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Register a new userSpectrum oscillations from features in the potential of single-field inflation
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We study single-field inflationary models with steep step-like features in the potential that lead to the temporary violation of the slow-roll conditions during the evolution of the inflaton. These features enhance the power spectrum of the curvature perturbations by several orders of magnitude at certain scales and also produce prominent oscillatory patterns. We study analytically and numerically the inflationary dynamics. We describe quantitatively the size of the enhancement, as well as the profile of the oscillations, which are shaped by the number and position of the features in the potential. The induced tensor power spectrum inherits the distinctive oscillatory profile of the curvature spectrum and is potentially detectable by near-future space interferometers. The enhancement of the power specrtum by step-like features, though significant, may be insufficient to trigger the production of a sizeable number of primordial black holes if radiation dominates the energy density of the early universe. However, it can result in sufficient black hole production if the universe is dominated by non-relativistic matter. For the latter scenario, we find that deviations from the standard monochromatic profile of the mass spectrum of primordial black holes are possible because of the multiple-peak structure of the curvature power spectrum.
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We investigate the consequences of general curved trajectories in multi-field inflation. After setting up a completely general formalism using the mass basis, which naturally accommodates the notion of light and heavy modes, we study in detail the simple case of two successive turns in two-field system. We find the power spectrum of the curvature perturbation receives corrections that exhibit oscillatory features sinusoidal in the logarithm of the comoving wavenumber without slow-roll suppression. We show that this is because of the resonance of the heavy modes inside and outside the mass horizon.
We revisit the notion of slow-roll in the context of general single-field inflation. As a generalization of slow-roll dynamics, we consider an inflaton $phi$ in an attractor phase where the time derivative of $phi$ is determined by a function of $phi$, $dotphi=dotphi(phi)$. In other words, we consider the case when the number of $e$-folds $N$ counted backward in time from the end of inflation is solely a function of $phi$, $N=N(phi)$. In this case, it is found that we need a new independent parameter to properly describe the dynamics of the inflaton field in general, in addition to the standard parameters conventionally denoted by $epsilon$, $eta$, $c_s^2$ and $s$. Two illustrative examples are presented to discuss the non-slow-roll dynamics of the inflaton field consistent with observations.
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.
Massive fields in the primordial universe function as standard clocks and imprint clock signals in the density perturbations that directly record the scale factor of the primordial universe as a function of time, a(t). A measurement of such signals would identify the specific scenario of the primordial universe in a model-independent fashion. In this Letter, we introduce a new mechanism through which quantum fluctuations of massive fields function as standard clocks. The clock signals appear as scale-dependent oscillatory signals in the power spectrum of alternative scenarios to inflation.
We take a pragmatic, model independent approach to single field slow-roll canonical inflation by imposing conditions, not on the potential, but on the slow-roll parameter $epsilon(phi)$ and its derivatives $epsilon^{prime }(phi)$ and $epsilon^{primeprime }(phi)$, thereby extracting general conditions on the tensor-to-scalar ratio $r$ and the running $n_{sk}$ at $phi_{H}$ where the perturbations are produced, some $50$ $-$ $60$ $e$-folds before the end of inflation. We find quite generally that for models where $epsilon(phi)$ develops a maximum, a relatively large $r$ is most likely accompanied by a positive running while a negligible tensor-to-scalar ratio implies negative running. The definitive answer, however, is given in terms of the slow-roll parameter $xi_2(phi)$. To accommodate a large tensor-to-scalar ratio that meets the limiting values allowed by the Planck data, we study a non-monotonic $epsilon(phi)$ decreasing during most part of inflation. Since at $phi_{H}$ the slow-roll parameter $epsilon(phi)$ is increasing, we thus require that $epsilon(phi)$ develops a maximum for $phi > phi_{H}$ after which $epsilon(phi)$ decrease to small values where most $e$-folds are produced. The end of inflation might occur trough a hybrid mechanism and a small field excursion $Deltaphi_eequiv |phi_H-phi_e |$ is obtained with a sufficiently thin profile for $epsilon(phi)$ which, however, should not conflict with the second slow-roll parameter $eta(phi)$. As a consequence of this analysis we find bounds for $Delta phi_e$, $r_H$ and for the scalar spectral index $n_{sH}$. Finally we provide examples where these considerations are explicitly realised.
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