Time as a Cosmological Phenomenon

TL;DR

The work posits that the macroscopic arrow of time arises from the universe's cosmological structure rather than from microphysical laws, arguing that a global time direction compatible with entropy increase requires a specific geometric/topological framework. It outlines a program built on $ds^2 = -dt^2 + g_{ij}(t,\vec{x}) dx^i dx^j$ (Weyl's postulate), the Past Hypothesis with a Weyl curvature constraint, time-orientability, and chronology to ensure a globally defined arrow of time, and it analyzes entropy's geometric role via the Weyl curvature hypothesis and gravitational entropy. The paper then addresses quantum gravity's problem of time, presenting a semiclassical deparametrization in which the scale factor $a$ acts as an internal clock to recover Schrödinger evolution for matter fields on a classical spacetime background, while noting that a full quantum gravity solution remains unresolved. Overall, it argues that time, change, and memory are emergent properties rooted in the universe's large-scale geometry and topology, and it outlines how this cosmological perspective could extend to other time-dependent phenomena.

Abstract

We show that the arrow of time is intimately related to the geometry and topology of the whole universe, and is therefore best understood as a cosmological phenomenon.

Figures (6)

• Figure : If the world lines of particles (a,b,c,d) do not intersect and do not twist around each other (zero vorticity) then it is possible to find a family of hypersurfaces orthogonal to them (left). This is impossible if the world lines intersect or fail to form a bundle (right), as in this case there is no global family of hypersurfaces that remains orthogonal to all world lines at all times.
• Figure : In a Big Bounce scenario (left) one can impose the regularity condition (\ref{['PHW']}) to ensure that the gravitational entropy is negligible at $t=0$. However, given the spacetime is past-extendible, entropy would then be expected to increase in both directions of time, and neither could be chosen as proceeding from past to future. On the other hand, if spacetime is non-extendible (right), as in the case of a cosmological singularity, there is only one branch of thermodynamic evolution possible, which implicitly determines the "arrow of time", i.e. time's orientation from past (Big Bang) to future.
• Figure : The universe could have sections that look like a Möbius strip, as in the picture, with time going vertically and space horizontally. Going around the strip once would flip the direction of time, with consequent global loss of orientability.
• Figure : Spacetimes with non-zero vorticity, such as Gödel's universe, may contain closed timelike curves (CTCs, shown in red). In these spacetimes, the light cones (in blue) tilt sufficiently to allow world lines to loop back on themselves, making time travel to the past theoretically possible. In Gödel's universe, this behavior arises due to the rigid rotation of spacetime around the central axis depicted. Beyond the radius $r = \log(1 + \sqrt{2})$, there exists a timelike congruence consisting of circular trajectories.
• Figure : The spacetime on the left describes a perfectly homogeneous, flat, matter-dominated FRW universe, while the one on the right a flat, matter-dominated FRW universe with small initial inhomogeneities. Both spacetimes are temporally asymmetric but only the one on the right will display an arrow of time; one that proceeds from the regular Big Bang to the irregular future with a more lumpy matter distribution.