  In this work we ask how an Unruh-DeWitt (UD) detector with harmonic
oscillator internal degrees of freedom $Q$ measuring an evolving quantum matter
field $\Phi(\bm{x}, t)$ in an expanding universe with scale factor $a(t)$
responds. We investigate the detector's response which contains non-Markovian
information about the quantum field squeezed by the dynamical spacetime. The
challenge is in the memory effects accumulated over the evolutionary history.
We first consider a detector $W$, the `\textsl{Witness}', which co-existed and
evolved with the quantum field from the beginning. We derive a nonMarkovian
quantum Langevin equation for the detector's $Q$ by integrating over the
squeezed quantum field. The solution of this integro-differential equation
would answer our question, in principle, but very challenging, in practice.
Striking a compromise, we then ask, to what extent can a detector $D$
introduced at late times, called the `\textsl{Detective}', decipher past
memories. This situation corresponds to many cosmological experiments today
probing specific stages in the past, such as COBE targeting activities at the
surface of last scattering. Somewhat surprisingly we show that it is possible
to retrieve to some degree certain global physical quantities, such as the
resultant squeezing, particles created, quantum coherence and correlations. The
reason is because the quantum field has all the fine-grained information from
the beginning in how it was driven by the cosmic dynamics $a(t)$. How long the
details of past history can persist in the quantum field depends on the memory
time. The fact that a squeezed field cannot come to complete equilibrium under
constant driving, as in an evolving spacetime, actually helps to retain the
memory. We discuss interesting features and potentials of this
`\textit{archaeological}' perspective toward cosmological issues.
