Temperature encoding rates of two-level probes in de Sitter spacetime

We investigate the temperature encoding process of two-level probes in de Sitter spacetime within the framework of open quantum systems. From a quantum-metrological perspective, we quantify the temperature encoding rate, which characterizes the precision of estimating a temperature parameter with a fixed total probe time. The maximal encoding rate is obtained by optimizing the initial state, evolution time, and measurement basis of each probe. For a static probe separated by a finite distance from a freely falling observer, both the intrinsic Gibbons--Hawking temperature and the position-dependent Unruh temperature are encoded in the probe state. We find that the encoding rate of the effective temperature is equal to the sum of the encoding rates of the intrinsic temperature and the Unruh temperature associated with the probe's inherent acceleration. Interestingly, when the intrinsic temperature is sufficiently small, the encoding rate of the intrinsic temperature initially increases with the Unruh temperature, reaches a maximum, and then decreases to zero. Thus, a nonzero inherent acceleration does not necessarily suppress the encoding of the intrinsic temperature. Instead, there exists an optimal inherent acceleration at which its encoding rate is maximized. Furthermore, we investigate the encoding rate of the Unruh temperature and the minimum total probe time required to estimate it with sufficient precision as functions of the separation distance. We find that the required total probe time and the corresponding number of probes remain experimentally feasible even when the probes are located relatively far from the cosmological horizon, with a radial position as large as 0.1 times the horizon radius.