arXiv:0812.4892v1 [astro-ph] 29 Dec 2008 Title : will be set by the publisher Editors : will be set by the publisher EAS Publications Series, Vol. ?, 2008 QUANTUM VACUUM AND ACCELERATED EXPANSION Boguslaw Broda 1 and Michal Szanecki 1 Abstract. A new approach to extraction of quantum vacuum energy, in the context of the accelerated expansion, is proposed, and it is shown that experimentally realistic orders of values can be derived. The idea has been implemented in the framework of the Friedmann–Lemaˆ ıtre– Robertson–Walker geometry in the language of the effective action in the relativistic formalism of Schwinger’s proper time and Seeley– DeWitt’s heat kernel expansion. 1 Introduction The following three, well-known problems of modern physics and cosmology, accel- erated expansion of the Universe (Riess et al. 1998; Perlmutter et al. 1999), very small but non-vanishing cosmological constant or dark energy (Weinberg 1989), (Carroll 2001; Padmanabhan (2003, 2006)), and theoretically extraordinarily huge quantum vacuum energy density (Zel‘dovich 1967), (Volovik (2005, 2006)) can be treated as mutually related or as independent problems. An old approach to the issue of the cosmological constant Λ utilizes quantum vacuum energy as a solution of this issue, but unfortunately it does not work properly. Namely, it appears that directly calculated, Casimir-like value of quantum vacuum energy is more than one hundred orders greater than expected. Such a huge value of quantum vacuum energy is a serious theoretical problem in itself. Lowering the UV cutoff scale down from the planckian to the supersymmetric one is a symbolic improvement (roughly, it cuts the order by two (Weinberg 1989)). A more radical reduction of the cutoff could cure the situation but it would create new problems. Sometimes, it is claimed that vacuum energy for one or another reason does not influence gravitational field. In this paper, following ideas presented in (Broda et al. 2008), we show in what sense quantum vacuum energy influences gravitational field, and in what 1 Department of Theoretical Physics, University of L´ od´ z Pomorska 149/153, 90–236 L´ od´ z, Poland; e-mail: bobroda@uni.lodz.pl & michalszanecki@wp.pl c EDP Sciences 2008 DOI: (will be inserted later)