Boson stars may consist of a new type of light singlet scalar particles with nontrivial self-interactions, and may compose a fraction of the dark matter in the Universe. In this work, we study the dynamics of boson stars with Liouville and logarithmic scalar self-interaction potentials as benchmarks. We perform a numerical analysis as well as a semi-analytic study on how the compactness and the total mass will deviate from that of the usual boson stars formed with a quartic repulsive self-interaction. We apply the recently suggested Swampland conjecture to examine whether boson stars with such benchmark potentials belong to the Landscape of a quantum gravity. Using the mass constraint on the macroscopic compact halo object (MACHO) and the cold dark matter (CDM) isocurvature mode constraint from the cosmic microwave background (CMB), we derive the allowed mass range of scalar particles which compose the boson star. We further analyze applications of the lensing of fast radio bursts (FRBs) and the gravitational wave (GW) detection to probe the presence of such boson stars and constrain the parameter space of their corresponding models. We discuss how the two types of boson star potentials can be discriminated by the FRB and GW measurements.
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