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    Inflationary Dynamics with a Smooth Slow-Roll to Constant-Roll Era Transition

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    In this paper we investigate the implications of having a varying second slow-roll index on the canonical scalar field inflationary dynamics. We shall be interested in cases that the second slow-roll can take small values and correspondingly large values, for limiting cases of the function that quantifies the variation of the second slow-roll index. As we demonstrate, this can naturally introduce a smooth transition between slow-roll and constant-roll eras. We discuss the theoretical implications of the mechanism we introduce and we use various illustrative examples in order to better understand the new features that the varying second slow-roll index introduces. In the examples we will present, the second slow-roll index has exponential dependence on the scalar field, and in one of these cases, the slow-roll era corresponds to a type of α\alpha-attractor inflation. Finally, we briefly discuss how the combination of slow-roll and constant-roll may lead to non-Gaussianities in the primordial perturbations.Comment: JCAP Accepte

    Slow-roll versus stochastic slow-roll inflation

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    We consider the classical wave equation with a thermal and Starobinsky-Vilenkin noise which in a slow-roll and long wave approximation describes the quantum fluctuations of the graviton-inflaton system in an expanding metric. We investigate the resulting consistent stochastic Einstein-Klein-Gordon system in the slow-roll regime. We show in some models that the slow-roll requirements (of the negligence of ∂t2ϕ\partial_{t}^{2}\phi) can be satisfied in the probabilistic sense for the stochastic system with quantum and thermal noise for arbitrarily large time and an infinite range of fields. We calculate expectation values of some inflationary variables taking into account quantum and thermal noise. We show that the mean acceleration ⟨∂t2a⟩\langle \partial_{t}^{2}a\rangle can be negative or positive (depending on the model) when the random fields take values beyond the classical range of inflation.Comment: 8 page

    Interactions between teaching assistants and students boost engagement in physics labs

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    Through in-class observations of teaching assistants (TAs) and students in the lab sections of a large introductory physics course, we study which TA behaviors can be used to predict student engagement and, in turn, how this engagement relates to learning. For the TAs, we record data to determine how they adhere to and deliver the lesson plan and how they interact with students during the lab. For the students, we use observations to record the level of student engagement and pre- and post-tests of lab skills to measure learning. We find that the frequency of TA-student interactions, especially those initiated by the TAs, is a positive and significant predictor of student engagement. Interestingly, the length of interactions is not significantly correlated with student engagement. In addition, we find that student engagement was a better predictor of post-test performance than pre-test scores. These results shed light on the manner in which students learn how to conduct inquiry and suggest that, by proactively engaging students, TAs may have a positive effect on student engagement, and therefore learning, in the lab.Comment: 27 pages, 8 figures. v2: Revised for clarity and concision. Version accepted to Physical Review Special Topics - Physics Education Researc
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