Related papers: The Cosmological Time Function
All differences between the role of space and time in nature are explained by proposing the principles in which none of the spacetime coordinates has an {\it a priori} special role. Spacetime is treated as a non-dynamical manifold, with a…
Classical mechanics, relativity, electrodynamics and quantum mechanics are often depicted as separate realms of physics, each with its own formalism and notion. This remains unsatisfactory with respect to the unity of nature and to the…
In this work we scrutinize the deterministic nature of globally hyperbolic space-times from the point of view of an observer. We show that a space-time point $q \in M$ that lies to the future of an observer at $p \in M$, receives signals…
We consider general relativity with cosmological constant minimally coupled to the electromagnetic field and assume that the four-dimensional space-time manifold is a warped product of two surfaces with Lorentzian and Euclidean signature…
We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when…
A new vision of the beginning and expansion of our universe has produced a solution to the vacuum energy problem (also known as "cosmological constant problem"). A new dynamic of cellular spaces and a discrete time has space being produced…
Granular space-time posits that everything can be expressed as a function of space-time and matter. And this includes the quantum wave function {\Psi} . To give a geometric interpretation of {\Psi} , we first need to examine time. The fact…
We use the effective field theory of dark energy to explore the space of modified gravity models which are capable of driving the present cosmic acceleration. We identify five universal functions of cosmic time that are enough to describe a…
The discovery that the expansion of the universe is accelerating in time is a major discovery which still awaits adequate explanation. It is generally agreed that this implies a cosmic repulsion as a result of the existence of a…
Despite the ultraviolet problems with canonical quantum gravity, as an effective field theory its infrared phenomena should enjoy fully quantum mechanical unitary time evolution. Currently this is not possible, the impediment being what is…
We introduce conformal transformations in the synthetic setting of metric spaces and Lorentzian (pre-)length spaces. Our main focus lies on the Lorentzian case, where, motivated by the need to extend classical notions to spaces of low…
The cosmological constant problem can be understood as the failure of the decoupling principle behind effective field theory, so that some quantities in the low-energy theory are extremely sensitive to the high-energy properties. While this…
We show differentiability of a class of Geroch's volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz…
In this paper we address the problem of the arrow of time from a cosmological point of view, rejecting the traditional entropic approach that defines the future direction of time as the direction of the entropy increase: from our…
In this manuscript we initiate a systematic examination of the physical basis for the time concept in cosmology. We discuss and defend the idea that the physical basis of the time concept is necessarily related to physical processes which…
This relativistic, time-travel spacetime is everywhere metrically flat, excepting a conical singularity. Observers following timelike geodesics can eventually encounter their past selves, aging in the opposite time sense. The spacetime is…
The essay is devoted to the problem of time in the context of quantum cosmology, which acquires a philosophical level to date. At an example of the minisuperspace model, we show that this problem is illusive in the sense that it does not…
In this paper we propose that cosmological time is a quantum observable that does not commute with other quantum operators essential for the definition of cosmological states, notably the cosmological constant. This is inspired by…
This work discusses the apriori possible asymptotic behavior to the future, for (vacuum) space-times which are geodesically complete to the future and which admit a foliation by compact constant mean curvature Cauchy surfaces.
Let $(M,\mathsf{d},\mathfrak{m},\ll,\leq,\tau)$ be a causally closed, $\mathscr{K}$-globally hyperbolic, regular measured Lorentzian geodesic space satisfying the weak timelike curvature-dimension condition $\smash{\mathrm{wTCD}_p^e(K,N)}$…