Related papers: Expectation values of minimum-length Ricci scalar
The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements ("COM microscope") it is shown that the spacetimes of Quantum…
The minimal-length paradigm, a possible implication of quantum gravity at low energies, is commonly understood as a phenomenological modification of Heisenberg's uncertainty relation. We show that this modification is equivalent to a…
We attempt to find new symmetries in the space-time structure, leading to a modified gravitation at large length scales, which provides the foundations of a quantum gravity at very low energies. This search begins by considering a unified…
We construct a Lorentzian length space with an orthogonal splitting on a product $I\times X$ of an interval and a metric space, and use this framework to consider the relationship between metric and causal geometry, as well as synthetic…
In recent work of Chan-Huang-Lee, it is shown that if a manifold enjoys uniform bounds on (a) the negative part of the scalar curvature, (b) the local entropy, and (c) volume ratios up to a fixed scale, then there exists a Ricci flow for…
Inspired by the work of Wheeler among others, we have studied the problem of quantum measurements of space-time distances by applying the general principles of quantum mechanics as well as those of general relativity. Contrary to the…
We study scaling symmetry in a class of non-minimally coupled scalar field in a background of Friedmann-Robertson-Walker (FRW) spacetime. We use a non-minimally coupling $R L^{(\varphi)}$. We find the corresponding conserved charge of that…
Typical existence result on Ricci-flat metrics is in manifolds of finite geometry, that is, on $F=\bar F-D$ where $\bar F$ is a compact K\"ahler manifold and $D$ is a smooth divisor. We view this existence problem from a different…
It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2} that the hypothesis of existence of a minimal observer-independent (Planck) length scale is hard to reconcile with special relativity. As a remedy he postulated to…
The class of minimal difference partitions MDP($q$) (with gap $q$) is defined by the condition that successive parts in an integer partition differ from one another by at least $q\ge 0$. In a recent series of papers by A. Comtet and…
It is generally believed that any quantum theory of gravity should have a generic feature --- a quantum of length. We provide a physical ansatz to obtain an effective non-local metric tensor starting from the standard metric tensor such…
We give six arguments that the Planck scale should be viewed as a fundamental minimum or boundary for the classical concept of spacetime, beyond which quantum effects cannot be neglected and the basic nature of spacetime must be…
In this article we introduce and characterize a pseudo generalized Ricci-recurrent spacetimes. At first, we produce an example to justify the existence of such a spacetime. Then, it is provided that a pseudo generalized Ricci-recurrent…
In this paper, we define a reduced distance function based at a point at the singular time $T<\infty$ of a Ricci flow. We also show the monotonicity of the corresponding reduced volume based at time T, with equality iff the Ricci flow is a…
We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity in vacuum regions.…
Recently, a proposal has been made to figure out the expected discrete nature of spacetime at the smallest scales in terms of atoms of spacetime, capturing their effects through a scalar $\rho$, related to their density, function of the…
Theories of emergent gravity have established a deep connection between entropy and the geometry of spacetime by looking at the latter through a thermodynamic lens. In this framework, the macroscopic properties of gravity arise in a…
First principles do imply a non-zero minimal distance between events in spacetime, but no positive lower bound to the precision of the measurement of a single coordinate.
The existence of a minimum length in quantum gravity is investigated by computing the in-in expectation value of the proper distance in the Schwinger-Keldysh formalism. No minimum geometrical length is found for arbitrary gravitational…
The paper aims to introduce a new symmetry principle in the space-time geometry through the elimination of the classical idea of rest and by including a universal minimum limit of speed in the subatomic world. Such a limit, unattainable by…