**UM Math Graduate Student Seminar**

Eric Ling

* University of Miami *

**will present**

**Before the Big Bang?**

Friday, April 1, 2016, 5:00pm

Ungar Building Room 402

**Abstract: **

The Friedman-Robertson- Walker (FRW) spacetimes are the standard models of cosmology which accurately describe the universe as a whole. However, they make the striking prediction that the universe began a finite amount of time ago at the big bang. Mathematically, this means that one cannot embed the FRW spacetimes as a proper subset of another spacetime, (M,g), so long as the the metric regularity class of g is at least C^2. Therefore a natural question to ask is if one can extend an FRW spacetime properly into another spacetime, (M,g), with g satisfying a lower regularity class, say C^0? In this talk I will explain the origin of the FRW spacetimes and why they are good models for describing the universe. Then I will show how they predict the big bang and why extensions are impossible if g is at least C^2. Finally, I will show that if one considers 2-dimensional FRW spacetimes (i.e. one time dimension and one space dimension), then a C^0 extension is possible. The question remains open for higher dimensional FRW spacetimes.

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