arXiv:1312.6559v1 [hep-th] 23 Dec 2013 Cosmology with non-minimally coupled Yang–Mills field Evgeny A. Davydov Bogoliubov Laboratory of Theoretical Physics, JINR, 141980, Dubna, Moscow region, Russia Dmitry V. Gal’tsov Department of Theoretical Physics, Moscow State University, 119899, Moscow, Russia We discuss cosmological model with homogeneous and isotropic Yang-Mills field non- minimally coupled to gravity through an effective mass term. In this model conformal symmetry is violated which leads to possibility of inflationary expansion. Parameters of non-minimal coupling have relatively “natural” values in the regime of sufficiently long ac- celeration stage. PACS numbers: I. INTRODUCTION Vector fields were suggested in cosmology as alternative to scalar fields as inflation and dark energy drivers [1–4]. Apart from being physically appealing as well-understood and common com- ponent of all existing theories,they may be useful, in particular, in generating appropriate curvature perturbations [5–7]. Especially attractive seem to be non-Abelian models, which admit magnetic type field configurations compatible with isotropy and homogeneity of space-time [8–11] and may therefore be used in the standard Friedmann-Robertson-Walker setting without averaging needed in the case of vector singlet to avoid anisotropy. If their dynamics is ruled by the standard Yang-Mills (YM) conformally invariant action, the corresponding equation of state is that of the hot universe [8], but violation of conformal symmetry may lead to different equations of state. In particular, the Born-Infeld lagrangian generates an equation of state which interpolates between the hot regime at low densities and a zero acceleration regime at high density [12–15]. Stronger violation of conformal symmetry in the purely YM sector may produce accelerating expansion of inflationary dark energy type [16] exhibiting typically a finite acceleration period. Various realizations of this scenario were suggested [17]–[23] with different motivation. Cosmological perturbations in the YM cosmology * Electronic address: eugene00@mail.ru Electronic address: galtsov@phys.msu.ru