An investigation into the dark energy associated with cosmological initial conditions through observations on CMB and the large-scale structure of the universe

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Dark energy is generally considered as a repulsive homogeneous background driving the accelerated expansion in the standard ΛCDM cosmology following the cosmological principle that assumes homogeneity and isotropy on the largest scales. In addition to tensions and anomalies in observations challenging the ΛCDM model, increasing observations indicate the possible breakdown of the cosmological principle.Dark energy is a mystery to be illuminated in the future decades, whose nature may reveal the fate of our Universe, and the secrets of new physics beyond the standard models of cosmology and particle physics. It will be ground-breaking if dark energy inhomogeneities are found in future observations.This research focuses on a general formulation of possible dark energy inhomogeneities as a modification to the standard perturbation theory as a forecasting effort, a step forward from the long-lasting consideration of dynamical dark energy models. Sourced by some ultralight scalar field, dark energy carries isocurvature-type superhorizon fluctuations. These fluctuations translate into inhomogeneous dark energy clustering and consequently anisotropies in cosmological observables within the horizon. Using constraints on these fluctuations from the initial conditions of the cosmic microwave background, the research formulated and discussed the impacts of dark energy clustering on observables such as dark energy equation of state, luminosity distance and matter spectrum of the large-scale structure, which are worth testing by future surveys like Subaru PFS, DESI, LSST, etc.