Inflationary spacetimes are not past-complete

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating -- or just expanding sufficiently fast -- must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.Comment: We improve the basic argument to apply to a wider class of spacetimes, use a better title and add a discussion of cyclic models. 4 pages, 1 figure, RevTe

Online Cycle Detection for Models with Mode-Dependent Input and Output Dependencies

In the fields of co-simulation and component-based modelling, designers import models as building blocks to create a composite model that provides more complex functionalities. Modelling tools perform instantaneous cycle detection (ICD) on the composite models having feedback loops to reject the models if the loops are mathematically unsound and to improve simulation performance. In this case, the analysis relies heavily on the availability of dependency information from the imported models. However, the cycle detection problem becomes harder when the model's input to output dependencies are mode-dependent, i.e. changes for certain events generated internally or externally as inputs. The number of possible modes created by composing such models increases significantly and unknown factors such as environmental inputs make the offline (statical) ICD a difficult task. In this paper, an online ICD method is introduced to address this issue for the models used in cyber-physical systems. The method utilises an oracle as a central source of information that can answer whether the individual models can make mode transition without creating instantaneous cycles. The oracle utilises three types of data-structures created offline that are adaptively chosen during online (runtime) depending on the frequency as well as the number of models that make mode transitions. During the analysis, the models used online are stalled from running, resulting in the discrepancy with the physical system. The objective is to detect an absence of the instantaneous cycle while minimising the stall time of the model simulation that is induced from the analysis. The benchmark results show that our method is an adequate alternative to the offline analysis methods and significantly reduces the analysis time.Comment: \c{opyright} 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0

Eternal inflation and the initial singularity

It is shown that a physically reasonable spacetime that is eternally inflating to the future must possess an initial singularity.Comment: 11 pages, Tufts University cosmology preprin

Violations of the Weak Energy Condition in Inflating Spacetimes

We argue that many future-eternal inflating spacetimes are likely to violate the weak energy condition. It is possible that such spacetimes may not enforce any of the known averaged conditions either. If this is indeed the case, it may open the door to constructing non-singular, past-eternal inflating cosmologies. Simple non-singular models are, however, unsatisfactory, and it is not clear if satisfactory models can be built that solve the problem of the initial singularity.Comment: 18 pages, 1 figure (which emerges automatically if you use dvips

Open and Closed Universes, Initial Singularities and Inflation

The existence of initial singularities in expanding universes is proved without assuming the timelike convergence condition. The assumptions made in the proof are ones likely to hold both in open universes and in many closed ones. (It is further argued that at least some of the expanding closed universes that do not obey a key assumption of the theorem will have initial singularities on other grounds.) The result is significant for two reasons: (a)~previous closed-universe singularity theorems have assumed the timelike convergence condition, and (b)~the timelike convergence condition is known to be violated in inflationary spacetimes. An immediate consequence of this theorem is that a recent result on initial singularities in open, future-eternal, inflating spacetimes may now be extended to include many closed universes. Also, as a fringe benefit, the time-reverse of the theorem may be applied to gravitational collapse.Comment: 27 pages, Plain TeX (figures are embedded in the file itself and they will emerge if it is processed according to the instructions at the top of the file