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Inflation with Weyl scaling symmetry provides a viable scenario that can generate both the nearly scaling invariant primordial density fluctuation and a dark matter candidate. Here we point out that, in additional to the primordial gravitational waves (GWs) from quantum fluctuations, the production of high-frequency GWs from preheating in such inflation models can provide an another probe of the inflationary dynamics. We conduct both linear analytical analysis and nonlinear numerical lattice simulation in a typical model. We find that significant stochastic GWs can be produced and the frequency band is located around $10^8$ Hz $\sim$ $10^9$ Hz, which might be probed by future resonance-cavity experiments., Comment: 21 pages, 6 figures

The cosmological observations of cosmic microwave background and large-scale structure indicate that our universe has a nearly scaling invariant power spectrum of the primordial perturbation. However, the exact origin for this primordial spectrum is still unclear. Here, we propose the Weyl scaling invariant $R^2+R^3$ gravity that gives rise to inflation that is responsible for the primordial perturbation in the early universe. We develop both analytic and numerical treatments on inflationary observables, and find this model gives a distinctive scalar potential that can support two different patterns of inflation. The first one is similar to that occurs in the pure $R^2$ model, but with a wide range of tensor-to-scalar ratio $r$ from $\mathcal O(10^{-4})$ to $\mathcal O(10^{-2})$. The other one is a new situation with not only slow-roll inflation but also a short stage of oscillation-induced accelerating expansion. Both patterns of inflation have viable parameter spaces that can be probed by future experiments on cosmic microwave background and primordial gravitational waves., Comment: 26 pages, 6 figures, match the published version in Phys.Rev.D

Dark matter and inflation are two key elements to understand the origin of cosmic structures in modern cosmology, and yet their exact physical models remain largely uncertain. The Weyl scaling invariant theory of gravity may provide a feasible scheme to solve these two puzzles jointly, which contains a massive gauge boson playing the role of dark matter candidate, and allows the quadratic scalar curvature term, namely $R^2$, to realize a viable inflationary mechanism in agreement with current observations. We ponder on the production of dark matters in the Weyl $R^2$ model, including the contribution from the non-perturbative production due to the quantum fluctuations from inflationary vacuum and perturbative ones from scattering. We demonstrate that there are generally three parameter ranges for viable dark matter production: (1) If the reheating temperature is larger than $10^3~\mathrm{GeV}$, the Weyl gauge boson as dark matter can be produced abundantly with mass larger than the inflation scale $\sim 10^{13}~\mathrm{GeV}$. (2) Small mass region with $3\times10^{-13}~\mathrm{GeV}$ for a higher reheating temperature. (3) Annihilation channel becomes important in the case of higher reheating temperature, which enables the Weyl gauge boson with mass up to $4\times10^{16}~\mathrm{GeV}$ to be produced through freeze-in., Comment: 26 pages, 5 figures

In recent years, the educational data mining and user modeling communities have been aggressively introducing models for predicting student performance on external measures such as standardized tests as well as within-tutor performance. While these models have brought statistically reliable improvement to performance prediction, the real world significance of the differences in errors has been largely unexplored. In this paper we take a deeper look at what reported errors actually mean in the context of high stakes test score prediction as well as student mastery prediction. We report how differences in common error and accuracy metrics on prediction tasks translate to impact on students and depict how standard validation methods can lead to overestimated accuracies in these prediction tasks. Two years of student tutor use and corresponding student state test scores are used for the analysis of test prediction while a simulation study is conducted to investigate the correspondence between performance prediction error and latent knowledge prediction. (Contains 7 tables and 2 footnotes.) [For the complete proceedings, "Proceedings of the International Conference on Educational Data Mining (EDM) (5th, Chania, Greece, June 19-21, 2012)," see ED537074.]