Related papers: Something about Inter-universal Teichmuller Theory
This report provides my mathematical findings regarding the Mochizuki-Scholze-Stix controversy surrounding Mochizuki's Inter-Universal Teichm\"uller Theory.
We analyze cosmology assuming unitary quantum mechanics, using a tripartite partition into system, observer and environment degrees of freedom. This generalizes the second law of thermodynamics to "The system's entropy can't decrease unless…
In this dissertation, we introduce a general way of modeling inflation in a framework that is independent of the exact nature of the inflationary potential. Because of the choice of our initial conditions and the continuity of the scale…
We consider modifications to the Friedmann equation motivated by recent proposals along these lines pursuing an explanation to the observed late time acceleration. Here we show those modifications can be framed within a theory with…
Homogeneous isotropic cosmological models with two torsion functions filled with scalar fields and usual gravitating matter are built and investigated in the framework of the Poincar\'e gauge theory of gravity. It is shown that by certain…
In the hunt for WIMPish dark matter and testing our new theory, we extend the results obtained for the Kepler problem in NQG I and NQG II to the Euler two-centre problem and to other classical Hamiltonian systems with planar periodic…
This thesis deals with the averaging problem in cosmology, which has gained considerable interest in recent years, and is concerned with correction terms (after averaging inhomogeneities) that appear in the Einstein equations when working…
This thesis focuses on two research areas: non-relativistic field theories and complexity. In the first part we review the general classification of the trace anomaly for 2+1 dimensional field theories coupled to a Newton-Cartan background…
The Hamiltonian structure of General Relativity (GR), for both metric and tetrad gravity in a definite continuous family of space-times, is fully exploited in order to show that: i) the "Hole Argument" can be bypassed by means of a specific…
This paper deals with consequences of the existence of Arithmetic Teichmuller spaces established in arXiv:2106.11452 and arXiv:2210.11635. Theorem~9.2.1 provides a proof of a local version of Mochizuki's Corollary~3.12. Local means for a…
We discuss in the framework of black hole thermodynamics some aspects relative to the third law in the case of black holes of the Kerr-Newman family. In the light of the standard proof of the equivalence between the unattainability of the…
A generalization of the Hartogs theorem is proved for a class of Tubes structures. We assume that the intervening commutative Lie algebra admits at least a number of globally solvable generators greater or equal to the structure…
The precision cosmological model describing the origin and expansion history of the universe, with observed structure seeded at the inflationary cosmic horizon, demands completion in the ultraviolet and in the infrared. The dynamics of the…
The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a…
(Abridged) Fundamental tensions between observations and dark-matter based cosmological models have emerged. This updated review has two purposes: to explore new tensions that have arisen in recent years, compounding the unresolved tensions…
We consider gravitational collapse of a fluid sphere with torsion generated by spin, which forms a black hole. We use the Tolman metric and the Einstein$-$Cartan field equations with a relativistic spin fluid as a source. We show that…
Although the current galaxy models yield calculations consistent with much of the data, many irregularities exist, exceptions have been found to the current models, the $\Lambda$CDM model apparently fails on galaxy scales, dark matter…
The early universe according to the big bang and the grand unified theories is discussed. The shortcomings of big bang are summarized together with their resolution by inflationary cosmology. Inflation, the subsequent oscillation and decay…
We construct new classes of modified theories in which the matter sector couples with the Einstein tensor, namely we consider direct couplings of the latter to the energy-momentum tensor, and to the derivatives of its trace. We extract the…
Within the Grassmannian $U(2N) / U(N) \times U(N)$ non-linear $\sigma $ model representation of localization one can study the low energy dynamics of both the free and interacting electron gas. We study the cross-over between these two…