Einstein attempted to construct a static universe model which exists eternally without contraction and expansion. He introduced a cosmological constant term in his cosmological equation, which gives repulsive force, in order to compensate the contraction due to gravity. Though the cosmological constant term is withdrawn by him immediately after the discovery of the dynamical expansion of the universe by Hubble, it is however thoroughly revived in modern cosmology on the ground of cosmological observations such as cosmic microwave background anisotropy measurements, large scale structure surveys, and distant supernova type Ia. In fact, the cosmological constant is directly tied to vacuum energy density. They have been used almost synonymously in modern cosmology since they differ from each other by only a constant times. The inflation at the early universe is often assumed to be triggered by enormous vacuum energy density of a scalar field. The deep inconsistency that is about 10123 times between theoretically estimated value of the cosmological constant from particle physics and observational limit is the so-called famous cosmological constant problem. Indeed, this problem became one of the major challenges in modern theoretical physics. It may be hard to make particle physics models, that provide more realistic physical background for cosmology, without clear understanding why the cosmological constant is so small today. The gigantic gap between observational data and theoretical predictions of the vacuum energy density has made cosmologists to think of another possibility for the actual candidate of dark energy. To the best of our scientific knowledge, about 73% of the energy of the universe consists of dark energy whereas dark matter and visible matter are about 23% and 4%, respectively. Dark energy is therefore the most dominant component in the energy budget of the universe. At present, it is widely accepted that the mysterious dark energy with negative pressure is responsible for the current cosmic acceleration. Even if inflationary universe model provides plausible solutions for the most cosmological puzzles, it is not easy to identify the origin and nature of dark energy on the basis of inflationary universe model. To settle the cosmological constant problem, various attempts have been made through the suggestion of alternative thoughts and ideas. Some of them are models known as phantom, quintom, quintessence, K-essence, tachyon, quantum informational energy, vacuum fluctuation energy, and holographic chaplygin gas. Nevertheless, the vacuum energy is still a potential candidate for the dark energy. This review book introduces several excellent ideas for the settlement of pending problem relevant to dark energy. Though it may not be likely that all of the theories and ideas presented here is suitable for and applicable to our universe even if there is no error in developing the mathematical procedure, most of them would be a good guideline for cosmologists, especially for the beginners of cosmology, who have interest in dark energy. I wish to thank all contributors who have made every effort to prepare quite a decent article in their particular theme.
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