Explaining the Big Bang’s temporal placement within a B-series-only account

Ascertain, within a model of time based solely on the B-series ordering from earlier times to later times, why the Big Bang occurred 13.8 billion years earlier than the present rather than one billion years earlier, given the apparent inability of a purely B-series account to answer this question.

Background

In discussing two extremal models for the Big Bang that involve both A-series and B-series features, the author notes a specific explanatory gap in a B-series-only framework: it does not clarify why the Big Bang is located 13.8 billion years earlier than now rather than at some other earlier time.

This motivates the paper’s proposal that approaching the Big Bang involves r → 0 in the defined rate of temporal flow, implying increasingly many A-series steps into the past per second in the B-series; however, the specific explanatory challenge is explicitly flagged as an open question in the B-series-only context.