Gravitational Waves and Perspectives for Quantum Gravity

Abstract

Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such ghosts violate stability and hence the theory becomes inconsistent. Several approaches to solve this contradiction were invented and we are proposing one more, which looks simpler than those what were considered before. We explore the dynamics of the gravitational waves on the background of classical solutions and give certain arguments that massive ghosts produce instability only when they are present as physical particles. At least on the cosmological background one can observe that if the initial frequency of the metric perturbations is much smaller than the mass of the ghost, no instabilities are present.

21 pages, 4 figures. LaTeX with WS style. Invited Brief Review published in Modern Physics Letters A

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• On the gravitational seesaw in higher-derivative gravity
• On the ghost-induced instability on de Sitter background
• Higher-order modified Starobinsky inflation
• Functional renormalization group approach and gauge dependence in gravity theories
• Weak-field limit and regular solutions in polynomial higher-derivative gravities
• Classical and tree-level approaches to gravitational deflection in higher-derivative gravity
• Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric
• Recent Progress in Fighting Ghosts in Quantum Gravity
• Probing alternative cosmologies through the inverse distance ladder
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• Interparticle potential energy for D-dimensional electromagnetic models from the corresponding scalar ones
• Removing Ostrogradski's ghost from cosmological perturbations in $f(R,R_{\mu \nu }^2,C_{\mu \nu \rho \sigma }^2)$ gravity