De Sitter symmetries and inflationary scalar-vector models

Field theory in de Sitter space is related to flat-spacetime theory via dimensional reduction. de Sitter space can be embedded in Minkowski space of one higher dimension as a hyperboloid of one sheet. This paper examines the field theory imposed on de Sitter space by a free, massless, real scalar field in the embedding space. This corresponds to a collection of massive de Sitter-space scalars, of all masses above a positive lower bound: Half of the field normal modes in hyperspherical Rindler coordinates specialize to such fields on an embedded de Sitter space, while the other half vanish there. Dimensional reduction simply eliminates those noncontributing modes. The quantized field theory in hyperspherical Rindler space, hence, in de Sitter space, is treated here using both canonical operator expansions and the functional Schr\"odinger formalism. Transformations between field operators and state wave functionals in the Rindler--de Sitter theory and those in the Minkowski-space formulation are calculated explicitly. The Minkowski vacuum state corresponds to the Chernikov-Tagirov or Euclidean vacuum of the de Sitter-space fields. The Rindler--de Sitter `` particle'' content of this state, for various simple mode choices, can be time dependent, even nonmonotonic; it can also exhibit ``thermal'' features recalling those of rectangular Rindler-space theory or of Euclidean field theory in de Sitter space.

We propose that the state represented by the Nariai black hole inside de Sitter space is the ground state of the de Sitter gravity, while the pure de Sitter space is the maximal energy state. With this point of view, we investigate thermodynamics of de Sitter space, we find that if there is a dual field theory, this theory can not be a CFT in a fixed dimension. Near the Nariai limit, we conjecture that the dual theory is effectively an 1+1 CFT living on the radial segment connecting the cosmic horizon and the black hole horizon. If we go beyond the de Sitter limit, the "imaginary" high temperature phase can be described by a CFT with one dimension lower than the spacetime dimension. Below the de Sitter limit, we are approaching a phase similar to the Hagedorn phase in 2+1 dimensions, the latter is also a maximal energy phase if we hold the volume fixed.

We present in this paper a covariant quantization of the “massive” vector field on de Sitter (dS) space based on analyticity in the complexified pseudo-Riemanian manifold. The correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter space–time is essential in our approach. We introduce the Wightman two-point function for the case of generalized free vector fields on de Sitter space. This function satisfies the conditions of (a) positiveness, (b) locality, (c) covariance, (d) normal analyticity, (e) transversality and (f) divergencelessness. The Hilbert space structure and the unsmeared field operators Kα(x) are also defined. This work is in the direct continuation of previous ones concerning the scalar and spinor cases.

We propose a novel prescription for computing the boundary stress tensor and charges of asymptotically de Sitter (dS) spacetimes from data at early or late time infinity. If there is a holographic dual to dS spaces, defined analogously to the AdS/conformal field theory correspondence, our methods compute the (Euclidean) stress tensor of the dual. We compute the masses of Schwarzschild--de Sitter black holes in four and five dimensions, and the masses and angular momenta of Kerr--de Sitter spaces in three dimensions. All these spaces are less massive than de Sitter space, a fact which we use to qualitatively and quantitatively relate de Sitter entropy to the degeneracy of possible dual field theories. Our results in general dimensions lead to a conjecture: Any asymptotically de Sitter spacetime with mass greater than de Sitter space has a cosmological singularity. Finally, if a dual to de Sitter space exists, the trace of our stress tensor computes the renormalized group (RG) equation of the dual field theory. Cosmological time evolution corresponds to RG evolution in the dual. The RG evolution of the c function is then related to changes in accessible degrees of freedom in an expanding universe.

<div class="section abstract"><div class="htmlview paragraph">High-frequency whine noise in electric vehicles (EVs) is a significant issue that impacts customer perception and alters their overall view of the vehicle. This undesirable acoustic environment arises from the interaction between motor polar resonance and the resonance of the engine mount rubber. To address this challenge, the proposal introduces an innovative approach to predicting and tuning the frequency response by precisely adjusting the shape of rubber flaps, specifically their length and width.</div><div class="htmlview paragraph">The approach includes the cumulation of two solutions: a precise adjustment of rubber flap dimensions and the integration of ML. The ML model is trained on historical data, derived from a mixture of physical testing conducted over the years and CAE simulations, to predict the effects of different flap dimensions on frequency response, providing a data-driven basis for optimization. This predictive capability is further enhanced by a Python program that automates the optimization of flap dimensions using a linear combination formula. The automation ensures that the desired frequency response is achieved efficiently and systematically.</div><div class="htmlview paragraph">By combining the insights from ML with the linear combination formula, the method not only addresses the dynamic peak during frequency sweeps but also mitigates resonance issues through the principles of dual dynamic absorber theory. This comprehensive approach improves the acoustic environment within the vehicle cabin and serves as a preventative measure against potential resonance problems, ultimately contributing to a higher-quality user experience.</div></div>

<div class="htmlview paragraph">A numerical methodology using 3D computational fluid dynamics (CFD) was developed to simulate the water flows on vehicles in order to check the specifications under rain (visibility of door mirror by the driver, sealing…), or to evaluate washing efficiency (washing headlight, washing windshield …). The CFD method is constituted by a three step procedure.</div> <div class="htmlview paragraph">In the first step, the aerodynamic field around the vehicle is calculated with Powerflow software in a large domain. It uses a Lattice Boltzmann approach to solve airflow. The existing process of Powerflow computation developed by aerodynamic and aeroacoustic teams of Renault SAS was adapted to refine results in high gradients of velocity zones.</div> <div class="htmlview paragraph">In the second step, the field of air velocity vectors calculated with Powerflow is mapped towards a small domain where the water flow will be solved.</div> <div class="htmlview paragraph">In the last step, the calculation carried out by N3S CFD code with a fluid film model gives the water distribution on different parts of the vehicle by taking into account the aerodynamic results. Several evolutions of the N3S code were performed by Renault to modelize the thin liquid film. It includes wall film formation by impinging rain and wall film separation by free surface instabilities. It considers also film transport such as governed by mass, momentum and energy equations with wall and air flow interactions.</div> <div class="htmlview paragraph">Results were compared with the tests carried out on the Modus car in a wind tunnel reproducing the main characteristics of moving traffic under the rain. The water flow on the panel is well reproduced by the computations for four different A-pillar shapes.</div> <div class="htmlview paragraph">This methodology is now applied by Renault to optimize design of next vehicles several months before the first physical prototype. In future works, we will use this tool to predict the rain evacuation of other parts of the vehicle, as for example the water-box under the hood.</div>

<div class="section abstract"><div class="htmlview paragraph">Shared autonomous vehicles systems (SAVS) are regarded as a promising mode of carsharing service with the potential for realization in the near future. However, the uncertainty in user demand complicates the system optimization decisions for SAVS, potentially interfering with the achievement of desired performance or objectives, and may even render decisions derived from deterministic solutions infeasible. Therefore, considering the uncertainty in demand, this study proposes a two-stage robust optimization approach to jointly optimize the fleet sizing and relocation strategies in a one-way SAVS. We use the budget polyhedral uncertainty set to describe the volatility, uncertainty, and correlation characteristics of user demand, and construct a two-stage robust optimization model to identify a compromise between the level of robustness and the economic viability of the solution. In the first stage, tactical decisions are made to determine autonomous vehicle (AV) fleet sizing and the initial vehicle distribution. In the second stage, operational decisions are made under scenarios of fluctuating user demand to optimize vehicle relocation strategies. To enhance the efficiency of model resolution, the original two-stage robust optimization model is decomposed into separable subproblems, which are transformed using duality theory and linearization. An effective solution is achieved through a precise algorithm utilizing column-and-constraint generation (C&CG). Numerical experiments are conducted on a small-scale network to validate the effectiveness of the model and algorithm. Furthermore, adjustments to the demand fluctuation scenarios are made to assess the impact of uncertain budget levels Γ on the total revenue of SAVS. This research provides AV sharing service operators with an optimal relocation scheduling strategy that balances robustness and economic efficiency.</div></div>

Over the last twenty years, the de Sitter and anti-de Sitter spaces of various dimensions have become the focus of all theoretical high-energy physics. This is primarily due to the correspondence between supergravity in the five-dimensional anti-de Sitter space and supersymmetric field theory in four dimensions. The anti-de Sitter space turned out to be the most suitable manifold, on which nonperturbative results were obtained in the theory of superstrings and on which the theory of higher spin fields is naturally built. In turn, de Sitter's space is closely connected with the problems of modern cosmology, being essentially the theoretical basis of inflationary cosmology. On the other hand, de Sitter space-time and quantum field theory on this manifold are the subject of intensive study, mainly in connection with the task of constructing a quantum theory of gravitation in curved spaces. The central issue in the study of fields in the de Sitter space is a detailed analysis of a homogeneous group to this space — the de Sitter group. It is necessary to classify and describe homogeneous spaces of the group SO (1,4) up to subgroups SO (1,3) (Lorentz group), SO (4) (maximal compact subgroup of the group SO (1,4)), and SU (2). This problem is considered by determining all homogeneous spaces of the form M = SO (1,4) / H, where H is a stationary subgroup. The elements of the group are represented as the product of one-parameter matrices, which allows you to clearly see the relevance with the Euler angles in the classical three-dimensional case.

We consider the AdS/dS CFT correspondence and study the nature of the thermal bath of the de Sitter field theory using holography. Unlike the temperature of a thermal field theory in flat spacetime, the temperature of a superconformal field theory on de Sitter space is an integral part of the theory and leaves intact the conformal symmetry and supersymmetry. In the dual AdS side, there is no black hole. Instead we have cosmological expansion of the de Sitter factor. We consider a number of different observables, such as the entanglement entropy, two point correlation function, Wilson loops corresponding to static and spinning mesons in the field theory, and study their thermal properties using holography. The former two quantities have trivial temperature dependence due to conformal symmetry. We compute the energy of the quark anti-quark bound state for a static meson, as well as the energy and the angular momentum for a spinning meson. We find that there is a maximum distance, as well as a maximum spin for the latter case, beyond which the bound state become unstable. The temperature behavior of the physical quantities in these meson systems are similar to that of the usual thermal field theory with holographic black hole dual. With these examples, we show clearly how the field theory observables get their thermal properties from the bulk despite the absence of a black hole, with the role of the black hole horizon played by the cosmological expansion of the de Sitter factor of the AdS metric.

The Hadamard regularization calculation is carried out to obtain the renormalized stress tensor of scalar fields with respect to the de Sitter invariant vacuum. We discuss how the condition of de Sitter invariance fixes the form of the Hadamard series expansion of the Hadamard elementary function. We obtain the value of the mass scale appearing in the logarithmic term in the Hadamard series expansion. We also compare the renormalized stress tensor of conformally invariant field in the de Sitter invariant and conformal vacua. For the purpose of investigating the role of quantized fields in cosmology, quantum field theory in de Sitter space is an interesting problem because the high symmetry of de Sitter space enables us to obtain the simple exact solution of the field equation. It is also expected to give fruitful information on the inflationary model of the early universe. It is one of the most important subjects to obtain the renormal­ ized expectation value of stress tensor of quantized fields with respect to certain vacuum states,. because the particle concept is very obscure in curved space and the renormalized stress tensor acts as the source term in the Einstein equation by con­ sidering the semi-classical back-reaction of quantized fields on the background geome­ try. The problem of how to select a physically meaningful vacuum state, however, remains unsolved. Vacuum states are sometimes characterized by symmetric prop­ erties or coordinatization of the background manifold. The most symmetric vacuum in de Sitter space is the de Sitter invariant one, which was first described by Chernikov and Tagirov 1 ) and have been studied by Schomblond, Spindel,2) Mottola 3 ) and Allen. 4 ) Several authors have evaluated the renormalized stress tensor with respect to the de Sitter invariant vacuum. Bunch and Davies investigated the behaviour of quantized scalar field and evaluated the renormalized stress tensor in de Sitter space with point-splitting regularization. 5 ) Their regularization method was formulated in the Friedmann universe not in the general curved spacetime. 6 ) Thus the subtracted divergent terms can be ambiguous. Dowker and Critchley evaluated the renormal­ ized stress tensor with the zeta function regularization,7) and Birrell and Davies did with the dimensional regularization. 8 ) Since they evaluated only the trace of the stress tensor with the effective Lagrangian, they could not obtain the state-dependent contribution. Allen, Bernard and Folacci applied their Hadamard regularization scheme to the de Sitter invariant vacuum. 9 ),IO) They used the Lagrangian with an additional term to give the limiting value in the flat space limit. There have been many works on this problem, but a few works with straightforward calculation. And the results for massive scalar fields are obscure. It is also still not clear how the

We study the most general contributions due to scalar field perturbations, vector field perturbations, and anisotropic expansion to the generation of statistical anisotropy in the primordial curvature perturbation \zeta. Such a study is done using the \delta N formalism where only linear terms are considered. Here, we consider two specific cases that lead to determine the power spectrum P_\zeta(k) of the primordial curvature perturbation. In the first one, we consider the possibility that the n-point correlators of the field perturbations in real space are invariant under rotations in space (statistical isotropy); as a result, we obtain as many levels of statistical anisotropy as vector fields present and, therefore, several preferred directions. The second possibility arises when we consider anisotropic expansion, which leads us to obtain I+a additional contributions to the generation of statistical anisotropy of \zeta compared with the former case, being I and a the number of scalar and vector fields involved respectively.

The recent observations of the global 21cm signal by EDGES and gravitational waves by LIGO/VIGO have revived interest in PBHs. Different from previous works, we investigate the influence of PBHs on the evolution of the IGM for the mass range $6\times 10^{13} {\rm g} \lesssim M_{\rm PBH}\lesssim 3\times 10^{14} \rm g$. Since the lifetime of these PBHs is smaller than the present age of the Universe, they have evaporated by the present day. Due to Hawking radiation, the heating effects of PBHs on the IGM can suppress the absorption amplitude of the global 21cm signal. In this work, by requiring that the differential brightness temperature of the global 21cm signals in the redshift range of $10\lesssim z \lesssim 30$, e.g., $\delta T_{b} \lesssim -100~\rm mK$, we obtain upper limits on the initial mass fraction of PBHs. We find that the strongest upper limit is $\beta_{\rm PBH} \sim 2\times 10^{-30}$. Since the formation of PBHs is related to primordial curvature perturbations, by using the constraints on the initial mass fraction of PBHs we obtain the upper limits on the power spectrum of primordial curvature perturbations for the scale range $8.0\times 10^{15}\lesssim k \lesssim 1.8\times 10^{16}~\rm Mpc^{-1}$, corresponding to the mass range considered here. We find that the strongest upper limit is $\mathcal P_{\mathcal R}(k) \sim 0.0046$. By comparing with previous works, we find that for the mass range (or the scale range) investigated in this work the global 21cm signals or the 21cm power spectrum should give the strongest upper limits on the initial mass fraction of PBHs and on the power spectrum of primordial curvature perturbations.

<div class="section abstract"><div class="htmlview paragraph">Rotating flow inside an internal combustion engine cylinder is deliberately engineered for improved fuel-air mixing and combustion. The details of the rotating flow structure vary temporally over an engine cycle as well as cyclically at the same engine phase. Algorithms in the literature to identify these structural details of the rotating flow invariably focus on locating its center and, on occasion, measuring its rotational strength and spatial extent. In this paper, these flow structure parameters are evaluated by means of complex moments, which have been adapted from image (scalar field) recognition applications to two-dimensional flow pattern (vector field) analysis. Several additional detailed characteristics of the rotating flow pattern - the type and extent of its deviation from the ideal circular pattern, its rotational and reflectional symmetry (if exists), and thus its orientation - are also shown to be related to the first few low-order complex moments of the flow pattern. The introduction of complex moments as an organizing framework for vortex identification and characterization, therefore, constitutes the major contribution of this paper. The analysis tool is applied to a set of in-cylinder flow fields obtained by high-speed particle image velocimetry at mid-intake stroke in the middle tumble plane of a research optical engine. The cycle-to-cycle variations of the large-scale tumble flow pattern characteristics - in location, strength, and orientation - are quantified and discussed.</div></div>

Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N+1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2^N, but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N-torus) topology.

Investigations of quantum fields in the de Sitter space have a long history (a bibliography of studies made up to 1981 can be found in the monograph of [i]). Being a curved sPace with maximal symmetry, the de Sitter space makes it possible to construct explicitly a quantum theory of free fields and also some models of interacting fields and investigate effects associated with the influence of the gravitational field on quantum processes. The de Sitter space is an example of a manifold that possesses an event horizon -the cosmological horizon. In the behavior of quantum fields in this space there is an organic intertwining of thermal effects (due to the finiteness of the Hawking temperature [2] associated with the cosmological horizon) with the effects of acceleration and curvature. It is no surprise that problems of quantum field theory in de Sitter space, which are of fundamental interest, have long attracted attention. In recent years a new stimulus to such investigations has been given by the appearance of the theory of an inflationary universe [3,4].