$, whose leading contribution, in the cosmological-constant limit, is $\alpha^2$, while departures from $\omega_{DE}=-1$ generate corrections through both $\delta\omega=1+\omega_{DE}$ and the distinctive term $-3\omega_{DE}'$. Unlike first-order analyses, this contribution is independent of the interaction strength and directly identifies dynamical dark energy. Applying the diagnostic to a CPL model with parameters consistent with DESI constraints, we recover $\omega_{DE}'$ across the full redshift range for both weak and strong interactions. Noise propagation shows that the diagnostic is detectable with signal-to-noise ratio exceeding three for $\sigma_H/H\lesssim1.5\%$, while the degeneracy between $\alpha$ and $\omega_{DE}'$ remains negligible for $\alpha\lesssim0.1$. In the non-interacting limit, the formalism naturally recovers the Caldwell--Linder thawing/freezing classification and extends it to interacting dark-energy models.

gr-qc↗
arXiv2026

Kinetic Theory of Cosmological Magnetogenesis at Second Order: A New Density-Gradient Source and Comparison with the Harrison Mechanism

We derive and compare three mechanisms of cosmological magnetogenesis: the Thomson-scattering velocity-difference mechanism of Takahashi et al.\ (2005), a new density-gradient source identified here for the first time, and the Harrison bulk-flow mechanism of Cembranos et al.\ (2020). Starting from the coupled Maxwell-Boltzmann equations, the complete kinetic theory chain is derived in a single document -- from the BBGKY hierarchy and Thomson collision term, through the generalised Ohm's law, to the second-order magnetic induction equation. The Ohm's law correction terms are each bounded by $m_e/m_p\approx5.4\times10^{-4}$, confirming the standard single-fluid approximation to better than $0.1\%$. At second order in cosmological perturbations, products of first-order scalar source vorticity, we identify a coupling between the photon density contrast $\delta_\gamma \equiv \delta\rho^{(1)}_\gamma / \bar\rho_\gamma$ and the electron-photon velocity difference $(u_e-u_\gamma)^{(1)}$ that was implicitly present in previous treatments but never isolated. Numerical evaluation with CAMB~v1.6.6 at $z=1100$ shows that this term contributes at ${\approx}0.97\times B_{\rm Tak}$, giving a scattering-mechanism total ${\approx}1.4\times$ the Takahashi result. The Harrison mechanism at the Planck bulk-flow limit ($\beta<8.5\times10^{-4}$) yields $B\approx5.7\times10^{-24}$~G at 1~Mpc today and dominates for $\beta\gtrsim2\times10^{-3}$, mildly above the Planck limit. All seed fields exceed the galactic dynamo threshold by many orders of magnitude.

gr-qc↗
arXiv2026

Non-Perturbative Bounds on Cosmological Backreaction, the Non-Linear Scale, and Gauge-Invariant Mutual Information from the Matter Power Spectrum

We apply the mesoscopic coarse-graining framework of~\cite{OsanoMeso,OsanoExtensivity,OsanoPerturbation} to three problems in Cosmological Perturbation Theory and the backreaction debate. \textbf{(i)}~A non-perturbative lower bound on the kinematic backreaction $\QD$ in the Buchert equations, derived from the Gibbs--Bogoliubov inequality: $\QD$ cannot be suppressed below its linear-perturbation-theoryvalue, regardless of the degree of non-linearity, provided the system satisfies stability and temperedness. \textbf{(ii)}~The radius of convergence of the mesoscopic cumulant expansion equals $O(\kNL^{-1})$, the non-linear scale of the matter power spectrum, providing a KAM-theorem explanation for why standard perturbation theory fails at $k>\kNL$. \textbf{(iii)}~For a Gaussian matter field, the inter-cell mutual information is exactly $I(i,j)=-\tfrac{1}{2}\ln(1-r_{ij}^2)$, gauge-invariant at linear order and computable directly from the observed $P(k)$; for $\Lambda$CDM at $\ell=50\,\mathrm{Mpc}\,h^{-1}$, $I_{\rm NN}\approx 0.10$.The total mutual information gives a data-computable measure of the backreaction correction to the FRW free energy. The gauge proof holds at linear order; the KAM identification is exact; the backreaction bound rests on a stated conjecture.

gr-qc↗
arXiv2026

Entropy additivity from exponential decay of correlations: a coarse-grained operator approach

Thermodynamic extensivity is commonly introduced as a postulate -- the homogeneity of degree one in thermodynamic potentials. We provide a constructive derivation of this property from microscopic conditions on the pair potential, without assuming it. Working with the one- and two-particle reduced densities of the $N$-body canonical Gibbs state, we introduce a combined coarse-graining operator $\mathcal{C}$ on single-particle phase space $\mathcal{M}=\Lambda\times\mathbb{R}^3$, producing dimensionless mesoscopic probabilities over spatial--momentum cells $\{V_i\times\Pi_\alpha\}$. Under three conditions on the pair potential -- stability, temperedness, and exponential cluster decomposition with correlation length $\xi$ -- we show, using the Ursell cluster expansion, that the coarse-grained entropy satisfies \[S_{\mathrm{CG}}=\sum_i S_i+O\!\left(\frac{|\Lambda|}{\ell^d}e^{-\ell/\xi}\right),\] where $\ell\gg\xi$ is the cell diameter. The correction is exponentially suppressed per cell, making entropy additive and recovering the thermodynamic limit of Ruelle and Fisher in explicit operator language. For systems with long-range interactions, where temperedness fails, the correction does not vanish, and non-additivity is quantified through inter-cell mutual information. We further show that spatial averaging does not commute with nonlinear thermodynamic functionals such as the entropy density -- a thermodynamic analogue of the cosmological averaging problem -- and we derive the generalised Euler relation with explicit surface corrections.

cond-mat.stat-mech↗
arXiv2026

Perturbation Theory of the Free Energy via the Mesoscopic Combined Partition Function

We develop a systematic perturbation theory for the Helmholtz free energy of a classical $N$-body system within the mesoscopic framework of~\cite{OsanoMeso,OsanoExtensivity}. The combined coarse-graining operator $\mathcal{C}=\mathcal{C}_x\circ\mathcal{C}_p$ acting on single-particle phase space partitions it into product cells $C_{i,\alpha}=V_i\times\Pi_\alpha$ and generates a mesoscopic partition function $\mathcal{Z}_{\rm meso}(\lambda)$ whose reference level factorises by the multinomial theorem: $\mathcal{Z}_{\rm meso}^{(0)}=(Z_1^{(0)})^N$. Perturbation theory for $\mathcal{F}_{\rm meso}(\lambda)=-k_BT\ln\mathcal{Z}_{\rm meso}(\lambda)$ in the inter-cell perturbation $\mathcal{V}_{\rm meso}$ yields the mesoscopic Gibbs--Bogoliubov inequality and an exact coupling-parameter integration formula. The full free energy satisfies \begin{equation*} F(\lambda)=\mathcal{F}_{\rm meso}(\lambda)-k_BT\!\sum_{i<j}I(i,j;\lambda)+O\!\left(|\Lambda|\ell^{-d}e^{-2\ell/\xi}\right), \end{equation*} where the inter-cell mutual informations $I(i,j;\lambda)$ are the corrections identified in the extensivity analysis. The first-order theory recovers the van der Waals equation and the Barker--Henderson result; the second-order term converges to the structure-factor formula in the fine-cell limit. For long-range interactions, factorisation fails, and the mutual-information corrections quantify the resulting non-extensivity.

cond-mat.stat-mech↗
arXiv2026

The Mesoscopic Partition Function:A Combined Spatial and Phase-Space Cell Structure

We develop a mesoscopic formulation of equilibrium statistical mechanics based on coarse-grained occupation-number sectors of one-particle phase space. A mesoscopic partition function is constructed by averaging the microscopic Hamiltonian over configurations compatible with a given occupation profile. The construction converges to the canonical Gibbs partition function in the fine-graining limit and remains compatible with interacting many-body systems. Within this framework, thermodynamic extensivity is shown to be equivalent to asymptotic factorisation of the mesoscopic partition function, while residual inter-cell correlations generate subextensive corrections. The resulting formalism provides a mathematically consistent bridge between microscopic Gibbs theory and mesoscopic thermodynamics.

cond-mat.stat-mech↗
arXiv2025

Interacting Dark Sector: An Isobaric Approximation

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 regarding the phenomenological behaviour of such an evolving system. In this study, we explore the simultaneous evolution and interaction of two hypothetical components within the context of an interacting dark sector, examining their implications for our understanding of cosmological dynamics.

gr-qc↗
arXiv2024

Matter-Dark Energy Transition: A Dynamical Systems Approach

In this study, we deviate from the traditional examination of the evolving universe through the scale factor and instead consider a parameter \(\chi_{ME}\), defined by the ratio of two competing energy densities: matter (DM) and dynamic dark energy (DDE). While the scale factor's role is not neglected, it is inherently embedded within the evolution equations of these competing energy densities. By employing dynamical systems techniques, we investigate the behaviour of this ratio \(\chi_{ME}\) to understand the dynamics surrounding the cosmological transition from matter domination to dark energy domination. This methodological shift allows for a more nuanced analysis of the matter-to-dark energy transition.

gr-qc↗
arXiv2024

Dynamics of the transitions epochs in cosmological evolution

We study two transition periods in cosmology: radiation-to-matter and matter-to-dark energy. In each case, we define a new parameter $\chi$ given by the ratios of the two energy densities involved in the transition. Our study of the second epoch is motivated by the need to understand cosmic acceleration. Assuming a dynamic dark energy is the driving force for cosmic acceleration, we formulate a new equation of state for the dark energy given in terms of the ratio $\chi$ and the deceleration parameter, $q$. We have analysed the resultant system of equations, where we vary different parameters and examine the effect on the universe's evolution. For cosmic acceleration to occur, the EoS of the dynamic dark energy must lie in the interval $\omega_{DDE}<-2/3$ at matter-dynamic dark energy equality( equivalently $\omega_{DDE}<-0.47$ today)

gr-qc↗
arXiv2020

The Thermodynamics for Relativistic Multi-Fluid Systems

This article extends the single-fluid relativistic irreversible thermodynamics theory of {\it M{ü}ller}, {\it Israel} and {\it Stewart} (hereafter the {MIS} theory) to a multi-fluid system with inherent species interactions. This is illustrated in a two-fluid toy-model where an effective complex 4-velocity plays the role of a primary dynamical parameter. We find that an observer who resides in the {\it real}-part of this universe will notice that their knowledge of the universe parametrized using {\it real}, rather than {\it imaginary}, quantities are insufficient to fully determine properties such as the total energy density, pressure or entropy, In fact, such an observer will deduce the existence of some negative energy that affects the expansion of their perceived {\it real} universe.

gr-qc↗
arXiv2020

Post inflationary evolution of inflation-produced, large-scale magnetic fields using a generalised cosmological Ohm's law and both standard and modified Maxwell's equations

In most of the literature on evolution of cosmological magnetic fields, it is found that large-scale magnetic fields evolve as $B^{2}\propto a^{-4}$ (adiabatic magnetic decay) where $a$ is the cosmological scale factor and $B$ is the cosmological magnetic field. This rapid decay has been considered as the main obstacle against magnetic fields produced during the inflationary epoch from surviving until today and seeding the observed fields. However, recent reports of first ever detection of intergalactic fields, with strengths around $10^{-6}G$ are a mystery [1-4]. One possible explanation is that large-scale magnetic fields could have been superadiabatically amplified in their evolutionary history. Superadiabatic amplification may mean that there is an actual increase in the strength of the magnetic field or that magnetic decay-rates are slower than the standard adiabatic magnetic decay rate [5] . This can be demonstrated if we use the generalised cosmological Ohm's law and both standard and modified Maxwell field equations; this is the goal of this study.

gr-qc↗
arXiv2020

A transient phase in cosmological evolution : A multi-fluid approximation for a quasi-thermodynamics equilibrium

This article presents the study of a multi-species fluid characterised by a freeze-out or break-away of one or more species. Whereas single-fluid approximation suffices for modelling of the pre {\it freeze-out} period, multi-fluid approximation is required for the post freeze-out period. Embedded in this is a transition period where neither one of the two approximations is singly appropriate. We examine the thermodynamics of this fluid and find that the second law holds before, during and after the freeze-out. Our application to cosmological modelling involving interacting dark-section species indicates that the species' equations of state are modified.

gr-qc↗
arXiv2020

Evolution of Cosmological Total Energy Density and Transient Periods in Cosmology

The evolution of the Universe is traditionally examined by monitoring how its material content evolves as it expands. This model of an isolated system is expressed as the equation of motion of the bulk but segmented into different epochs. In particular, the evolution of the {\it $Friedmann-Lema\hat{i}tre-Robertson - Walker$} (FRLW) Universe is separated into different epochs that are characterised by the dynamics of whichever mass-energy density constituent is dominant at the time. The standard analysis of the evolution of the Universe in a particular epoch often considers the evolution of the dominant energy density only, disregarding all others. Whereas this represents the limiting case, in principle the contributions from others cannot always be ignored particularly in the vicinity of the equality of the various competing mass-energy densities or the transition periods between epochs. We examine the evolution of the total energy density rather than individual energy densities during the different epochs. We find that taking into account the contributions from the various constituents lead to a broader range of possible evolution histories which enriches the standard picture.

gr-qc↗
arXiv2019

Stability analysis of a Boeing 737-800

The Anthena Vortex Lattice (AVL) [1] program describes aerodynamic and flight-dynamic analysis of rigid aircraft of arbitrary configuration and we use it to analyse the stability modes of a Boeing 737-800 under various small perturbations about trimmed equilibrium. We perturb the aircraft's free-stream velocity, its banking angle, its mass (which can be considered in conditions such as fuel dumping) and also analyse how it behaves at different heights (different air densities). We then compute the time it takes the various stability modes to return to equilibrium and show that this time obeys the logistic growth model for the Dutch roll and Short period mode when the velocity is perturbed and when varying the height above sea level of the aircraft.

eess.SY↗
arXiv2018

Multi-fluid Theory and Cosmology: A Convective Variational Approach to Interacting Dark-Sector

This article examines the foundation of the recently developed relativistic variational formalism[1]. Our work is heavily based on [2, 27] which extends this approach to the multi-fluid theory and examines its utility in astrophysics and cosmology. Unlike the extension to the formalism mentioned above, that looks at the general interaction between different types of matter, we use the formalism to examine the interaction involving, ordinary matter, dark matter (DM) and dark energy (DE). We focus on entrainment phenomena involving the dark-sector constituents.

gr-qc↗
arXiv2017

The Weyl Curvature Tensor, Cotton-York Tensor and Gravitational Waves: A covariant consideration

1+3 covariant approach to cosmological perturbation theory often employs the electric part ($E_{ab}$), the magnetic part ($H_{ab}$) of the Weyl tensor or the shear tensor ($σ_{ab}$) in a phenomenological description of gravitational waves. The Cotton-York tensor is rarely mentioned in connection with gravitational waves in this approach. This tensor acts as a source for the magnetic part of the Weyl tensor which should not be neglected in studies of gravitational waves in the 1+3 formalism. The tensor is only mentioned in connection with studies of 'silent model' but even there the connection with gravitational waves is not exhaustively explored. In this study, we demonstrate that the Cotton-York tensor encodes contributions from both electric, magnetic part of the Weyl tensor and in directly from the shear tensor. In our opinion, this makes the Cotton-York tensor arguably the natural choice for linear gravitational waves in the 1+3 covariant formalism. The tensor is cumbersome to work with but that should negate its usefulness. It is conceivable that the tensor would equally be useful in the metric approach, although we have not demonstrated this in the current study. We contend that the use of only one of the Weyl tensor or the shear tensor, although phenomenologically correct, leads to loss of information. Such information is vital particularly when examining the contribution of gravitational waves to the anisotropy of an almost -Friedmann-Lamitre-Robertson-Walker (FLRW) universe. The recourse to this loss is the use Cotton-York tensor.

gr-qc↗
arXiv2017

Toward the analogue of thermally generated electromagnetic fields

Magnetic and vorticity fields evolution equations are known to obey the same equation when effects of dissipation and sources terms are negligible. We investigate the analogy between the two fields for non-vanishing dissipation and sources. In addition to the Reynolds (Re)and Prandtl (Pr_M) numbers, we define a new number (S_M) that is given by the ratio of the diffusive term to the Biermann battery term and which allows for a different classification of magnetised fluid behaviour. Numerical simulations of the two fields are then carried out given a parameter space made of Reynolds, Prandtl and Source numbers. We find it appropriate to present and discuss the findings against Prandtl numbers given that these provide the link between viscous and magnetic diffusion. Our simulations indicate that there exists a range of Prandtl numbers for which the fields remain analogues which raises the important question of how far the analogy goes.

gr-qc↗