Cosmological disformal invariance

The invariance of physical observables under disformal transformations is considered. It is known that conformal transformations leave physical observables invariant. However, whether it is true for disformal transformations is still an open question. In this paper, it is shown that a pure disformal transformation without any conformal factor is equivalent to rescaling the time coordinate. Since this rescaling applies equally to all the physical quantities, physics must be invariant under a disformal transformation, that is, neither causal structure, propagation speed nor any other property of the fields are affected by a disformal transformation itself. This fact is presented at the action level for gravitational and matter fields and it is illustrated with some examples of observable quantities. We also find the physical invariance for cosmological perturbations at linear and high orders in perturbation, extending previous studies. Finally, a comparison with Horndeski and beyond Horndeski theories under a disformal transformation is made.Comment: 23 pages + Appendix, updated versio

The gain-loss asymmetry and single-self preferences

Kahneman and Tversky asserted a fundamental asymmetry between gains and losses, namely a “reflection effect” which occurs when an individual prefers a sure gain of $pz to an uncertain gain of$ z with probability p, while preferring an uncertain loss of $z with probability p to a certain loss of$ pz. We focus on this class of choices (actuarially fair), and explore the extent to which the reflection effect, understood as occurring at a range of wealth levels, is compatible with single-self preferences. We decompose the reflection effect into two components, a “probability switch” effect, which is compatible with single-self preferences, and a “translation effect,” which is not. To argue the first point, we analyze two classes of single-self, nonexpected utility preferences, which we label “homothetic” and “weakly homothetic.” In both cases, we characterize the switch effect as well as the dependence of risk attitudes on wealth. We also discuss two types of utility functions of a form reminiscent of expected utility but with distorted probabilities. Type I always distorts the probability of the worst outcome downwards, yielding attraction to small risks for all probabilities. Type II distorts low probabilities upwards, and high probabilities downwards, implying risk aversion when the probability of the worst outcome is low. By combining homothetic or weak homothetic preferences with Type I or Type II distortion functions, we present four explicit examples: All four display a switch effect and, hence, a form of reflection effect consistent a single self preferences.Reflection, gains, losses, experiments, risk attitude, Leex

Hamiltonian approach to 2nd order gauge invariant cosmological perturbations

In view of growing interest in tensor modes and their possible detection, we clarify the definition of tensor modes up to 2nd order in perturbation theory within the Hamiltonian formalism. Like in gauge theory, in cosmology the Hamiltonian is a suitable and consistent approach to reduce the gauge degrees of freedom. In this paper we employ the Faddeev-Jackiw method of Hamiltonian reduction. An appropriate set of gauge invariant variables that describe the dynamical degrees of freedom may be obtained by suitable canonical transformations in the phase space. We derive a set of gauge invariant variables up to 2nd order in perturbation expansion and for the first time we reduce the 3rd order action without adding gauge fixing terms. In particular, we are able to show the relation between the uniform-$\phi$ and Newtonian slicings, and study the difference in the definition of tensor modes in these two slicings.Comment: Revised versio

Conformal Frame Dependence of Inflation

Physical equivalence between different conformal frames in scalar-tensor theory of gravity is a known fact. However, assuming that matter minimally couples to the metric of a particular frame, which we call the matter Jordan frame, the matter point of view of the universe may vary from frame to frame. Thus, there is a clear distinction between gravitational sector (curvature and scalar field) and matter sector. In this paper, focusing on a simple power-law inflation model in the Einstein frame, two examples are considered; a super-inflationary and a bouncing universe Jordan frames. Then we consider a spectator curvaton minimally coupled to a Jordan frame, and compute its contribution to the curvature perturbation power spectrum. In these specific examples, we find a blue tilt at short scales for the super-inflationary case, and a blue tilt at large scales for the bouncing case.Comment: 17 pages, 5 figure

Imitation of succesful behavior in Cournot markets

In an experimental standard Cournot Oligopoly we test the importance of models of behavior characterized by imitation of succesful behavior. We find that the players appear to the rather reluctant to imitate.Oligopoly, cournot, bounded rationality, spite effect, Leex

On the role of non-equilibrium focal points as coordination devices

Considering a pure coordination game with a large number of equivalent equilibria, we argue, first, that a focal point that is itself not a Nash equilibrium and is Pareto dominated by all Nash equilibria, may attract the players' choices. Second, we argue that such a non-equilibrium focal point may act as an equilibrium selection device that the players use to coordinate on a closely related small subset of Nash equilibria. We present theoretical as well as experimental support for these two new roles of focal points as coordination devices.Coordination game, Focal point, Nash equilibrium, Equilibrium selection, Coordination device, LeeX