Path Integrals in Quadratic Gravity

Abstract

Using the invariance of Quadratic Gravity in FLRW metric under the group of diffeomorphisms of the time coordinate, we rewrite the action $A$ of the theory in terms of the invariant dynamical variable $g(\tau ).$ We propose to consider the path integrals $\int F(g)\exp \left\{-A\right\}dg$ as the integrals over the functional measure $\mu (g)=\exp \left\{-A_2\right\}dg,$ where $A_2$ is the part of the action $A$ quadratic in $R.$ The rest part of the action stands in the exponent in the integrand as the "interaction" term. We prove the measure $\mu (g)$ to be equivalent to the Wiener measure, and, as an example, calculate the averaged scale factor in the first nontrivial perturbative order.

arXiv comment19 pages

References in corpus (37)

• Modified Gravity and Cosmology
• Agravity
• Black Holes in Higher-Derivative Gravity
• Approaches to Quantum Cosmology
• Lorentzian Quantum Cosmology
• Aspects of Quadratic Gravity
• Quadratic Gravity
• Unitarity, stability and loops of unstable ghosts
• Benign vs malicious ghosts in higher-derivative theories
• Conformal Symmetry and Central Charges in 4 Dimensions
• No Rescue for the No Boundary Proposal
• The Real No-Boundary Wave Function in Lorentzian Quantum Cosmology
• Complex actions in two-dimensional topology change
• Ghost-free higher-derivative theory
• Metastability in Quadratic Gravity
• A QCD analogy for quantum gravity
• Do we have unitary and (super)renormalizable Quantum Gravity below Planck scale?
• Tunneling wave function of the universe
• Physical States of the Quantum Conformal Factor
• Gauge Assisted Quadratic Gravity: A Framework for UV Complete Quantum Gravity
• On the ghost-induced instability on de Sitter background
• Classical and Quantum Dynamics of Higher-Derivative Systems
• Supersymmetry vs ghosts
• Scaling behavior of quantum four-geometries
• Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion
• Protected $SL(2,\mathbb{R})$ Symmetry in Quantum Cosmology
• The Exact Solution of the Schwarzian Theory
• Supersymmetric field theory with benign ghosts
• Quantum Diffeomorphisms and Conformal Symmetry
• Renormalization group and logarithmic corrections to scaling relations in conformal sector of 4D gravity
• On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization
• No-boundary Wave Function, Wheeler-DeWitt Equation and Path Integral Analysis of the Bouncing `Quantum' Cosmology
• Correlation functions in the Schwarzian theory
• Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric
• Schwarzian functional integrals calculus
• Paths with singularities in functional integrals of quantum field theory
• Black Hole Solutions in $R^2$ Gravity