| Summary: | This review considers the theoretical approaches to the understanding of dark energy, which comprises approximately 68% of the energy of our Universe and explains the acceleration in its expansion. Following a discussion of the main approach based on Einstein’s equations with the cosmological term, the explanations of dark energy using the concept of some kind of scalar field are elucidated. These include the concept of a quintessence and modifications of the general theory of relativity by means of the scalar–tensor gravity exploiting the chameleon, symmetron and environment-dependent dilaton fields and corresponding particles. After mentioning several laboratory experiments allowing us to constrain the hypothetical scalar fields modeling the dark energy, special attention is devoted to the possibility of constraining the parameters of chameleon, symmetron and environment-dependent dilaton fields from measuring the Casimir force. It is concluded that the parameters of each of these fields can be significantly strengthened in near future by using the next-generation setups in preparation suitable for measuring the Casimir force at larger separations.
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