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Register a new userOn the slope of curvature power spectrum in non-attractor inflation
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Ogan Ozsoy Swansean University
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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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Non-attractor inflation is known as the only single field inflationary scenario that can violate non-Gaussianity consistency relation with the Bunch-Davies vacuum state and generate large local non-Gaussianity. However, it is also known that the non-attractor inflation by itself is incomplete and should be followed by a phase of slow-roll attractor. Moreover, there is a transition process between these two phases. In the past literature, this transition was approximated as instant and the evolution of non-Gaussianity in this phase was not fully studied. In this paper, we follow the detailed evolution of the non-Gaussianity through the transition phase into the slow-roll attractor phase, considering different types of transition. We find that the transition process has important effect on the size of the local non-Gaussianity. We first compute the net contribution of the non-Gaussianities at the end of inflation in canonical non-attractor models. If the curvature perturbations keep evolving during the transition - such as in the case of smooth transition or some sharp transition scenarios - the $mathcal{O}(1)$ local non-Gaussianity generated in the non-attractor phase can be completely erased by the subsequent evolution, although the consistency relation remains violated. In extremal cases of sharp transition where the super-horizon modes freeze immediately right after the end of the non-attractor phase, the original non-attractor result can be recovered. We also study models with non-canonical kinetic terms, and find that the transition can typically contribute a suppression factor in the squeezed bispectrum, but the final local non-Gaussianity can still be made parametrically large.
We study multifield inflation in scenarios where the fields are coupled non-minimally to gravity via $xi_I(phi^I)^n g^{mu u}R_{mu u}$, where $xi_I$ are coupling constants, $phi^I$ the fields driving inflation, $g_{mu u}$ the space-time metric, $R_{mu u}$ the Ricci tensor, and $n>0$. We consider the so-called $alpha$-attractor models in two formulations of gravity: in the usual metric case where $R_{mu u}=R_{mu u}(g_{mu u})$, and in the Palatini formulation where $R_{mu u}$ is an independent variable. As the main result, we show that, regardless of the underlying theory of gravity, the field-space curvature in the Einstein frame has no influence on the inflationary dynamics at the limit of large $xi_I$, and one effectively retains the single-field case. However, the gravity formulation does play an important role: in the metric case the result means that multifield models approach the single-field $alpha$-attractor limit, whereas in the Palatini case the attractor behaviour is lost also in the case of multifield inflation. We discuss what this means for distinguishing between different models of inflation.
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.
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 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.
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