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Register a new userA non-Gaussian landscape
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Authors
Sami Nurmi
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Primordial perturbations with wavelengths greater than the observable universe shift the effective background fields in our observable patch from their global averages over the inflating space. This leads to a landscape picture where the properties of our observable patch depend on its location and may significantly differ from the expectation values predicted by the underlying fundamental inflationary model. We show that if multiple fields are present during inflation, this may happen even if our horizon exit would be preceded by only a few e-foldings of inflation. Non-Gaussian statistics are especially affected: for example models of local non-Gaussianity predicting |f_NL|>> 10 over the entire inflating volume can have a probability up to a few tens of percent to generate a non-detectable bispectrum in our observable patch |fNL^{obs.}|<10. In this work we establish systematic connections between the observable local properties of primordial perturbations and the global properties of the inflating space which reflect the underlying high energy physics. We study in detail the implications of both a detection and non-detection of primordial non-Gaussianity by Planck, and discover novel ways of characterising the naturalness of different observational configurations.
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A detection of primordial non-Gaussianity could transform our understanding of the fundamental theory of inflation. The precision promised by upcoming CMB and large-scale structure surveys raises a natural question: if a detection given a particular template is made, what does this truly tell us about the underlying theory? In this paper we present a systematic way to constrain a wide range of non-Gaussian shapes, including general single and multi-field models and models with excited initial states. We present a separable, divergent basis able to recreate many shapes in the literature to high accuracy with between three and seven basis functions. The basis allows shapes to be grouped into broad template classes, satisfying theoretically-relevant priors on their divergence properties in the squeezed limit. We forecast how well a Planck-like CMB survey could not only detect a general non-Gaussian signal but discern more about its shape, using existing templates and new ones we propose. This approach offers an opportunity to tie together minimal theoretical priors with observational constraints on the shape in general, and in the squeezed limit, to gain a deeper insight into what drove inflation.
In the context of transient constant-roll inflation near a local maximum, we derive the non-perturbative field redefinition that relates a Gaussian random field with the true non-Gaussian curvature perturbation. Our analysis shows the emergence of a new critical amplitude $zeta_*$, corresponding to perturbations that prevent the inflaton from overshooting the local maximum, thus becoming trapped in the false minimum of the potential. For potentials with a mild curvature at the local maximum (and thus small non-Gaussianity), we recover the known perturbative field redefinition. We apply these results to the formation of primordial black holes, and discuss the cases for which $zeta_*$ is smaller or of the same order than the critical value for collapse of spherically symmetric overdensities. In the latter case, we present a simple potential for which the power spectrum needs an amplitude 10 times smaller that in the Gaussian case for producing a sizeable amount of primordial black holes.
Power suppression of the cosmic microwave background on the largest observable scales could provide valuable clues about the particle physics underlying inflation. Here we consider the prospect of power suppression in the context of the multifield landscape. Based on the assumption that our observable universe emerges from a tunnelling event and that the relevant features originate purely from inflationary dynamics, we find that the power spectrum not only contains information on single-field dynamics, but also places strong con- straints on all scalar fields present in the theory. We find that the simplest single-field models giving rise to power suppression do not generalise to multifield models in a straightforward way, as the resulting superhorizon evolution of the curvature perturbation tends to erase any power suppression present at horizon crossing. On the other hand, multifield effects do present a means of generating power suppression which to our knowledge has so far not been considered. We propose a mechanism to illustrate this, which we dub flume inflation.
Using the quantum information picture to describe the early universe as a time dependent quantum density matrix, with time playing the role of a stochastic variable, we compute the non-gaussian features in the distribution of primordial fluctuations. We use a quasi de Sitter model to compute the corresponding quantum Fisher information function as the second derivative of the relative entanglement entropy for the density matrix at two different times. We define the curvature fluctuations in terms of the time quantum estimator. Using standard quantum estimation theory we compute the non-gaussian features in the statistical distribution of primordial fluctuations. Our approach is model independent and only relies on the existence of a quasi de Sitter phase. We show that there are primordial non-gaussianities, both in the form of squeezed and equilateral shapes. The squeezed limit gives a value of $f_{rm NL} sim n_s-1$. In the equilateral limit we find that $f_{rm NL} sim 0.03$. The equilateral non-gaussianity is due to the non-linearity of Einsteins equation. On the other hand, the squeezed one is due to the quantum nature of clock synchronization and thus real and cannot be gauged away as a global curvature. We identify a new effect: {it clock bias} which is a pure quantum effect and introduces a bias in the spectral tilt and running of the power spectrum of order $sim 10^{-4}$, which could be potentially measurable and yield precious information on the quantum nature of the early Universe.
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