Related papers: Ricci Flow Approach to The Cosmological Constant P…
One of the most enduring and unresolved challenges in modern theoretical and observational cosmology is the fine-tuning and coincidence problems associated with the cosmological constant. Rather than attempting to reconcile these issues…
The dynamics of the expanding universe is analyzed in terms of the quantum geometrodynamical model. It is shown that the equations of quantum theory in the form of the eigenvalues equation similar to the stationary Schr\"{o}dinger equation…
The Planck scale is usually believed to be an unpassable wall. Putting a cutoff there and thinking of it as a quantized spacetime entity shows that. However, this is exactly the cause of many problems in quantum gravity. The cosmological…
The concept of deformation of Riemannian geometry is reviewed, with applications to gravitation and cosmology. Starting with an analysis of the cosmological constant problem, it is shown that space-times are deformable in the sense of local…
In this study, by revisiting the quantum interpretation of the cosmological constant, we introduce its formal representation within standard General Relativity. Examining its behavior in a Friedmann-Robertson-Walker spacetime reveals a…
We examine Friedmann-Lema\^itre-Robertson-Walker cosmology, incorporating quantum gravitational corrections through the functional renormalization group flow of the effective action for gravity. We solve the Einstein equation with quantum…
This paper is a serious attempt at reconciling quantum and classical mechanics through the concept of dynamic space and the acceptance of non-zero Ricci tensor for vacuum. Starting with scalar particles, the paper shows that with those two…
In the first part of this paper we will work out a close and so far not yet noticed correspondence between the swampland approach in quantum gravity and geometric flow equations in general relativity, most notably the Ricci flow. We…
We have critically compared different approaches to the cosmological constant problem, which is at the edge of elementary particle physics and cosmology. This problem is deeply connected with the difficulties formulating a theory of quantum…
The idea is considered that a quantum wormhole in a spacetime foam can be described as a Ricci flow. In this interpretation the Ricci flow is a statistical system and every metric in the Ricci flow is a microscopical state. The probability…
A finite quantum gravity theory is used to resolve the cosmological constant problem. A fundamental quantum gravity scale, \Lambda_G \leq 10^{-3} eV, is introduced above which the quantum corrections to the vacuum energy density coupled to…
We introduce a flow of Riemannian metrics and positive volume forms over compact oriented manifolds whose formal limit is a shrinking Ricci soliton. The case of a fixed volume form has been considered in our previous work. We still call…
We present a systematic approach to embed $n$-dimensional vacuum general relativity in an $(n + 1)$-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimally-coupled to…
We present a monotonic expression for the Ricci flow, valid in all dimensions and without curvature assumptions. It is interpreted as an entropy for a certain canonical ensemble. Several geometric applications are given. In particular, (1)…
In general relativity, the description of spacetime relies on idealised rods and clocks, which identify a reference frame. In any concrete scenario, reference frames are associated to physical systems, which are ultimately quantum in…
We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent…
In this paper a framework is introduced to remove the huge discrepancy between the empirical value of the cosmological constant and the contribution to the cosmological constant predicted from the vacuum energy of quantum fields. An extra…
In the investigation and resolution of the cosmological constant problem the inclusion of the dynamics of quantum gravity can be a crucial step. In this work we suggest that the quantum constraints in a canonical theory of gravity can…
In this paper I continue the investigation in \cite{1,1b} concerning my proposal on the nature of the cosmological constant. In particular, I study both mathematically and physically the quantum Planckian context and I provide, in order to…
In the context of the Relativistic Quantum Geometry formalism, where the cosmological constant is promoted to a dynamical variable by attributing it a geometric interpretation as a result of a flux on the boundary of a manifold and…