English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Many inflating spacetimes are likely to violate the weak energy condition, akey assumption of singularity theorems. Here we offer a simple kinematicalargument, requiring no energy condition, that a cosmological model which isinflating -- or just expanding sufficiently fast -- must be incomplete in nulland timelike past directions. Specifically, we obtain a bound on the integralof the Hubble parameter over a past-directed timelike or null geodesic. Thusinflationary models require physics other than inflation to describe the pastboundary 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

Inflationary Spacetimes Are Incomplete in Past Directions