Unstable growth of curvature perturbations in nonsingular bouncing cosmologies

Bouncing cosmologies require an ekpyrotic contracting phase (w?1) in order to achieve flatness, homogeneity, and isotropy. Models with a nonsingular bounce further require a bouncing phase that violates the null energy condition (w<-1). We show that the transition from the ekpyrotic phase to the bouncing phase creates problems for cosmological perturbations. A component of the adiabatic curvature perturbations, though decaying and negligible during the ekpyrotic phase, is exponentially amplified just before w approaches -1, enough to spoil the scale-invariant perturbation spectrum.     

Bouncing cosmologies

We review the general features of nonsingular universes (i.e. those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also considered, with emphasis in the behavior of perturbations.     

Theoretical and numerical approach to "magic angle" of stone skipping

We investigate the condition for the bounce of circular disks which obliquely impacts on the fluid surface. An experiment [C. Clanet, F. Hersen, and L. Bocquet, Nature (London) 427, 29 (2004)] revealed that there exists a "magic angle" of 20 degrees between a disk's face and water surface in which the condition of the lowest impact speed necessary for a bounce is minimized. We perform a three-dimensional simulation of the disk-water impact by means of the smoothed particle hydrodynamics. Furthermore, we analyze the impact with a model of the ordinary differential equation (ODE). Our simulation is in good agreement with the experiment. The analysis with the ODE model gives us a theoretical insight into the "magic angle" of stone skipping.     

The CST bounce universe model——A parametric study

A bounce universe model with a scale-invariant and stable spectrum of primordial density perturbations was constructed using a consistent truncation of the D-brane dynamics from Type IIB string theory. A coupling was introduced between the tachyon field and the adjoint Higgs field on the D3-branes to lock the tachyon at the top of its potential hill and to model the bounce process,which is known as the Coupled Scalar and Tachyon Bounce(CSTB) Universe. The CSTB model has been shown to be ghost free,and it fulfils the null energy condition; in addition, it can also solve the Big Bang cosmic singularity problem. In this paper we conduct an extensive follow-up study of the parameter space of the CSTB model. In particular we are interested in the parameter values that can produce a single bounce to arrive at a radiation-dominated universe. We further establish that the CSTB universe is a viable alternative to inflation, as it can naturally produce a sufficient number of e-foldings in the locked inflation epoch and in the post-bounce expansion to overcome the four fundamental limitations of the Big Bang cosmology, which are flatness, horizon,homogeneity and singularity, resulting in a universe of the current size.     

Quantum bounce and cosmic recall

Loop quantum cosmology predicts that, in simple models, the big bang is replaced by a quantum bounce. A natural question is whether the universe retains, after the bounce, its memory about the previous epoch. More precisely, does the Universe retain various properties of the state after evolving unitarily through the bounce, or does it suffer from recently suggested cosmic amnesia? We show that this issue can be answered unambiguously at least within an exactly solvable model. A semiclassical state at late times on one side of the bounce, peaked on a pair of canonically conjugate variables, strongly bounds the fluctuations on the other side, implying semiclassicality. For a model universe growing to 1 megaparsec, the change in relative fluctuation across the bounce is less than 10(-56) (becoming smaller for larger universes). The universe maintains (an almost) total recall.     

Towards the bounce inflationary gravitational wave

In the bounce inflation scenario, the inflation is singularity-free, while the advantages of inflation are preserved. We analytically calculate the power spectrum of its primordial gravitational waves (GWs), and show a universal result including the physics of the bounce phase. The spectrum acquires a cutoff at large scale, while the oscillation around the cutoff scale is quite drastic, which is determined by the details of bounce. Our work highlights that the primordial GWs at large scale may encode the physics of the bounce ever happened at about \({\sim }60\) efolds before inflation.     

Antiproton cloud compression in the ALPHA apparatus at CERN

We have observed a new mechanism for compression of a non-neutral plasma, where antiprotons embedded in an electron plasma are compressed by a rotating wall drive at a frequency close to the sum of the axial bounce and rotation frequencies. The radius of the antiproton cloud is reduced by up to a factor of 20 and the smallest radius measured is ～ 0.2 mm. When the rotating wall drive is applied to either a pure electron or pure antiproton plasma, no compression is observed in the frequency range of interest. The frequency range over which compression is evident is compared to the sum of the antiproton bounce frequency and the system’s rotation frequency. It is suggested that bounce resonant transport is a likely explanation for the compression of antiproton clouds in this regime.     

Elastic and inelastic evanescent-wave mirrors for cold atoms

We report on experiments on an evanescent-wave mirror for cold ⁸⁷Rb atoms. Measurements of the bouncing fraction show the importance of the Van der Waals attraction to the surface. We have directly observed radiation pressure parallel to the surface, exerted on the atoms by the evanescent-wave mirror. We analyze the radiation pressure by imaging the motion of the atom cloud after the bounce. The number of photon recoils ranges from 2 to 31. This is independent of laser power, inversely proportional to the detuning and proportional to the evanescent-wave decay length. By operating the mirror on an open transition, we have also observed atoms that bounce inelastically due to a spontaneous Raman transition. The observed distributions consist of a dense peak at the minimum velocity and a long tail of faster atoms, showing that the transition is a stochastic process with a strong preference to occur near the turning point of the bounce.     

Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig Relations

We consider the general response theory recently proposed by Ruelle for describing the impact of small perturbations to the non-equilibrium steady states resulting from Axiom A dynamical systems. We show that the causality of the response functions entails the possibility of writing a set of Kramers-Kronig (K-K) relations for the corresponding susceptibilities at all orders of nonlinearity. Nonetheless, only a special class of directly observable susceptibilities obey K-K relations. Specific results are provided for the case of arbitrary order harmonic response, which allows for a very comprehensive K-K analysis and the establishment of sum rules connecting the asymptotic behavior of the harmonic generation susceptibility to the short-time response of the perturbed system. These results set in a more general theoretical framework previous findings obtained for optical systems and simple mechanical models, and shed light on the very general impact of considering the principle of causality for testing self-consistency: the described dispersion relations constitute unavoidable benchmarks that any experimental and model generated dataset must obey. The theory exposed in the present paper is dual to the time-dependent theory of perturbations to equilibrium states and to non-equilibrium steady states, and has in principle similar range of applicability and limitations. In order to connect the equilibrium and the non equilibrium steady state case, we show how to rewrite the classical response theory by Kubo so that response functions formally identical to those proposed by Ruelle, apart from the measure involved in the phase space integration, are obtained. These results, taking into account the chaotic hypothesis by Gallavotti and Cohen, might be relevant in several fields, including climate research. In particular, whereas the fluctuation-dissipation theorem does not work for non-equilibrium systems, because of the non-equivalence between internal and external fluctuations, K-K relations might be robust tools for the definition of a self-consistent theory of climate change.     

Causal horizons in a bouncing universe

As our understanding of the past in a bouncing universe is limited, it becomes difficult to propose a cosmological model which can give some understanding of the causal structure of the bouncing universe. In this article we address the issue related to the particle horizon problem in the bouncing universe models. It is shown that in many models the particle horizon does not exist, and consequently the horizon problem is trivially solved. In some cases a bouncing universe can have a particle horizon and we specify the conditions for its existence. In the absence of a particle horizon the Hubble surface specifies the causal structure of a bouncing universe. We specify the complex relationship between the Hubble surface and the particle horizon when the particle horizon exists. The article also address the issue related to the event horizon in a bouncing universe. A toy example of a bouncing universe is first presented where we specify the conditions which dictate the presence of a particle horizon. Next we specify the causal structures of three widely used bouncing models. The first case is related to quintom matter bounce model, the second one is loop quantum cosmology based bounce model and lastly f(R) gravity induced bounce model. We present a brief discussion on the horizon problem in bouncing cosmologies. We point out that the causal structure of the various bounce models fit our general theoretical predictions.     

Generalized causality condition in quantum field theory with torsion

The Schwinger-De Witt method of local expansion of the effective action is applied to a model vector field theory which satisfies a generalized causality condition. One loop divergences are computed. It is shown that the theory is non-renormalizable. The effective potential of the theory has a local minimum with a nonzero average value of the vector field, stable with respect to small slowly varying perturbations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 74–78, May, 1989.     

Landau damping of electrons with bouncing motion in a radio-frequency plasma

One-dimensional particle simulations have been conducted to study the interaction between a radio-frequency electrostatic wave and electrons with bouncing motion. It is shown that bounce resonance heating can occur at the first few harmonics of the bounce frequency (nω_b,n=1,2,3,...). In the parameter regimes in which bounce resonance overlaps with Landau resonance, the higher harmonic bounce resonance may accelerate electrons at the velocity much lower than the wave phase velocity to Landau resonance region, enhancing Landau damping of the wave. Meanwhile, Landau resonance can increase the number of electrons in the lower harmonic bounce resonance region. Thus electrons can be efficiently heated. The result might be applicable for collisionless electron heating in low-temperature plasma discharges.     

Thermal-lens measurement in a side-pumped 1.3 μm Nd:YVO4 bounce laser

We investigated thermal-lensing effects in a side-pumped 1.3 μm Nd:YVO₄ slab laser amplifier having a bounce geometry. The thermal-lens power during 1.3 μm laser action was 1.3-times larger than that without laser action. Excited-state absorption is the main cause for increased heat loading during laser operation. The heat-loading formula in end-pumped 1.3 μm vanadate lasers having low Nd doping can be extended to account for heat generation in diode-side-pumped vanadate bounce lasers having high Nd doping.     

Measurement of the thermal lens of grazing-incidence diode-pumped Nd:YVO4 laser amplifier

The thermally induced lensing effects of a diode-pumped Nd:YVO₄ laser amplifier in a grazing incidence bounce geometry are carefully measured experimentally. Measurements of the thermal effects are interpreted by considering the diode-pumped amplifier region as a thick lens. A more detailed modeling was made of a quadratic refractive index lens duct for the normal to the bounce plane distribution. Due to the asymmetric pumping the thermal lens shows significant astigmatism. The ratio between dioptric powers in the plane normal to bounce and in the bounce plane is measured to be approximately 20. A nonlinear component of the power dependence of the lens is observed and related to the nonlinear heating induced by energy transfer upconversion. Measurements made under non-lasing conditions are used to infer thermal lensing behavior under lasing conditions and this allows optimization of optical resonator design.     

Optical properties of a nematic twist cell

We show that many of the complicated static and dynamic optical transmission characteristics of a Schadt-Helfrich twist cell, including the “bounce” in transmission that is observed at negative oblique angles of incidence after switching it off, can be predicted quite well from a very simple dynamic model. The model ignores flow and has only a viscous resistance to angular reorientation, in addition to the Ossen-Frank elastic properties. The bounce observed in some cases with normally incident light cannot be predicted by the model. As expected, the model yields equilibrium configurations at any applied voltage that give the observed transmission very accurately. Dynamic observations in the upper part of the nematic temperature range, where the observed bounce at normal incidence is small, are well reproduced by the model. At lower temperatures the discrepancies are larger. When interpreted with the model, both dynamic and static measurements concur in indicating that the directors of the liquid crystal adjacent to the surfaces assumed a more or less permanent tilt of a few degrees in our cell. Alignment was obtained by rubbing the conducting electrodes in one direction with linen cloth.     

Quantum nature of cosmological bounces

Several examples are known where quantum gravity effects resolve the classical big bang singularity by a bounce. The most detailed analysis has probably occurred for loop quantum cosmology of isotropic models sourced by a free, massless scalar. Once a bounce has been realized under fairly general conditions, the central questions are how strongly quantum it behaves, what influence quantum effects can have on its appearance, and what quantum space-time beyond the bounce may look like. This, then, has to be taken into account for effective equations which describe the evolution properly and can be used for further phenomenological investigations. Here, we provide the first analysis with interacting matter with new effective equations valid for weak self-interactions or small masses. They differ from the free scalar equations by crucial terms and have an important influence on the bounce and the space-time around it. Especially the role of squeezed states, which have often been overlooked in this context, is highlighted. The presence of a bounce is proven for uncorrelated states, but as squeezing is a dynamical property and may change in time, further work is required for a general conclusion.     

Bouncing universe models in an extended gravity theory

Some bouncing models are investigated in the framework of an extended theory of gravity. The extended gravity model is a simple extension of the General Relativity where an additional matter geometry coupling is introduced to account for the late time cosmic speed up phenomena. The dynamics of the models are discussed in the background of a flat FRW universe. Some viable models are reconstructed for specifically assumed bouncing scale factors. The behavior of the models are found to be decided mostly by the parameters of the respective models. The extended gravity based minimal matter-geometry coupling parameter has a role to remove the omega singularity occurring at the bouncing epoch. It is noted that the constructed models violate the energy conditions, however, in some cases this violation leads to the evolution of the models in phantom phase. The stability of the models are analyzed under linear homogeneous perturbations and it is found that, near the bounce, the models show instability but the perturbations decay out smoothly to provide stable models at late times.     

跳动模式对微球CH涂层表面粗糙度的影响

 采用低压等离子体化学气相沉积方法（LPPCVD）,结合反弹盘系统制备了微球CH涂层,研究了跳动模式对微球CH涂层表面形貌的影响。利用光学显微镜和扫描电镜(SEM)对微球涂层表面形貌进行了分析;利用原子力显微镜（AFM）测定了微球CH涂层表面均方根粗糙度（RMS）并对球形度进行了表征;利用X光照相技术对同心度进行了表征。结果表明：采用间歇跳动模式可有效改善微球CH涂层的表面形貌,降低中高模数的粗糙度。在间歇跳动模式下,减小占空比,可使CH涂层的表面粗糙度得到进一步降低。在占空比为1/4的间歇跳动模式下制备的厚度为30 mm的CH涂层,其表面均方根粗糙度低于30 nm,碳氢-聚苯乙烯（CH-PS）微球的球形度与同心度均优于99%。