Multidimensional Physics - Quantum Gravity - Early Cosmology

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The study of general cosmological behaviors near the Big-Bang is motivated by some indications that the isotropic and homogeneous stage of the Universe is reached only relatively late in its history; we summarize below some of these circumstances:

- I) The Universe is not in thermal equilibrium at pre-inflationary temperatures; in fact, in this regime, the mean-free-path is super-horizon sized and the microphysics is no longer efficient in maintaining the thermal equilibrium. Since different causal regions evolve out of equilibrium, their dynamics becomes unpredictable and absence of large scales correlation prevents homogeneity from being a global symmetry.

- II) When viewed backward in time, the Robertson-Walker background results to be unstable with respect to tensor perturbations which grow like the cosmic scale factor inverse. Furthermore our investigation on dissipative cosmologies has shown that, in presence of relevant bulk viscosity, such a backward instability is extended to scalar perturbations, i.e. density contrasts. Since the history of the Universe had to be characterized by a suitable spectrum of scalar and tensor perturbations, then, the time reversibility of the Einstein equations, ensures that the very early cosmology had to be an inhomogeneous one (unless to restrict the Universe to a zero-measure set of Cauchy data).

- III) The quantum Universe, characterizing the Planck era, can “fluctuate” in a correlated picture at most on the causal scale and therefore global symmetries can not be preserved. On the other hand, topology fluctuations have to affect the quantum dynamics and to address homogeneity and isotropy constraint makes no sense in quantum gravity, where a generic gravitational field is always involved. As confirmed also by our investigations in chaotic as well as quantum cosmology, the real two degrees of freedom of the Universe are its anisotropy parameters.

- IV) Inflation offers a convincing scenario to connect a generic inhomogeneous early dynamics with the phenomenology of the actual Universe. If the scalar field vacuum energy dominates the early dynamics, before the Mixmaster evolution ends, then the anisotropy of the Universe exponentially decays as the slow-rolling phase develops. In this picture, a generic chaotic Universe is mapped by inflation onto a smother one which is homogeneous and isotropic on a given scale.

Our investigations in the early cosmology deal with different topics whose aim is to provide a contribution in the line of thinking outlined by the above four points. Of particular interest are to be regarded, the proof of the chaos covariance for the generic cosmological solution and to have outlined the possibility for a pre-inflationary origin of the perturbation spectrum. In this respect, an ambitious plan of research concerns the reformulation of the quantum dynamics of a generic universe in terms of Ashtekar-like variables, in order to understand if the Loop Quantum Cosmology framework gets light on the singularity properties and on the physical horizon.

Main publications:

- A.A. Kirillov and G. Montani, Quasi-Isotropization of the Inhomogeneous Mixmaster Universe Induced by an Inflationary Process, Phys. Rev. D, 66, 064010 (2002) [gr-qc/0209054] [pdf].

- G. Montani and R. Benini, Frame-independence of the Inhomogeneous Mixmaster Chaos via Misner-Chitré-like variables, Phys. Rev. D, 70, 103527 (2004) [gr-qc/0411044] [pdf].

- R. Benini, A.A. Kirillov and G. Montani, Oscillatory regime in the Multidimensional Homogeneous Cosmological Models Induced by a Vector Field, Class. Quant. Grav., 22, 1483 (2005) [gr-qc/0505027] [pdf].

- N. Carlevaro and G. Montani, Bulk Viscosity Effects on the Early Universe Stability, Mod. Phys. Lett. A, 20, 1729 (2005) [gr-qc/0506044] [pdf].

- N. Carlevaro and G. Montani, On the Gravitational Collapse of a Gas Cloud in Presence of Bulk Viscosity, Class. Quant. Grav., 22, 4715 (2005) [gr-qc/0510087] [pdf].

- G. Imponente and G. Montani, Inhomogeneous de Sitter Solution with Scalar Field and Perturbations Spectrum, Mod. Phys. Lett. A, 19, 1281 (2004) [gr-qc/0404031] [pdf].