Exorcising ghosts in induced gravity

Unitarity of the scale-invariant coupled theory of higher-derivative gravity and matter is investigated. A scalar field coupled with a Dirac fermion is taken as the matter sector. Following the idea of induced gravity the Einstein–Hilbert term is generated via dynamical symmetry breaking of scale invariance. The renormalisation group flows are computed and one-loop RG improved effective potential of scalar is calculated. The scalar field develops a new minimum via the Coleman–Weinberg procedure inducing the Newton constant and masses in the matter sector. The spin-2 problematic ghost and the spin-0 mode of the metric fluctuation get a mass in the broken phase of the theory. The energy dependence of the vacuum expectation value in the RG improved scenario implies a running for the induced parameters. This sets up platform to ask whether it is possible to evade the spin-2 ghost by keeping its mass always above the running energy scale? In broken phase this question is satisfactorily answered for a large domain of coupling parameter space where the ghost is evaded. The spin-0 mode can be made physically realisable or not depending upon the choice of the initial parameters. The induced Newton constant is seen to vanish in the ultraviolet case. By properly choosing parameters it is possible to make the matter fields physically unrealisable.