Inflation and inflation uncertainty: A dynamic framework

This paper aims to investigate the direct relationship between inflation and inflation uncertainty by employing a dynamic method for the monthly country–region–place United States data for the time period 1976–2007. While the bulk of previous studies has employed GARCH models in investigating the link between inflation and inflation uncertainty, in this study Stochastic Volatility in Mean models are used to capture the shocks to inflation uncertainty within a dynamic framework. These models allow researchers to assess the dynamic effects of innovations in inflation as well as inflation volatility on inflation and inflation volatility over time, by incorporating the unobserved volatility as an explanatory variable in the mean (inflation) equation. Empirical findings suggest that innovations in inflation volatility increases inflation. This evidence is robust across various definitions of inflation and different sub-periods.     

Mimicking trans-Planckian effects in the CMB with conventional physics

We investigate the possibility that fields coupled to the inflaton can influence the primordial spectrum of density perturbations through their coherent motion. For example, the second field in hybrid inflation might be oscillating at the beginning of inflation rather than at the minimum of its potential. Although this effect is washed out if inflation lasts long enough, we note that there can be up to 30e-foldings of inflation prior to horizon crossing of COBE fluctuations while still giving a potentially visible distortion. Such pumping of the inflaton fluctuations by purely conventional physics can resemble trans-Planckian effects which have been widely discussed. The distortions which they make to the CMB could leave a distinctive signature which differs from generic effects like tilting of the spectrum.     

Linear inflation from running kinetic term in supergravity

We propose a new class of inflation models in which the coefficient of the inflaton kinetic term rapidly changes with energy scale. This naturally occurs especially if the inflaton moves over a long distance during inflation as in the case of large-scale inflation. The peculiar behavior of the kinetic term opens up a new way to construct an inflation model. As a concrete example we construct a linear inflation model in supergravity. It is straightforward to build a chaotic inflation model with a fractional power along the same line. Interestingly, the potential takes a different form after inflation because of the running kinetic term.     

Does inflation provide natural initial conditions for the universe

If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomly-chosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly-empty spacetime. If empty space has a small vacuum energy, however, inflation can begin spontaneously in this background. This scenario explains why a universe like ours is likely to have begun via a period of inflation, and also provides an origin for the cosmological arrow of time. This work was supported in part by the U.S. Dept. of Energy, the National Science Foundation, the NDSEG Fellowship, and the David and Lucile Packard Foundation. Second Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.     

Inflation,LHC and the Higgs boson

After the Higgs boson has been discovered, the Standard Model of particle physics became a confirmed theory, potentially valid up to the Planck scale and allowing one to trace the evolution of the Universe from the inflationary stage till the present days. We discuss the relation between the results from the LHC and the inflationary cosmology. We overview the Higgs inflation, and its relation to the possible metastability of the electroweak vacuum. A short overview of the bounds on the metastability of the electroweak vacuum in the models with inflation not related to the Higgs boson is presented.     

Effects of adopting inflation targeting regimes on inflation variability

This paper investigates whether inflation-targeting programs have altered the pattern of inflation and its variability for five developed countries and four emerging economies implementing inflation-targeting programs. A GARCH specification is used to model inflation variability, which accounts for public perception of the future levels of inflation variability—conditional variance. We could not find lower conditional inflation expectations except for Australia, Chile and Sweden under various specifications. Moreover, the conditional variance decreases only for Chile and the UK. Therefore, the empirical support for the lower inflation and its variability for the inflation targeting regimes is limited.     

Developments in inflationary cosmology

This talk presents some recent work that has been done in inflationary cosmology. First a brief review is given of the inflation scenario and its basic models. After that, one of the main problems in developing inflationary models has been the requirement of a very flat inflation potential. In solving this problem, supersymmetry has played a major role, and the reasons will be discussed and a specific example of the SUSY hybrid model will be examined. Some problems introduced by SUSY such as the η and gravitino problems will then be discussed. Then in a different direction, the quintessential inflation model will be examined as a proposal where a single scalar field plays the role of both the inflaton at early time and the dark energy field later. The final topic covered is developments in understanding dissipation and particle production processes during the inflationary phase.      

A study on radial directional natural frequency and damping ratio in a vehicle tire

The measurement of radial directional natural frequency and damping ratio in a vehicle tire has been studied. Natural frequencies and damping ratios in the radial direction of various tires, from passenger car tires to truck bus tires, are reported. The radial direction modal parameters of tires subjected to different levels of inflation pressure, have been determined by using a frequency response function method. To obtain the theoretical natural frequency and mode shape, the plane vibration of a tire has been modeled as though it were that of a circular beam. By using the Tielking method that is based on Hamilton’s principle, theoretical results have been determined by considering the rotational velocity, tangential and radial stiffness, radial directional velocity and tension force which is due to tire inflation pressure. The results show that experimental conditions can be considered as the parameters that shift the natural frequency and damping ratio.     

A comparison of 2D and 3D digital image correlation for a membrane under inflation

Three-dimensional (3D) digital image correlation (DIC) is becoming widely used to characterize the behavior of structures undergoing 3D deformations. However, the use of 3D-DIC can be challenging under certain conditions, such as high magnification, and therefore small depth of field, or a highly controlled environment with limited access for two-angled cameras. The purpose of this study is to compare 2D-DIC and 3D-DIC for the same inflation experiment and evaluate whether 2D-DIC can be used when conditions discourage the use of a stereo-vision system. A latex membrane was inflated vertically to 5.41 kPa (reference pressure), then to 7.87 kPa (deformed pressure). A two-camera stereo-vision system acquired top-down images of the membrane, while a single camera system simultaneously recorded images of the membrane in profile. 2D-DIC and 3D-DIC were used to calculate horizontal (in the membrane plane) and vertical (out of the membrane plane) displacements, and meridional strain. Under static conditions, the baseline uncertainty in horizontal displacement and strain were smaller for 3D-DIC than 2D-DIC. However, the opposite was observed for the vertical displacement, for which 2D-DIC had a smaller baseline uncertainty. The baseline absolute error in vertical displacement and strain were similar for both DIC methods, but it was larger for 2D-DIC than 3D-DIC for the horizontal displacement. Under inflation, the variability in the measurements were larger than under static conditions for both DIC methods. 2D-DIC showed a smaller variability in displacements than 3D-DIC, especially for the vertical displacement, but a similar strain uncertainty. The absolute difference in the average displacements and strain between 3D-DIC and 2D-DIC were in the range of the 3D-DIC variability. Those findings suggest that 2D-DIC might be used as an alternative to 3D-DIC to study the inflation response of materials under certain conditions.     

Hybrid natural low scale inflation

We discuss the phenomenological implications of Hybrid Natural Inflation models in which the inflaton is a pseudo-Goldstone boson but inflation is terminated by a second scalar field. A feature of the scheme is that the scale of breaking of the Goldstone symmetry can be lower than the Planck scale and so gravitational corrections are under control. We show that, for supersymmetric models, the scale of inflation can be chosen anywhere between the Lyth upper bound and a value close to the electroweak breaking scale. The observed density perturbations and spectral index are readily obtained by the choice of the free parameters. The tensor to scalar ratio and the spectral tilt are extremely small.     

Primordial curvature perturbation during and at the end of multi-field inflation

We study the generation of the primordial curvature perturbation in multi-field inflation. Considering both the evolution of the perturbation during inflation and the effects generated at the end of inflation, we present a general formula for the curvature perturbation. We provide the analytic expressions of the power spectrum, spectral tilt and non-Gaussianity for the separable potentials of two inflaton scalars, and apply them to some specific models.     

Monetary policy rules in practice: Re-examining the case of Turkey

This paper investigates possible asymmetries in the monetary policy reaction function of the Central Bank of Republic of Turkey over the business cycles. It is found that the bank reacted more aggressively towards output stabilisation during recessions than expansions. The empirical evidence suggests that the inflation targeting policy of the Turkish Central Bank was accommodative rather than stabilising. Furthermore, it is found that although the Central Bank of Republic of Turkey responded to foreign reserves, real exchange rates and short-term capital inflows both in expansion and recession periods, the bank targeted money growth, budget deficits, and net foreign assets only in expansion periods.     

Chaotic dynamics in optimal monetary policy

There is by now a large consensus in modern monetary policy. This consensus has been built upon a dynamic general equilibrium model of optimal monetary policy as developed by, e.g., Goodfriend and King [NBER Macroeconomics Annual 1997 edited by B. Bernanke and J. Rotemberg (Cambridge, Mass.: MIT Press, 1997), pp. 231–282], Clarida et al. [J. Econ. Lit. 37, 1661 (1999)], Svensson [J. Mon. Econ. 43, 607 (1999)] and Woodford [Interest and Prices: Foundations of a Theory of Monetary Policy (Princeton, New Jersey, Princeton University Press, 2003)]. In this paper we extend the standard optimal monetary policy model by introducing nonlinearity into the Phillips curve. Under the specific form of nonlinearity proposed in our paper (which allows for convexity and concavity and secures closed form solutions), we show that the introduction of a nonlinear Phillips curve into the structure of the standard model in a discrete time and deterministic framework produces radical changes to the major conclusions regarding stability and the efficiency of monetary policy. We emphasize the following main results: (i) instead of a unique fixed point we end up with multiple equilibria; (ii) instead of saddle-path stability, for different sets of parameter values we may have saddle stability, totally unstable equilibria and chaotic attractors; (iii) for certain degrees of convexity and/or concavity of the Phillips curve, where endogenous fluctuations arise, one is able to encounter various results that seem intuitively correct. Firstly, when the Central Bank pays attention essentially to inflation targeting, the inflation rate has a lower mean and is less volatile; secondly, when the degree of price stickiness is high, the inflation rate displays a larger mean and higher volatility (but this is sensitive to the values given to the parameters of the model); and thirdly, the higher the target value of the output gap chosen by the Central Bank, the higher is the inflation rate and its volatility.     

Holographic cosmology from a system of M2–M5 branes

In this paper, we analyze the holographic cosmology using a M2–M5 brane configuration. In this configuration, a M2-brane will be placed in between a M5-brane and an anti-M5-brane. The M2-brane will act as a channel for energy to flow from an anti-M5-brane to a M5-brane, and this will increase the degrees of freedom on the M5-brane causing inflation. The inflation will end when the M5-brane and anti-M5-brane get separated. However, at a later stage the distance between the M5-brane and the anti-M5-bran can reduce and this will cause the formation of tachyonic states. These tachyonic states will again open a bridge between the M5-branes and the anti-M5-branes, which will cause further acceleration of the universe.     

Planck 2015 results and inflation

The Planck mission prime objective was a very accurate and complete measurement of the temperature anisotropies of the Cosmic Microwave Background (CMB). Cosmological results from the intensity data of the nominal mission of a duration of 15 months were disclosed on 21 March 2013. Fortunately, the satellite kept acquiring data for at least twice longer, and we announced in February 2015 new results based on all the data acquired, both in temperature and polarization. I provide a short overview of the latest data and findings of most interest for inflation, as a basis for the other contributions to this volume. This overview is entirely based on the published or submitted works of the Planck collaboration.     

Emergent universe from scale invariant two measures theory

The dilaton-gravity sector of a linear in the scalar curvature, scale invariant Two Measures Field Theory (TMT), is explored in detail in the context of closed FRW cosmology and shown to allow stable emerging universe solutions. The model possesses scale invariance which is spontaneously broken due to the intrinsic features of the TMT dynamics. We study the transition from the emerging phase to inflation, and then to a zero cosmological constant phase. We also study the spectrum of density perturbations and the constraints that impose on the parameters of the theory.     

Entropic Uncertainty for Two Coupled Dipole Spins Using Quantum Memory under the Dzyaloshinskii–Moriya Interaction

In the thermodynamic equilibrium of dipolar-coupled spin systems under the influence of a Dzyaloshinskii–Moriya (D–M) interaction along the z-axis, the current study explores the quantum-memory-assisted entropic uncertainty relation (QMA-EUR), entropy mixedness and the concurrence two-spin entanglement. Quantum entanglement is reduced at increased temperature values, but inflation uncertainty and mixedness are enhanced. The considered quantum effects are stabilized to their stationary values at high temperatures. The two-spin entanglement is entirely repressed if the D–M interaction is disregarded, and the entropic uncertainty and entropy mixedness reach their maximum values for equal coupling rates. Rather than the concurrence, the entropy mixedness can be a proper indicator of the nature of the entropic uncertainty. The effect of model parameters (D–M coupling and dipole–dipole spin) on the quantum dynamic effects in thermal environment temperature is explored. The results reveal that the model parameters cause significant variations in the predicted QMA-EUR.     

Welfare Cost of Model Uncertainty in a Small Open Economy

This paper extends the canonical small open-economy real-business-cycle model, when considering model uncertainty. Domestic households have multiplier preferences, which leads them to take robust decisions in response to possible model misspecification for the economy’s aggregate productivity. Using perturbation methods, the paper extends the literature on real business cycle models by deriving a closed-form solution for the combined welfare effect of the two sources of uncertainty, namely risk and model uncertainty. While classical risk has an ambiguous effect on welfare, the addition of model uncertainty is unambiguously welfare-deteriorating. Hence, the overall effect of uncertainty on welfare is ambiguous, depending on consumers preferences and model parameters. The paper provides numerical results for the welfare effects of uncertainty measured by units of consumption equivalence. At moderate (high) levels of risk aversion, the effect of risk on household welfare is positive (negative). The addition of model uncertainty—for all levels of concern about model uncertainty and most risk aversion values—turns the overall effect of uncertainty on household welfare negative. It is important to remark that the analytical decomposition and combination of the effects of the two types of uncertainty considered here and the resulting ambiguous effect on overall welfare have not been derived in the previous literature on small open economies.