Cosmological Perturbations and Structure Formation via Stochastic Gravity

The traditional theory for cosmological structure formation is based on quantized metric perturbations which operates at the level of quantum field theory in curved spacetime. An improvement is the semiclassical gravity (SCG) theory where the backreaction of the expectation values of the stress energy tensor of matter is included as source for a self-consistent determination of the background spacetime dynamics [1]. But SCG fails when the fluctuations of the quantum stress tensor become large, as could happen in the early universe or late stage of black hole collapse. The proper framework to address issues involving the dynamics of fluctuations in the matter field and in the metric tensor consistently is stochastic gravity [2]. The fluctuations in the matter field is contained in the noise kernel which is the expectation value of the stress energy bi-tensor acting as source for the Einstein-Langevin equation, from which one can obtain the induced metric fluctuations in the background spacetime. It has been shown that stochastic two-point metric correlations agree with quantum two-point metric correlations to order 1/N in a large N expansion, thus simplifying quantum correlation function calculations. We introduce this theory and show that [3] it gives result at linear order equivalent to the usual method of quantizing linear metric and inflaton perturbations (e.g., Mukhanov et al 1992) but can also treat quadratic order perturbations needed in R^2 type theories such as the trace anomaly driven inflation (e.g., Starobinsky 1980), something the traditional method of quantizing linear perturbations may find difficult. Stochastic gravity is currently being explored for application to problems related to metric fluctuations in Minkowsky space, evaporating black holes [4], non-Gaussianity in cosmological structures and spacetime foams in the Planckian primordial universe.

[1] e.g., E. Calzetta and B. L. Hu, "CLOSED TIME-PATH FUNCTIONAL FORMALISM IN CURVED SPACETIME: Application to Cosmological Backreaction Problems" Phys. Rev. D35, 495 (1987).
[2] B. L. Hu and Enric Verdaguer, Stochastic gravity: Theory and Applications, in Living Reviews in Relativity 7 (2004) 3. [gr-qc/0307032] lrr-2004-3 [update in arXiv:0802.0658]
[3] Albert Roura and Enric Verdaguer, Cosmological perturbations from stochastic gravity Phys. Rev. D 78, 064010 (2008)
[4] B. L. Hu and Albert Roura, Metric fluctuations of an evaporating black hole from back-reaction of stress tensor fluctuations, Phys. Rev. D 76 (2007) 124018