Dynamical Response of an Unruh-DeWitt Detector in a Quantum Field over the History of the Universe

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 detectors 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 detectors $Q$ 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.