Theinclusion of nonminimal term is necessary for the renormalizability of an interacting the-ory which includes scalars in curved background without Lorentz and/or CPT-violatingterms (see, e.g., for the introduction). Such considerations can indicate the existence of new physical phenomenaor, at least, improve our understanding of the limits of validity of the current one. Regardless of wherever these violations mightcome from, or if exposed scenarios may or may not occur, the experimental/observationalsearching of remaining small deviations from Lorentz and CPT symmetries in nowadaysattainable scales are of crucial importance, representing at the moment a very active areaof physics. As an example we can cite quantum eﬀects in stringtheory and loop quantum gravity, geometrical eﬀects as noncommutativity, tor-sion and nonmetricity and so on. Such viola-tions could emerge in a number of diﬀerent fashions, most of them related to a new physicsat the Planck scale M P ≃ GeV. It turns out that if we allowthe violating ﬁelds to transform, the classical conformal invariance of mass-less scalar ﬁelds can be maintained in the ξ = 1 / In the last years there was an intensive investigation of theoretical and experimentalaspects in theories where the Lorentz and/or CPT symmetries are violated. The conformal theory limit is also analyzed. In the most complicated case of complexscalar ﬁeld nonminimally interacting with gravity, the solution for the diver-gences is obtained in the ﬁrst order in the weak Lorentz violating parameter.The necessary form of the vacuum counterterms indicate the most importantstructures of Lorentz/CPT violations in the pure gravitational sector of the-ory. For the minimal case with real scalar ﬁeld, the counterterms areevaluated in a nonperturbative form in the CPT-even parameter through aredeﬁnition of space-time metric. We analyzetwo separate cases: minimal coupled scalar ﬁeld with gravity and nonmini-mal one. The one-loop divergences for the scalar ﬁeld theory with Lorentzand/or CPT breaking terms are obtained in curved space-time. Tib´erio de Paula Netto a (a) Departamento de F´ısica, ICE, Universidade Federal de Juiz de ForaJuiz de Fora, 36036-330, MG, Brazil. N ov One-loop renormalization of Lorentz/CPT violating scalar ﬁeldtheory in curved space-time Such gravitational effective action is important for cosmological applications and can be used for searching of Lorentz violation in primordial universe in the cosmological perturbations, especially gravitational waves.Īa r X i v. As a result, conformal anomaly and the anomaly-induced effective action are evaluated in the presence of extra Lorentz- and/or CPT-violating parameters. At quantum level the conformal symmetry is violated by trace anomaly. It turns out that if we allow the violating fields to transform, the classical conformal invariance of massless scalar fields can be maintained in theĬase. The necessary form of the vacuum counterterms indicate the most important structures of Lorentz/CPT violations in the pure gravitational sector of theory. In the most complicated case of complex scalar field nonminimally interacting with gravity, the solution for the divergences is obtained in the first order in the weak Lorentz violating parameter. For the minimal case with real scalar field, the counterterms are evaluated in a nonperturbative form in the CPT-even parameter through a redefinition of space-time metric. We analyze two separate cases: minimal coupled scalar field with gravity and nonminimal one. The one-loop divergences for the scalar field theory with Lorentz and/or CPT breaking terms are obtained in curved space-time.

Divergence in curved space