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