Functors of Actions

Pierros, Ntelis; Morris, A. B.

doi:10.1007/s10701-022-00628-z

Cited by 5 publications

(8 citation statements)

References 52 publications

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“…Having written a gravity action in terms of a probabilistic spacetime, can we reconcile quantum gravity by quantising the probabilistic gravity [53] ? ; How, can we reconcile other recently developed models of modified gravity, such as the ones listed in Clifton et al [32], Koyama [33], Ezquiaga and Zumalacárregui [34], Ntelis and Morris [35] ? ; How probabilistic manifold-metric pairs change our description for black hole/string transition [54] ?…”

Section: Discussion: An Interesting Outlookmentioning

confidence: 77%

“…The concepts, introduced in this study, enhance, combine, complement and extend the concepts introduced to previous studies such as the perturbed expanding universe description by C.-P. Ma & E. Bertschinger (1995) [48], the properties of statistical metrics by Karl Menger [37], Bianchi Classification (1897) [36], manifold metric pair description Hawking and Ellis [51], generalised manifold metric pairs [44], functors of actions [35].…”

Section: Discussion: An Interesting Outlookmentioning

confidence: 92%

“…4.5, or any MG action can be generalised further. In particular Ntelis and Morris [35] has shown that this is possible by considering the functors of actions which are simply modeled by an integral on all possible actions, using…”

Section: Mathematical and Physical Preliminariesmentioning

confidence: 99%

“…This theory assumes a four-dimensional pseudo-Riemannian manifold with a local metric background which satisfies Lorenzt invariance. It has been shown in a gravitology frame study that most of the current modifications of gravity (MG) [32][33][34] can be generalised in a mathematical frame study [35], namely functors of actions (FA), which means that all subsequently studied actions are a subset of this general set of actions, S FA . In other words, there is a general action that can be reduced to all studied actions with appropriate modeling.…”

Section: Introductionmentioning

confidence: 99%

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A probabilistic, and expanding Universe

Pierros

2023

Preprint

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Context: In this study, we embrace information by presenting important concepts of abstract information field theory, probabilities, and probabilistic dimensions, in the view of functors of actions theories and other abstract theories. Methodology: The methods used are the presentation of a collection of manifold-metric pairs, probabilistic notions, simple topology, and Einstein-Boltzman equations and the combination of this collection. Results: These combinations result to different flavours of an expanding sub-manifold and metric systems describing simpler dynamics of space around massive objects. Furthermore, we derive the equation of motion of a simplified gravity model in a probabilistic expanding Universe. We further introduce the notions of probabilistic actions and concepts of novel categories of abstract field-particles, such as the probablons and informatons. Conclusion: We conclude that the derived equations are the first steps towards a concrete description of a probabilistic gravity, and a probabilistic expanding Universe descriptions.

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Section: Discussion: An Interesting Outlookmentioning

confidence: 77%

Section: Discussion: An Interesting Outlookmentioning

confidence: 92%

Section: Mathematical and Physical Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A probabilistic, and expanding Universe

Pierros

2023

Preprint

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“…Note that category theory, has many contemporarily and recent applications, such as in physics, in Feynman diagrams [3], cosmology and functors of actions [4], statistics and computer science [5], and even epidemiology [6]. Therefore, it is highly importance to develop and establish further the concepts of category theory.…”

Section: Data Availability Statement 3 Introductionmentioning

confidence: 99%

Advancing categories with functors of functors

Pierros

2023

Preprint

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In this document, we review the basics of category theory and functors calculus, and we implement some novel concepts. In particular, we review the concepts of category, functors, and natural transformations. Furthermore we introduce the novel concept of func- tors of functors. We illustrate these concepts with diagrams to ameliorate the expression of these ideas. We conclude that these concepts open new avenues and are advancing category.

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Probing cosmic homogeneity in the Local Universe

Dias,

Avila,

Bernui

2023

Monthly Notices of the Royal Astronomical Society

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We investigate the transition scale to homogeneity, RH, using as cosmic tracer the spectroscopic sample of blue galaxies from the Sloan Digital Sky Survey (SDSS). Considering the spatial distribution of the galaxy sample, we compute the two point correlation function ξ(r), the scaled counts in spheres $\mathcal {N}(\lt r)$, and the fractal dimension $\mathcal {D}_2(r)$ to quantify the homogeneity scale in the Local Universe (0.04 < z < 0.20). The sample in analysis is compared with random and mock catalogues with the same geometry, and the same number of synthetic cosmic objects as the data set, to calculate the covariance matrix for the errors determination. The criteria adopted for the transition-to-homogeneity follows the literature, it is attained when $\mathcal {D}_2(r)$ reaches the 1 per cent level of the limit value 3 (i.e. where it reaches 2.97) as the scale increases. We obtain RH = 70.33 ± 10.74 Mpc h−1, at the effective redshift zeff = 0.128, for a sample containing $150\, 302$ SDSS blue galaxies with 0.04 < z < 0.20. Additionally, we perform robustness tests by analysing the homogeneity scale in sub-volumes of the original one, obtaining coherent results; we also check for a possible artefact in our procedure examining a homogeneous synthetic data set as a pseudo-data, verifying that such systematic is absent. Because our analyses concentrate in data at low redshifts, z < 0.20, we find interesting to use cosmography to calculate the radial comoving distances; therefore in this subject our analyses do not use fiducial cosmological model. For completeness, we evaluate the difference of the comoving distances estimation using cosmography and fiducial cosmology.

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Functors of Actions

Cited by 5 publications

References 52 publications

A probabilistic, and expanding Universe

A probabilistic, and expanding Universe

Advancing categories with functors of functors

Probing cosmic homogeneity in the Local Universe

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