  (1+1)-dimensional locally de Sitter Friedmann-Robertson-Walker cosmologies
with compact spatial sections allow cosh, sinh and exponential evolution laws,
each with a freely-specifiable spatial circumference parameter, and the value
of this parameter has an invariant geometric meaning for the cosh and sinh
evolution laws. We identify geometrically preferred states for a quantised
massive scalar field on these cosmologies, some singled out by adiabatic
criteria in the distant past, with an ambiguity remaining due to a massive zero
mode, and others induced from the Euclidean vacuum on standard
(1+1)-dimensional de Sitter space by a quotient construction. We show that a
comoving quantum observer, modelled as an Unruh-DeWitt detector, can
distinguish these states from the Euclidean vacuum on standard de Sitter space.
Numerical plots are given in selected parameter regimes. We also evaluate the
field's stress-energy tensor expectation value for those states that are
induced from the Euclidean vacuum by a quotient construction.
