Abstract
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.
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