Angular Correlation Functions for Models with Logarithmic Oscillations

Abstract

There exist several theoretical motivations for primordial correlation functions (such as the power spectrum) to contain oscillations as a logarithmic function of comoving momentum k. While these features are commonly searched for in k-space, an alternative is to use angular space; that is, search for correlations between the directional vectors of observation. We develop tools to efficiently compute the angular correlations based on a stationary phase approximation and examine several example oscillations in the primordial power spectrum, bispectrum, and trispectrum. We find that logarithmically-periodic oscillations are essentially featureless and therefore difficult to detect using the standard correlator, though others might be feasible.

13 pages, 11 figures

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• Planck 2018 results. X. Constraints on inflation
• Planck 2013 results. XXII. Constraints on inflation
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• A review of Axion Inflation in the era of Planck
• Searching for Oscillations in the Primordial Power Spectrum: Constraints from Planck (Paper II)
• Drifting Oscillations in Axion Monodromy
• Untangling features in the primordial spectra
• An optimal estimator for resonance bispectra in the CMB
• Searching for features of a string-inspired inflationary model with cosmological observations
• Consistency relations for sharp features in the primordial spectra
• Les Houches lectures on inflationary observables and string theory
• The Komatsu Spergel Wandelt estimator for oscillations in the cosmic microwave background bispectrum
• Combined features in the primordial spectra induced by a sudden turn in two-field DBI inflation
• Coupling structure of multi-field primordial perturbations
• Inflation in string theory confronts data/Les modèles d'inflation en théorie des cordes face aux observations
• Log-periodic gravitational-wave background beyond Einstein gravity