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We consider the steepest rate at which the power spectrum from single field inflation can grow, with the aim of providing a simple explanation for the k 4 growth found recently. With this explanation in hand we show that a slightly steeper k 5 (log k) 2 growth is in fact possible. Moreover, we argue that the power spectrum after a steep growth cannot immediately decay, but must remain large for the k modes which exit during a ∼ 2 e-fold period. We also briefly consider how a strong growth can affect the spectral index of longer wavelengths preceding the growth, and show that even the conversion of isocurvature modes likely cannot lead to a stronger growth. These results have implications for the formation of primordial black holes, and other phenomena which require a large amplitude of power spectrum at short scales. arXiv:1907.05237v1 [astro-ph.CO]

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We review the topic of 4D Einstein-Gauss-Bonnet gravity, which has been the subject of considerable interest over the past two years. Our review begins with a general introduction to Lovelock’s theorem, and the subject of Gauss-Bonnet terms in the action for gravity. These areas are of fundamental importance for understanding modified theories of gravity, and inform our subsequent discussion of recent attempts to include the effects of a Gauss-Bonnet term in four space-time dimensions by rescaling the appropriate coupling parameter. We discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well defined, self-consistent theories that enact it. We then move on to consider the gravitational physics that results from these theories, in the context of black holes, cosmology, and weak-field gravity. We show that 4D Einstein-Gauss-Bonnet gravity exhibits a number of interesting phenomena in each of these areas.