Wave asymptotics at a cosmological time-singularity: classical and quantum scalar fields

We investigate the propagation of the scalar waves in the FLRW universes beginning with a Big Bang and ending with a Big Crunch, a Big Rip, a Big Brake or a Sudden Singularity. We obtain the sharp description of the asymptotics for the solutions of the linear Klein-Gordon equation, and similar results for the semilinear equation with a subcritical exponent. We prove that the number of cosmological particle creation is finite under general assumptions on the initial Big Bang and the final Big Crunch or Big Brake.Comment: 40 p., 5 figure

Sailing through the big crunch-big bang transition

In a recent series of papers, we have shown that theories with scalar fields coupled to gravity (e.g., the standard model) can be lifted to a Weyl-invariant equivalent theory in which it is possible to unambiguously trace the classical cosmological evolution through the transition from big crunch to big bang. The key was identifying a sufficient number of finite, Weyl-invariant conserved quantities to uniquely match the fundamental cosmological degrees of freedom across the transition. In so doing we had to account for the well-known fact that many Weyl-invariant quantities diverge at the crunch and bang. Recently, some authors rediscovered a few of these divergences and concluded based on their existence alone that the theories cannot be geodesically complete. In this note, we show that this conclusion is invalid. Using conserved quantities we explicitly construct the complete set of geodesics and show that they pass continuously through the big crunch-big bang transition.Comment: 3 pages, 1 figure. In version v2 the last three paragraphs include a response to the Note added to Ref. 1

The most important factor in producing clubhead speed in golf

Substantial experiential research into x-factor, and to a lesser extent crunch-factor has been undertaken with the aim of increasing clubhead speed. However, a direct comparison of the golf swing kinematics associated with each ‘factor’ has not, and possible differences when using a driver compared to an iron. Fifteen low handicap male golfers who displayed a modern swing had their golf swing kinematic data measured when hitting their own driver and five-iron, using a 10-camera motion analysis system operating at 250 Hz. Clubhead speed was collected using a validated launch monitor. No between-club differences in x-factor and crunch-factor existed. Correlation analyses revealed within-club segment (trunk and lower trunk) interaction was different for the driver, compared to the five-iron, and that a greater number of kinematic variables associated with x-factor, compared to crunch-factor were shown to be correlated with faster clubhead speeds. This was further explained in the five-iron regression model, where a significant amount of variance in clubhead speed was associated with increased lower trunk x-factor stretch, and reduced trunk lateral bending. Given that greens in regulation was shown to be the strongest correlated variable with PGA Tour earnings (1990-2004), the findings suggests a link to player performance for approach shots. These findings support other empiric research into the importance of x-factor as well as anecdotal evidence on how crunch-factor can negatively affect clubhead speed

Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology

We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. The dust and radiation dominated closed Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity. Thus before the big crunch, the collapse of the universe is stopped by quantum effects and reversed to an expansion, so that the universe opens up entering a new era of classical behavior. Numerical examples of such space-times are given, and the dependence on various parameters is discussed. Generically, one has a collapse after a finite number of cycles. By fine-tuning the parameters we construct an example of a space-time which is time-periodic, thus running through an infinite number of contraction and expansion cycles.Comment: 8 pages, LaTeX, 4 figures, statement on energy conditions correcte

Bankruptcies, Indebtedness and the Credit Crunch

This paper deals with Finnish bankruptcies. It shows that bankruptcies are strongly related to the business cycle and that they are perhaps even more strongly related to indebtedness, real interest rates and asset prices. The importance of these financial factors probably increased when the financial markets were liberalized in the early 1980s. Although there is a lot of seasonal and cyclical variation in bankruptcies the long run level (especially when adjusted to the number of firms) is almost constant representing some sort of "a natural rate of bankruptcies". What makes bankruptcies so important is the fact that they directly affect production, employment and credit expansion. The credit crunch effect in particular is scrutinized in the paper.bankruptcies; indebtedness; credit crunch; business cycle

A systematic mapping study of crunch time in video game development

Abstract. Crunch time means heavy overtime work, which usually happens before deadlines when development is behind schedule. It is common in game development and causes stress and social harm to developers. The purpose of this thesis was to study how crunch time is discussed in scientific literature by finding the trends and gaps using a systematic mapping study research method. The main research question was: How is crunch time in video game development discussed in scientific literature? Three assisting research questions were used to help with answering the main research question: How are the causes for crunch time in video game development discussed in the literature? How are the effects for crunch time in video game development discussed in the literature? How are the solutions for crunch time in video game development discussed in the literature? A search string was defined along with inclusion and exclusion criteria in a way that the resulting papers could best be used to answer the research questions. A total of 36 relevant, primary studies were included for this study after conducting the search on Google Scholar and applying the inclusion and exclusion criteria. The papers were categorised based on their contributions to the causes, effects and solutions related to crunch time. These papers were used as the source material for this research. It was found that the number of studies is increasing and the most common contribution of these studies is presenting the causes of crunch time. The most common causes presented were cultural, planning and process, and structural causes. Health and social effects were the most common effects. Process changes and no-crunch policies were the most common types of solutions to crunch time. The main contribution of this study was presenting an overview of how crunch time is discussed in scientific literature. It can be used by researchers to determine what kind of research might be necessary. The study could also be useful for game developers and managers in deciding what actions to take to avoid crunch time. This study found that there are gaps in the literature regarding solutions to crunch time, but often the causes seem to imply solutions. This study suggested that more research into feature creep and structural changes to the game development companies could be useful for learning how to reduce crunch time

Future Singularities of Isotropic Cosmologies

We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing `big crunch', can accommodate singularities of only one kind, namely, those having a non-integrable Hubble parameter, $H$. We analyze several examples from recent literature which illustrate this result and show that such behaviour may arise in a number of different ways. We also discuss the existence of new types of lapse singularities in inhomogeneous models, impossible to meet in the isotropic ones.Comment: v2: 16 pages, references added, clarrifications throughout, version to appear in the J.Geom.Phy