Reconstruction of aether scalar tensor theory for variouscosmological scenarios* * Supported by the National Natural Science Foundation of China (11975072, 11875102, 11835009), National SKA Program of China (2022SKA0110200, 2022SKA0110203), Shaanxi Provincial Education Department (21JK0556), and Shaanxi Provincial Department of Science and Technology (2023-JC-QN-0077)

In this paper, we present several explicit reconstructions for the aether scalar tensor (AeST) theory derived from the background of the Friedmann-Lemaître-Robertson-Walker cosmological evolution. It is shown that the Einstein-Hilbert Lagrangian with a positive cosmological constant is the only Lagrangian capable of accurately replicating the exact expansion history of the Λ cold dark matter (ΛCDM) universe filled solely with dust-like matter. However, the ΛCDM-era can be produced within the framework of the AeST theory for some other fluids, including a perfect fluid with , multifluids, and nonisentropic perfect fluids. Moreover, we demonstrate that the ΛCDM-era can be replicated with no real matter field for the AeST theory. The cosmic evolution resulting from both the power-law and de-Sitter solutions can also be obtained.