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We examine relativistic diffusion through the frame and observer bundles associated with a Lorentzian manifold (M, g). Our focus is on spacetimes with a non-trivial isometry group, and we detail the conditions required to find symmetric solutions of the relativistic diffusion equation. Additionally, we analyze the conservation laws associated with the presence of Killing vector fields on (M, g) and their implications for the expressions of the geodesic spray and the vertical Laplacian on both the frame and the observer bundles. Finally, we present several relevant examples of symmetric spacetimes., QC 20240715

The question about the relation between spacetime structure and the symmetries of laws has received renewed attention in a recent discussion about the status of Minkowski spacetime in Special Relativity. In that context we find two extreme positions (either spacetime explains symmetries of laws or vice-versa) and a general assumption about the debate being mainly about explanation. The aim of this paper is twofold: first, to argue that the ontological dimension of the debate cannot be ignored; second, to claim that taking ontology into account involves considering a third perspective on the relation between spacetime and symmetries of laws; one in which both terms would be somehow derived from common assumptions on the formulation of a given physical theory., La pregunta sobre la relación entre las simetrías espacio-temporales y las simetrías de las leyes ha recibido atención renovada en la reciente discusión sobre el estatus de la métrica de Minkowsi en la Teoría de la Relatividad Especial. En ese contexto, encontramos dos posiciones extremas (o bien las simetrías espaciotemporales explican las simetrías de las leyes o viceversa) y el supuesto general de que el debate tiene que ver primariamente con la cuestión de la prioridad explicativa. El objetivo de este artículo es doble: primero, argumentar que la dimensión ontológica del debate no puede ser ignorada; segundo, defender que atender a esta dimensión implica considerar una tercera perspectiva sobre la relación entre espaciotiempo y simetrías, en la cual ambos términos se derivarían de los presupuestos implicados en la formulación de cierta teoría física.

The question about the relation between spacetime structure and the symmetries of laws has received renewed attention in a recent discussion about the status of Minkowski spacetime in Special Relativity. In that context we find two extreme positions (either spacetime explains symmetries of laws or vice-versa) and a general assumption about the debate being mainly about explanation. The aim of this paper is twofold: first, to argue that the ontological dimension of the debate cannot be ignored; second, to claim that taking ontology into account involves considering a third perspective on the relation between spacetime and symmetries of laws; one in which both terms would be somehow derived from common assumptions on the formulation of a given physical theory., La pregunta sobre la relación entre las simetrías espacio-temporales y las simetrías de las leyes ha recibido atención renovada en la reciente discusión sobre el estatus de la métrica de Minkowsi en la Teoría de la Relatividad Especial. En ese contexto, encontramos dos posiciones extremas (o bien las simetrías espaciotemporales explican las simetrías de las leyes o viceversa) y el supuesto general de que el debate tiene que ver primariamente con la cuestión de la prioridad explicativa. El objetivo de este artículo es doble: primero, argumentar que la dimensión ontológica del debate no puede ser ignorada; segundo, defender que atender a esta dimensión implica considerar una tercera perspectiva sobre la relación entre espaciotiempo y simetrías, en la cual ambos términos se derivarían de los presupuestos implicados en la formulación de cierta teoría física.

We review recent theoretical progress and observational constraints on multifractional spacetimes, geometries that change with the probed scale. On the theoretical side, the basic structure of the Standard Model and of the gravitational action is discussed. On the experimental side, we recall the bounds on the scales of the geometry coming from particle physics, astrophysics and the cosmic microwave background.

We present a two-field model that generalizes Natural Inflation, in which the inflaton is the pseudo-Goldstone boson of an approximate symmetry that is spontaneously broken, and the radial mode is dynamical. Within this model, which we designate as ``Generalized Natural Inflation'', we analyze how the dynamics fundamentally depends on the mass of the radial mode and determine the size of the non-Gaussianities arising from such a scenario. We also motivate ongoing research within the coset construction formalism, that aims to clarify how the spontaneous symmetry breaking pattern of spacetime, gauge, and internal symmetries may allow us to get a deeper understanding, and an actual algebraic classification in the spirit of the so-called ``zoology of condensed matter'', of different possible ``cosmic states'', some of which may be quite relevant for model-independent statements about different phases in the evolution of our universe. The outcome of these investigations will be reported elsewhere.