Conformal Anomaly and Large-Scale Gravitational Coupling

Abstract

We present a model in which the breakdown of conformal symmetry of a quantum stress-tensor due to the trace anomaly is related to a cosmological effect in a gravitational model. This is done by characterizing the traceless part of the quantum stress-tensor in terms of the stress-tensor of a conformal invariant classical scalar field. We introduce a conformal frame in which the anomalous trace is identified with a cosmological constant. In this conformal frame we establish the Einstein field equations by connecting the quantum stress-tensor with the large-scale distribution of matter in the universe. In the absence of a full theory of quantum gravity, one of the theoretical frameworks in which we may improve our understanding of quantum processes in a gravitational field is a semiclassical approximation. In this framework the matter is described by quantum field theory while the gravitational field itself is regarded as a classical object. The gravitational coupling of a quantum field is then investigated through the study of the quantum stresstensor, i.e., the expectation value of the stress-tensor of the quantum field taken in some physical state. However, since the quantum stress-tensor contains singularities, some renormalization prescriptions [1] are used to obtain a meaningful expression. One of the most remarkable consequences of these prescriptions is the so-called conformal anomaly. This means that the trace of the quantum stress-tensor of a conformal invariant field obtains a nonzero expression while the trace of the classical stress-tensor vanishes identically. The appearance of a nonvanishing trace may be regarded as the breakdown of conformal symmetry. Since the conformal invariance of a theory reflects