  Expanding edge experiments are promising to open new physics windows of
quantum Hall systems. In a static edge, the edge excitation, which is described
by free fields decoupled with the bulk dynamics, is gapless, and the dynamics
preserve conformal symmetry. When the edge expands, such properties need not be
preserved. We formulate a quantum field theory in 1+1 dimensional curved
spacetimes to analyze the edge dynamics. We propose methods to address the
following questions using edge waveforms from the expanding region: Does the
conformal symmetry survive? Is the nonlinear interaction of the edge
excitations induced by edge expansion? Do the edge excitations interact with
the bulk excitations? We additionally show that the expanding edges can be
regarded as expanding universe simulators of two-dimensional dilaton-gravity
models, including the Jackiw-Teitelboim gravity model. As an application, we
point out that our theoretical setup might simulate emission of analog Hawking
radiation with the Gibbons-Hawking temperature from the future de Sitter
horizon formed in the expanding edge region.
