  The Gao-Wald theorem says that de Sitter spacetime reacts to a positive
energy perturbation by getting "taller." How does this change in the presence
of timelike boundaries? We study this question in two-dimensional de Sitter JT
gravity coupled to conformal matter. The effect of the boundaries has its roots
in quantum corrections to the vacuum energy of the CFT due to Casimir-like
effects. We consider two different kinds of timelike boundaries, either at
locations where the coordinate $\varphi$ is constant or at locations where the
dilaton is constant. For each kind we compute the vacuum expectation value of
the matter CFT stress tensor. The stress tensor violates the null energy
condition in the first case and saturates it in the second case, with each case
exhibiting a negative energy density in the vacuum state. We then compute the
semiclassical backreaction of this energy density and show how it can make the
spacetime "fatter" or "taller" or a combination of both, depending on the
regime. The spacetime getting fatter corresponds to an increase in the value of
the dilaton at the horizon and hence also in the static patch horizon area in
the higher-dimensional solution. We comment on the implications of our results
for the quantum theories living on the timelike boundaries.
