MG14 - Talk detail

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Perturbation theory applied to Einstein's gravitation can give satisfactory results to many problems in general relativity and quantum field theory. Perturbation theory allows to find approximate solutions that slightly deviate from an exact solution. Einstein's equation is linearized so that we establish a linear theory for general relativity. By quantizing gravitational perturbations, we obtain a linear theory for a tensorial field of spin 2: the graviton. Due to its relevance to the inflationary cosmology, the study of phenomena in de Sitter spacetime has increased. Quantum gravitational perturbations in de Sitter spacetime can have an impact in the evolution of an inflationary universe, which seems to be the case of our own Universe according to recent observations. The properties of the graviton two-point function are especially important within this context. Due to the gauge invariance of the linearized theory, divergences in the graviton two-point function can be non physical. Particularly, infrared divergences in the graviton two-point function, if they are physical, may act as mechanisms to break the de Sitter symmetry, thus leading to the failing of perturbative approach in which the background is non-dynamical. In this talk, we present the gravitational perturbations in de Sitter spacetime. Using a gauge-invariant formalism for gravitational perturbations, we compute the graviton two-point function in the static patch of de Sitter spacetime. We analyze its properties, including its behavior in the infrared limit. The static patch of de Sitter spacetime represents the region accessible to an inertial observer in de Sitter spacetime. In the Bunch-Davies like vacuum state, which represents a thermal bath with temperature $H/2 \pi$, $H$ being the Hubble constant, the two-point function we have found is finite in the infrared limit. The two-point function in the static patch has the additional property of time-translation invariance.

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