Abstract:
We consider spatially averaged inhomogeneous universe models and argue that, already in the absence of sources, an effective scalar field arises through foliating and spatially averaging inhomogeneous geometrical curvature invariants of the Einstein vacuum. This scalar field (the `morphon') acts as an inflaton, if we prescribe a potential of some generic form. We show that, for any initially negative average spatial curvature, the morphon is driven through an inflationary phase and leads - on average - to a spatially flat, homogeneous and isotropic universe model, providing initial conditions for pre-heating and, by the same mechanism, a possibly natural self-exit.

Abstract:
In this contribution we summarize two recent applications of a correspondence between backreaction terms in averaged inhomogeneous cosmologies and an effective scalar field (the `morphon'). Backreaction terms that add to the standard sources of Friedmannian kinematical laws and that emerge from geometrical curvature invariants built from inhomogeneities, can be interpreted in terms of a minimally coupled scalar field in the case of a dust matter source. We consider closure conditions of the averaged equations that lead to different evolution scenarii: a) the standard Chaplygin equation of state imposed as an effective relation between kinematical fluctuations and intrinsic curvature of space sections, and b) an inflationary scenario that emerges out of inhomogeneities of the Einstein vacuum, where averaged curvature inhomogeneities model the potential of an effective classical inflaton.

Abstract:
Background Several generic methods have been proposed to estimate transmission parameters during an outbreak, especially the reproduction number. However, as of today, no dedicated software exists that implements these methods and allow comparisons. Results A review of generic methods used to estimate transmissibility parameters during outbreaks was carried out. Most methods used the epidemic curve and the generation time distribution. Two categories of methods were available: those estimating the initial reproduction number, and those estimating a time dependent reproduction number. We implemented five methods as an R library, developed sensitivity analysis tools for each method and provided numerical illustrations of their use. A comparison of the performance of the different methods on simulated datasets is reported. Conclusions This software package allows a standardized and extensible approach to the estimation of the reproduction number and generation interval distribution from epidemic curves.

Abstract:
The standard model of cosmology is based on homogeneous-isotropic solutions of Einstein's equations. These solutions are known to be gravitationally unstable to local inhomogeneous perturbations, commonly described as evolving on a background given by the same solutions. In this picture, the FLRW backgrounds are taken to describe the average over inhomogeneous perturbations for all times. We study in the present article the (in)stability of FLRW dust backgrounds within a class of averaged inhomogeneous cosmologies. We examine the phase portraits of the latter, discuss their fixed points and orbital structure and provide detailed illustrations. We show that FLRW cosmologies are unstable in some relevant cases: averaged models are driven away from them through structure formation and accelerated expansion. We find support for the proposal that the dark components of the FLRW framework may be associated to these instability sectors. Our conclusion is that FLRW cosmologies have to be considered critically as for their role to serve as reliable models for the physical background.

Abstract:
A way to address the conundrum of Quantum Gravity is to illustrate the potentially fundamental interplay between quantum field theory, curved space-times physics and thermodynamics. So far, when studying moving quantum systems in the vacuum, the only known perfectly thermal temperatures are those obtained for constant (or null) accelerations $A$ in constant (or null) Hubble parameters $H$ space-times. In this Letter, restricting ourselves to conformally coupled scalar fields, we present the most comprehensive expression for the temperature undergone by a moving observer in the vacuum, valid for any time-dependent linear accelerations and Hubble parameters: $T=\sqrt{A^2 + H^2 + 2 \dot H\dot t}/{2\pi}$ where $\dot t=\d t/\d\t$ is the motion's Lorentz factor. The inequivalence between a constant $T$ and actual thermality is explained. As a byproduct, all the Friedman universes for which observers at rest feel the vacuum as a thermal bath are listed.

Abstract:
We consider two-level detectors, coupled to a quantum scalar field, moving inside cavities. We highlight some pathological resonant effects due to abrupt boundaries, and decide to describe the cavity by switching smoothly the interaction by a time-dependent gate-like function. Considering uniformly accelerated trajectories, we show that some specific choices of non-adiabatic switching have led to hazardous interpretations about the enhancement of the Unruh effect in cavities. More specifically, we show that the emission/absorption ratio takes arbitrary high values according to the emitted quanta properties and to the transients undergone at the entrance and the exit of the cavity, {\it independently of the acceleration}. An explicit example is provided where we show that inertial and uniformly accelerated world-lines can even lead to the same ``pseudo-temperature''.

Abstract:
We show that without Lorentz invariance, the Unruh effect does not exist. We use modified dispersion relations and describe in turn: the non-thermal nature of the vacuum (defined in the preferred frame) restricted to the Rindler wedge, the loss of the KMS property of the Wigthman function, the transition amplitudes and transition rates of a uniformaly accelerated detector. This situation seems to contrast with the Hawking radiation of acoustic black holes, which under certain assumptions has been shown to be robust to a breaking of Lorentz symmetry. We explain this discrepancy.

Abstract:
We consider two-level detectors coupled to a scalar field and moving on arbitrary trajectories in Minkowski space-time. We first derive a generic expression for the response function using a (novel) regularization procedure based on the Feynmann prescription that is explicitly causal, and we compare it to other expressions used in the literature. We then use this expression to study, analytically and numerically, the time dependence of the response function in various non-stationarity situations. We show that, generically, the response function decreases like a power in the detector's level spacing, $E$, for high $E$. It is only for stationary world-lines that the response function decays faster than any power-law, in keeping with the known exponential behavior for some stationary cases. Under some conditions the (time dependent) response function for a non-stationary world-line is well approximated by the value of the response function for a stationary world-line having the same instantaneous acceleration, torsion, and hyper-torsion. While we cannot offer general conditions for this to apply, we discuss special cases; in particular, the low energy limit for linear space trajectories.

Abstract:
The Davies-Fulling (DF) model describes the scattering of a massless field by a non-inertial mirror in two dimensions. In this paper, we generalize this model in two different ways. First, we consider partially reflecting mirrors. We show that the Bogoliubov coefficients relating inertial modes can be expressed in terms of the frequency dependent reflection factor which is specified in the rest frame of the mirror and the transformation from the inertial modes to the modes at rest with respect to the mirror. In this perspective, the DF model is simply the limiting case when this factor is unity for all frequencies. In the second part, we introduce an alternative model which is based on self-interactions described by an action principle. When the coupling is constant, this model can be solved exactly and gives rise to a partially reflecting mirror. The usefulness of this dynamical model lies in the possibility of switching off the coupling between the mirror and the field. This allows to obtain regularized expressions for the fluxes in situations where they are singular when using the DF model. Two examples are considered. The first concerns the flux induced by the disappearance of the reflection condition, a situation which bears some analogies with the end of the evaporation of a black hole. The second case concerns the flux emitted by a uniformly accelerated mirror.

Abstract:
The Davies-Fulling model describes the scattering of a massless field by a moving mirror in 1+1 dimensions. When the mirror travels under uniform acceleration, one encounters severe problems which are due to the infinite blue shift effects associated with the horizons. On one hand, the Bogoliubov coefficients are ill-defined and the total energy emitted diverges. On the other hand, the instantaneous mean flux vanishes. To obtained well-defined expressions we introduce an alternative model based on an action principle. The usefulness of this model is to allow to switch on and off the interaction at asymptotically large times. By an appropriate choice of the switching function, we obtain analytical expressions for the scattering amplitudes and the fluxes emitted by the mirror. When the coupling is constant, we recover the vanishing flux. However it is now followed by transients which inevitably become singular when the switching off is performed at late time. Our analysis reveals that the scattering amplitudes (and the Bogoliubov coefficients) should be seen as distributions and not as mere functions. Moreover, our regularized amplitudes can be put in a one to one correspondence with the transition amplitudes of an accelerated detector, thereby unifying the physics of uniformly accelerated systems. In a forthcoming article, we shall use our scattering amplitudes to analyze the quantum correlations amongst emitted particles which are also ill-defined in the Davies-Fulling model in the presence of horizons.