# Erratum: Questions on calculation of primordial power spectrum with large spikes: the resonance model case

Keisuke Inomata, Matteo Braglia, Xingang Chen, Sébastien Renaux-Petel

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Keisuke Inomata, Matteo Braglia, Xingang Chen, Sébastien Renaux-Petel. Erratum: Questions on calculation of primordial power spectrum with large spikes: the resonance model case. Journal of Cosmology and Astroparticle Physics, 2023, 2023 (09), pp.E01. 10.1088/1475-7516/2023/09/E01 hal-04241709

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Submitted on 13 Oct 2023

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# Erratum: Questions on calculation of primordial power spectrum with large spikes: the resonance model case

Keisuke Inomata,ª Matteo Bragliaᵇ,ᶜ and Xingang Chenᵈ,<fnref n="1" />

E-mail: inomata@uchicago.edu, mb9289@nyu.edu, xingang.chen@cfa.harvard.edu

Received September 15, 2023

Accepted September 15, 2023

Published September 27, 2023

Erratum to: JCAP04(2023)011

ArXiv ePrint: 2211.02586

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<footnote>ªKavli Institute for Cosmological Physics, The University of Chicago, Chicago, IL 60637, U.S.A.</footnote>

<footnote>ᵇCenter for Cosmology and Particle Physics, New York University, 726 Broadway, New York, NY 10003, U.S.A.</footnote>

<footnote>ᶜINAF/OAS Bologna, via Gobetti 101, I-40129 Bologna, Italy</footnote>

<footnote>ᵈInstitute for Theory and Computation, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138, U.S.A.</footnote>

<footnote n="1">¹Additional (new) author: Sébastien Renaux-Petel; affiliation: Institut d'Astrophysique de Paris, UMR 7095 du CNRS et de Sorbonne Université, 98 bis bd Arago, 75014 Paris, France; email: renaux@iap.fr.</footnote>
We point out one correction in this erratum, which does not change the main conclusions of our paper.

In our previous manuscript, we missed one term in the symmetric part, which cancels parts of the contributions from the asymmetric part, $P_{\delta\phi,2vx,A}$. Given this, we change the splitting of the power spectrum as

$$ \langle \delta\phi_k(\eta)\delta\phi_{k'}(\eta) \rangle_{2vx} \equiv (2\pi)^3 \delta(\mathbf{k} + \mathbf{k}') \frac{2\pi^2}{k^3} [P_{\delta\phi,2vx,S}(k, \eta) + P_{\delta\phi,2vx,A}(k, \eta)] \quad (\text{old}) $$

$$ \Rightarrow \langle \delta\phi_k(\eta)\delta\phi_{k'}(\eta) \rangle_{2vx} \equiv (2\pi)^3 \delta(\mathbf{k} + \mathbf{k}') \frac{2\pi^2}{k^3} [P_{\delta\phi,2vx}^a(k, \eta) + P_{\delta\phi,2vx}^b(k, \eta)] \quad (\text{new}), $$

where $P_{\delta\phi,2vx,S} = P_{\delta\phi,2vx}^a$ while $P_{\delta\phi,2vx}^b$ is the sum of the asymmetric part and the contribution from the missed term in the symmetric part. Specifically, $P_{\delta\phi,2vx}^b$ is given by

$$ \begin{aligned} P_{\delta\phi,2vx}^b(k, \eta) = & 8 \int_0^\infty dv \int_{|1-v|}^{1+v} du \frac{uv}{4\pi^4} k^6 \int_{-\infty}^\eta d\eta' \int_{-\infty}^{\eta'} d\eta'' \lambda(\eta')\lambda(\eta'') \\ & \times \mathrm{Im}[U_k(\eta)U_k^*(\eta')] \Re[U_k(\eta)U_k^*(\eta'')] (\mathrm{Im}[U_{kv}(\eta')U_{kv}^*(\eta'')] \Re[U_{ku}(\eta')U_{ku}^*(\eta'')] \\ & + (u \leftrightarrow v)). \end{aligned} $$

This causes some changes in several equations and figures that are associated with the asymmetric part contributions, such as equations in section 2.1, 4.2, 4.5, and 5, and figures 5, 6, 7, 9, 10, and 13. However, the main qualitative conclusions of this paper remain unchanged.

For a coherent reading of the corrected manuscript, we refer readers to the latest version of our manuscript on arXiv, arXiv:2211.02586.