https://insu.hal.science/insu-03644760Münchmeyer, MoritzMoritzMünchmeyerIAP - Institut d'Astrophysique de Paris - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche ScientifiqueMeerburg, P. DanielP. DanielMeerburgWandelt, Benjamin D.Benjamin D.WandeltIAP - Institut d'Astrophysique de Paris - INSU - CNRS - Institut national des sciences de l'Univers - SU - Sorbonne Université - CNRS - Centre National de la Recherche ScientifiqueUPCité - Université Paris CitéOptimal estimator for resonance bispectra in the CMBHAL CCSD201598.80.-k98.80.Cq98.80.EsCosmologyParticle-theory and field-theory models of the early UniverseObservational cosmologyAstrophysics - Cosmology and Nongalactic Astrophysics[SDU] Sciences of the Universe [physics]Sorbonne Université, Gestionnaire HAL 42022-04-29 07:36:052023-05-01 03:58:102022-04-29 07:36:06enJournal articleshttps://insu.hal.science/insu-03644760/document10.1103/PhysRevD.91.043534application/pdf1We propose an (optimal) estimator for a CMB bispectrum containing logarithmically spaced oscillations. There is tremendous theoretical interest in such bispectra, and they are predicted by a plethora of models, including axion monodromy models of inflation and initial state modifications. The number of resolved logarithmical oscillations in the bispectrum is limited due to the discrete resolution of the multipole bispectrum. We derive a simple relation between the maximum number of resolved oscillations and the frequency. We investigate several ways to factorize the primordial bispectrum, and conclude that a one-dimensional expansion in the sum of the momenta ∑k<SUB>i</SUB>=k<SUB>t</SUB> is the most efficient and flexible approach. We compare the expansion to the exact result in multipole space and show for ω<SUB>eff</SUB>=100 that O (1 0<SUP>3</SUP>) modes are sufficient for an accurate reconstruction. We compute the expected σ<SUB>f<SUB>NL</SUB></SUB> and find that within an effective field theory (EFT) the overall signal to noise scales as S /N ∝ω<SUP>3 /2</SUP>. Using only the temperature data we find S /N ∼O (1 - 1 0<SUP>2</SUP>) for the frequency domain set by the EFT.