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Register a new userDressed Power-law Inflation with Cuscuton
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We study dressed inflation with a cuscuton and find a novel exact power-law solution. It is well known that the conventional power-law inflation is inconsistent with the Planck data. In contrast to this standard lore, we find that power-law inflation with a cuscuton can be reconciled with the Planck data. Moreover, we argue that the cuscuton generally ameliorates inflation models so that predictions are consistent with observations.
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The possibility that primordial black holes constitute a fraction of dark matter motivates a detailed study of possible mechanisms for their production. Black holes can form by the collapse of primordial curvature fluctuations, if the amplitude of their small scale spectrum gets amplified by several orders of magnitude with respect to CMB scales. Such enhancement can for example occur in single-field inflation that exhibit a transient non-attractor phase: in this work, we make a detailed investigation of the shape of the curvature spectrum in this scenario. We make use of an analytical approach based on a gradient expansion of curvature perturbations, which allows us to follow the changes in slope of the spectrum during its way from large to small scales. After encountering a dip in its amplitude, the spectrum can acquire steep slopes with a spectral index up to $n_s-1,=,8$, to then relax to a more gentle growth with $n_s-1,lesssim,3$ towards its peak, in agreement with the results found in previous literature. For scales following the peak associated with the presence of the non-attractor phase, the spectrum amplitude then mildly decays, during a transitional stage from non-attractor back to attractor evolution. Our analysis indicates that this gradient approach offers a transparent understanding of the contributions controlling the slope of the curvature spectrum. As an application of our findings, we characterise the slope in frequency of a stochastic gravitational wave background generated at second order from curvature fluctuations, using the more accurate information we gained on the shape of curvature power spectrum.
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Slow-roll inflation may simultaneously solve the horizon problem and generate a near scale-free fluctuation spectrum P(k). These two processes are intimately connected via the initiation and duration of the inflationary phase. But a recent study based on the latest Planck release suggests that P(k) has a hard cutoff, k_min > 0, inconsistent with this conventional picture. Here we demonstrate quantitatively that most---perhaps all---slow-roll inflationary models fail to accommodate this minimum cutoff. We show that the small parameter `epsilon must be > 0.9 throughout the inflationary period to comply with the data, seriously violating the slow-roll approximation. Models with such an epsilon predict extremely red spectral indices, at odds with the measured value. We also consider extensions to the basic picture (suggested by several earlier workers) by adding a kinetic-dominated or radiation-dominated phase preceding the slow-roll expansion. Our approach differs from previously published treatments principally because we require these modifications to---not only fit the measured fluctuation spectrum, but to simultaneously also---fix the horizon problem. We show, however, that even such measures preclude a joint resolution of the horizon problem and the missing correlations at large angles.
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