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The Big Bang Cosmology stands on the observations that the Universe has been expanding, as Hubble first discovered from the observations of the redshifts of the faraway galaxies. The expansion of the universe means that if you go back in time, the universe was denser, and eventually reaches to an extremely high density and temperature. The success of the Big Bang Nucleosynthesis tells us that the universe was indeed so hot that nuclear fusion could happen. While successful, the Big Bang Cosmology requires the Universe at its beginning to be extremely homogeneous. The Big Bang Cosmology itself cannot explain why the initial condition was so finely tuned. Cosmic inflation was invented to naturally prepare such a homogeneous Universe before the Big Bang. Moreover, while inflation prepares a very homogeneous Universe, it is not completely homogeneous; though tiny, there is a certain amount of density fluctuation, which later evolves, by the gravitational attraction, into the large-scale structure observed in the distribution of the galaxies. Amusingly, according to the inflation scenario, this initial tiny density fluctuation has its origin in quantum vacuum fluctuation. Inflation is supposed to have happened at such high-energy scales where elementary particle physics is relevant. Elementary particle physics is described by Quantum Field Theory (QFT). While inflation naturally explains the initial condition of the Big Bang Cosmology, it has its own fine-tuning problem: The required tuning of model parameters is very fine, in the QFT standards. Moreover, there has been speculation that quantum gravity, though we do not currently have a full understanding of it, may make inflation even harder to take place. I will discuss these challenges in constructing a natural inflation model, possible ways forward, and associated predictions for future cosmological observations.