Surreal Decisions

Although expected utility theory has proven a fruitful and elegant theory in the finite realm, attempts to generalize it to infinite values have resulted in many paradoxes. In this paper, we argue that the use of John Conway's surreal numbers shall provide a firm mathematical foundation for transfinite decision theory. To that end, we prove a surreal representation theorem and show that our surreal decision theory respects dominance reasoning even in the case of infinite values. We then bring our theory to bear on one of the more venerable decision problems in the literature: Pascal's Wager. Analyzing the wager showcases our theory's virtues and advantages. To that end, we analyze two objections against the wager: Mixed Strategies and Many Gods. After formulating the two objections in the framework of surreal utilities and probabilities, our theory correctly predicts that (1) the pure Pascalian strategy beats all mixed strategies, and (2) what one should do in a Pascalian decision problem depends on what one's credence function is like. Our analysis therefore suggests that although Pascal's Wager is mathematically coherent, it does not deliver what it purports to, a rationally compelling argument that people should lead a religious life regardless of how confident they are in theism and its alternatives

Compensated isocurvature perturbations in the curvaton model

Primordial fluctuations in the relative number densities of particles, or isocurvature perturbations, are generally well constrained by cosmic microwave background (CMB) data. A less probed mode is the compensated isocurvature perturbation (CIP), a fluctuation in the relative number densities of cold dark matter and baryons. In the curvaton model, a subdominant field during inflation later sets the primordial curvature fluctuation $\zeta$. In some curvaton-decay scenarios, the baryon and cold dark matter isocurvature fluctuations nearly cancel, leaving a large CIP correlated with $\zeta$. This correlation can be used to probe these CIPs more sensitively than the uncorrelated CIPs considered in past work, essentially by measuring the squeezed bispectrum of the CMB for triangles whose shortest side is limited by the sound horizon. Here, the sensitivity of existing and future CMB experiments to correlated CIPs is assessed, with an eye towards testing specific curvaton-decay scenarios. The planned CMB Stage 4 experiment could detect the largest CIPs attainable in curvaton scenarios with more than 3$\sigma$ significance. The significance could improve if small-scale CMB polarization foregrounds can be effectively subtracted. As a result, future CMB observations could discriminate between some curvaton-decay scenarios in which baryon number and dark matter are produced during different epochs relative to curvaton decay. Independent of the specific motivation for the origin of a correlated CIP perturbation, cross-correlation of CIP reconstructions with the primary CMB can improve the signal-to-noise ratio of a CIP detection. For fully correlated CIPs the improvement is a factor of $\sim$2$-$3.Comment: 20 pages, 8 figures, minor changes matching publicatio

Golden Probe of the Top Yukuwa

We perform a preliminary study of the ability of the Higgs decay to four leptons to shed light on the top quark Yukawa couplings. In particular we examine whether the $h\to 4\ell$ `golden channel' is sensitive to the $CP$ properties of the top quark couplings to the Higgs boson. We show that kinematic distributions are sensitive to interference of the next-to-leading order electroweak corrections with the tree level $ZZ$ contribution. This translates into a sensitivity to the top quark Yukawa couplings such that meaningful constraints on their $CP$ properties can begin to be obtained once $\sim 300$ fb$^{-1}$ of data has been collected at $\sim 14$ TeV, with significant improvements at higher luminosity or with a higher energy hadron collider. This makes the $h\to4\ell$ channel a useful probe of the top quark Yukawa couplings that is qualitatively different from already established searches in $h\to V\gamma$ two body decays, $tth$, and $gg\to h$. We also briefly discuss other potential possibilities for probing the top Yukawa $CP$ properties in $h\to2\ell\gamma$ and $\ell^+\ell^-\to h Z, h\gamma$.Comment: references and footnote adde