Mounting observational data confirm that about 73% of the energy density consists of dark energy which is responsible for the current accelerated expansion of the Universe. We present observational evidences and dark energy projects. We then review various theoretical ideas that have been proposed to explain the origin of dark energy; they contain the cosmological constant, modified matter models, modified gravity models and the inhomogeneous model. The cosmological constant suffers from two major problems: one regarding fine-tuning and the other regarding coincidence. To solve them there arose modified matter models such as quintessence, k-essence, coupled dark energy and unified dark energy. We compare those models by presenting attractive aspects, new rising problems and possible solutions. Furthermore, we review modified gravity models that lead to late-time accelerated expansion without invoking a new form of dark energy; they contain f(R) gravity and the Dvali–Gabadadze–Porrati (DGP) model. We also discuss observational constraints on those models and on future modified gravity theories. Finally we review the inhomogeneous Lemaître–Tolman–Bondi (LTB) model that drops an assumption of the spatial homogeneity of the Universe. We also present basics of cosmology and scalar field theory, which are useful especially for students and novices to understand dark energy models.

Galaxy clusters contain a diffuse stellar component outside the cluster’s galaxies, which is observed as faint intracluster light (ICL). Using Gemini/GMOS-N deep imaging and multi-object spectroscopy of a massive fossil cluster at a redshift of z = 0.47, RX J105453.3+552102 (J1054), we improve the observational constraints on the formation mechanism of the ICL. We extract the ICL surface brightness and colour profiles out to 155 kpc from the brightest cluster galaxy (BCG) with a detection limit of 28.7 mag/arcsec2 (1σ, 4.8″ × 4.8″; i–band). The colour of the diffuse light is similar to that of the BCG and central bright galaxies out to ∼ 70 kpc, becoming slightly bluer toward the outside. We find that the ICL distribution shows better agreement with the spatial distribution of member galaxies than with the BCG-dominated cluster luminosity distribution. We report the ICL fraction of J1054 as $15.07 \pm 4.57 \%$ in the range of 60 ∼ 155 kpc from the BCG, which appears to be higher than the ICL fraction-redshift trend in previous studies. Our findings suggest that intracluster stars seems not to be explained by one dominant production mechanism. However, a significant fraction of the ICL of J1054 may have been generated from the outskirts of infalling/satellite galaxies more recently rather than by the BCG at the early stage of the cluster.

In a galaxy cluster, the relative spatial distributions of dark matter, member galaxies, gas, and intracluster light (ICL) may connote their mutual interactions over the cluster’s evolution. However, it is a challenging problem to provide a quantitative measure for matching the shapes between two multidimensional scalar distributions. We present a novel methodology, named the weighted overlap coefficient (WOC), to quantify the similarity of two-dimensional spatial distributions. We compare the WOC with a standard method known as the modified Hausdorff distance (MHD) method. We find that our method is robust, and performs well even with the existence of multiple substructures. We apply our methodology to search for a visible component whose spatial distribution resembles that of dark matter. If such a component could be found to trace the dark-matter distribution with high fidelity for more relaxed galaxy clusters, then the similarity of the distributions could also be used as a dynamical stage estimator of the cluster. We apply the method to six galaxy clusters at different dynamical stages, simulated within a GRT simulation, which is an N-body simulation using the galaxy replacement technique. Among the various components (stellar particles, galaxies, ICL), the ICL+brightest cluster galaxy (BCG) component most faithfully traced the dark-matter distribution. Among the sample galaxy clusters, the relaxed clusters show stronger similarity in the spatial distribution of the dark matter and ICL+BCG than the dynamically young clusters, while the results of the MHD method show a weaker trend with the dynamical stages.