Abstract
Inflationary perturbations are considered in a renormalizable but non-unitary theory of gravity with the additional Weyl term. We obtained that ghost degrees of freedom do not spoil the inflation and the scalar perturbation amplitude at the linear level even in a case of the ghost with mass smaller than Hubble parameter at inflation. The ghost impact to the observables is also estimated to be negligible for the range of masses allowed by the experiment. The non-linear level of the theory and its possible application are also discussed.
Highlights
General relativity, providing a good explanation for all known experimental results, fails all attempts to quantize it consistently
The Einstein-Hilbert action leads to the non-renormalizable theory which means the loss of its predictive force at Planck energies
Despite the low energy physics is described by the effective field theory, there are examples showing that some processes below the Planck scale may be sensitive to the UV completion of the theory [1, 2]
Summary
General relativity, providing a good explanation for all known experimental results, fails all attempts to quantize it consistently. We discuss the limit in which the Weyl ghost becomes interacting very weakly and hereafter we impose the negative norm prescription for the ghost states. In order to check the validity of the effective description in terms of non-unitary theory we calculate the evolution of the scalar perturbations in a theory with light Weyl ghost starting from vacuum initial conditions (this case is not yet studied in literature).
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