Chapter 12 Interacting Quintessence Model and Accelerated Expansion of the Universe Debasis Sahu and Bibekananda Nayak Abstract In our present work, we study the dynamics of the universe by using an interacting quintessence model, where equation of state parameter of dark energy varies between -1 and 0. First we calculated the dark energy density parameter and using that we have picturised the evolution of the deceleration parameter. From our analysis, we found that present universe is undergoing an accelerated phase of expansion where as the early time expansion was decelerated one. Our result also predicts that the transition from deceleration to acceleration would be occurred at 0.189t 0 where t 0 is the present age of the universe. 12.1 Introduction Along with Friedmann–Robertson–Walker metric which describes a homogeneous and isotropic universe, Einstein’s field equation builds the backbone of Standard Model of Cosmology. Some of current observations [1] show that the present uni- verse is expanding at an accelerated rate where as the Standard Model of Cosmology demands a decelerated expanding universe. For removing this controversy, in the- oretical cosmology, generally two ways have been used. One is by modifying the theory of gravity like F(R) gravity and the other is by introducing an unknown form of energy having negative pressure termed as dark energy. This dark energy is homo- geneous, less dense, permeate of all space, an intrinsic property of space and does not get diluted with the expansion of space. Further recent observational data [2] shows that nearly 68.3% of present universe is filled with this dark energy. Among many models of dark energy, the most general forms of dark energy are vacuum energy, phantom energy [3] and quintessence [4] etc. Though vacuum energy, D. Sahu (B ) · B. Nayak P. G. Department of Applied Physics and Ballistics, Fakir Mohan University, Balasore 756019, Odisha, India e-mail: debasissahu777@gmail.com B. Nayak e-mail: bibekanandafm@gmail.com © Springer Nature Singapore Pte Ltd. 2020 A. Giri and R. Mohanta (eds.), Workshop on Frontiers in High Energy Physics 2019, Springer Proceedings in Physics 248, https://doi.org/10.1007/978-981-15-6292-1_12 93