Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: BGV theorem, Geodesic deviation, and Quantum fluctuations   I point out a simple expression for the "Hubble" parameter $\mathscr{H}$,
defined by Borde, Guth and Vilenkin (BGV) in their proof of past incompleteness
of inflationary spacetimes. I show that the parameter $\mathscr{H}$ which an
observer $O$ with four-velocity $\bf v$ will associate with a congruence $\bf
u$ is equal to the fractional rate of change of the magnitude $\xi$ of the
Jacobi field associated with $\bf u$, measured along the points of intersection
of $O$ with $\bf u$, with its direction determined by $\bf v$. I then analyse
the time dependence of $\mathscr{H}$ and $\xi$ using the geodesic deviation
equation, computing these exactly for some simple spacetimes, and
perturbatively for spacetimes close to maximally symmetric ones. The
perturbative solutions are used to characterise the rms fluctuations in these
quantities arising due to possible fluctuations in the curvature tensor.

32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
2
The categories of this paper are: math
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas