Marcelo J. Reboucas

In general relativity, cosmology and quantum field theory, spacetime is assumed to be an orientable manifold endowed with a Lorentz metric that makes it spatially and temporally orientable. The question as to whether the laws of physics require these orientability assumptions is ultimately of observational or experimental nature, or the answer might come from a fundamental theory of physics. The possibility that spacetime is time non-orientable lacks investigation, and so should not be dismissed straightaway. In this paper, we argue that it is possible to locally access a putative time non-orientability of Minkowski empty spacetime by physical effects involving quantum vacuum electromagnetic fluctuations. We set ourselves to study the influence of time non-orientability on the stochastic motions of a charged particle subject to these electromagnetic fluctuations in Minkowski spacetime equipped with a time non-orientable topology and with its time orientable counterpart. To this end, we introduce and derive analytic expressions for a statistical time orientability indicator. Then we show that it is possible to pinpoint the time non-orientable topology through an inversion pattern displayed by the corresponding orientability indicator, which is absent when the underlying manifold is time orientable.

In general relativity, cosmology and quantum field theory, spacetime is assumed to be an orientable manifold endowed with a Lorentz metric that makes it spatially and temporally orientable. The question as to whether the laws of physics require these orientability assumptions is ultimately of observational or experimental nature, or the answer might come from a fundamental theory of physics. The possibility that spacetime is time non-orientable lacks investigation, and so should not be dismissed straightaway. In this paper, we argue that it is possible to locally access a putative time non-orientability of Minkowski empty spacetime by physical effects involving quantum vacuum electromagnetic fluctuations. We set ourselves to study the influence of time non-orientability on the stochastic motions of a charged particle subject to these electromagnetic fluctuations in Minkowski spacetime equipped with a time non-orientable topology and with its time orientable counterpart. To this end, we introduce and derive analytic expressions for a statistical time orientability indicator. Then we show that it is possible to pinpoint the time non-orientable topology through an inversion pattern displayed by the corresponding orientability indicator, which is absent when the underlying manifold is time orientable.

The statistical properties of the temperature anisotropies and polarization of the of cosmic microwave background (CMB) radiation offer a powerful probe of the physics of the early universe. In recent works a statistical procedure based upon the calculation of the kurtosis and skewness of the data in patches of CMB sky-sphere has been proposed and used to investigate the large-angle deviation from Gaussianity in WMAP maps. Here we briefly address the question as to how this analysis of Gaussianity is modified if the foreground-cleaned Planck maps are considered. We show that although the foreground-cleaned Planck maps present significant deviation from Gaussianity of different degrees when a less severe mask is used, they become consistent with Gaussianity, as detected by our indicators, when masked with the union mask U73.

The statistical properties of the temperature anisotropies and polarization of the of cosmic microwave background (CMB) radiation offer a powerful probe of the physics of the early universe. In recent works a statistical procedure based upon the calculation of the kurtosis and skewness of the data in patches of CMB sky-sphere has been proposed and used to investigate the large-angle deviation from Gaussianity in WMAP maps. Here we briefly address the question as to how this analysis of Gaussianity is modified if the foreground-cleaned Planck maps are considered. We show that although the foreground-cleaned Planck maps present significant deviation from Gaussianity of different degrees when a less severe mask is used, they become consistent with Gaussianity, as detected by our indicators, when masked with the union mask U73.

The immediate observational consequence of a non-trivial spatial topology of the Universe is that an observer could potentially detect multiple images of radiating sources. In particular, a non-trivial topology will generate pairs of correlated circles of temperature fluctuations in the anisotropies maps of the cosmic microwave background (CMB), the so-called circles-in-the-sky. In this way, a detectable non-trivial spatial topology may be seen as an observable attribute, which can be probed through the circles-in-the-sky for all locally homogeneous and isotropic universes with no assumptions on the cosmological dark energy (DE) equation of state (EOS) parameters. We show that the knowledge of the spatial topology through the circles-in-the-sky offers an effective way of reducing the degeneracies in the DE EOS parameters. We concretely illustrate the topological role by assuming, as an exanple, a Poincar\'{e} dodecahedral space topology and reanalyzing the constraints on the parameters of a specific EOS which arise from the supernovae type Ia, baryon acoustic oscillations and the CMB plus the statistical topological contribution.