Speaker
Description
In this talk, I will present recent advancements in mathematical and cosmological frameworks, drawing from my key studies. I will introduce functorial methods in Functors of Actions Theories (FAT), bridging mathematical rigor with cosmological phenomena, by predicting actionions [1,2]. Noticing the need of advanced math, I will introduce the exploration of novel tensor-based approaches from Advancing Tensor Theories (ATT) [3], and Advanced Manifold-Metric Pairs (AMMP) [4], offering new tools for modeling. ATT merges novel advanced indices, with corresponding tensors which are defined using standard calculus operators, and fractional calculus operators. AMMP introduces more abstract manifold metric pairs in which the line elements is constructured through a functional tensor of (U,L)-rank, rather than a (0,2)-rank, which opens a new road to introduce more sophisticated mathematical structure to physics problems. Finally, I will discuss the dynamics of the quintessence in the ϕCDM, simple ϕΛCDM, and a polyΛCDM models, providing insights into scalar field-driven cosmology and its implications for dark energy and modified gravity [5,6,7]. The analytical polyΛCDM model includes scalar-vector-tensor modified gravity theories to a lagrangian, and under appropriate assumption it results to a polynomial depenence in energy density ratios that can be measured by observational data, and distinguish which modified gravity model is more apparent from the background cosmology data. If time permits, I will talk about a novel test of fundamental principles of gravity in extra dimensions given large scale structure surveys with contaminated samples [8]. These works collectively highlight innovative mathematical methods to advance our understanding of the universe’s evolution and structure.
References:
1) Ntelis P. & A. Morris. 2023. Functors of Actions. Foundations of Physics. available at: https://arxiv.org/abs/2010.06707
2) Ntelis P. 2025 CosmoFATs. under review. available at https://www.preprints.org/manuscript/202506.0322/v1
3) Ntelis, P. 2025. Advancing Tensor Theories. Symmetry: Mathematics: Advances in Topology and Algebraic Geometry. Available at: https://www.mdpi.com/2073-8994/17/5/777
4) Ntelis, P. 2025. Advanced Manifold-Metric Pairs. MDPI Mathematics. Available at: https://www.mdpi.com/2227-7390/13/15/2510
5) Ntelis, P. & J. L. Said. 2025. Analytical polyΛCDM dynamics. Physics of the Dark Universe, available at: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5243299
6) Ntelis, P. & J. L. Said. 2025. Exploring ϕCDM Model Dynamics. The European Physical Journal C. arXiv:2502.03486, available at: https://arxiv.org/abs/2502.03486
7) Ntelis, P. & J. L. Said. 2025. Simple ϕΛCDM Dynamics. International Journal of Geometric Methods in Modern Physics. Available at: https://www.researchgate.net/publication/391905442_Simple_phiLambdaCDM_dynamics
8) Ntelis, P. 2022-2026. A (Dτ,Dx)-manifold with N-correlators of Nt-objects. International Journal of Geometric Methods in Modern Physics. arXiv:2209.07472, available at: https://arxiv.org/abs/2209.07472
| Mini Symposia (Invited Talks Only) | Mini Symposia (Invited Talks Only) |
|---|---|
| Plenary (Invited talks only) | Plenary (Invited Talks Only) |