Euclid: The search for primordial features^⋆

¹ Dipartimento di Fisica e Scienze della Terra, Università degli Studi di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
² Istituto Nazionale di Fisica Nucleare, Sezione di Ferrara, Via Giuseppe Saragat 1, 44122 Ferrara, Italy
³ INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
e-mail: mario.ballardini@unife.it
⁴ Instituto de Física Teórica UAM-CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
⁵ CERCA/ISO, Department of Physics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106, USA
⁶ INFN – Bologna, Via Irnerio 46, 40126 Bologna, Italy
⁷ Department of Physics and Astronomy, University of the Western Cape, Bellville, Cape Town 7535, South Africa
⁸ Department of Physics, Institute for Computational Cosmology, Durham University, South Road DH1 3LE, UK
⁹ Department of Physics & Astronomy, University of Sussex, Brighton BN1 9QH, UK
¹⁰ Université St Joseph; Faculty of Sciences, Beirut, Lebanon
¹¹ Institut de Recherche en Astrophysique et Planétologie (IRAP), Université de Toulouse, CNRS, UPS, CNES, 14 Av. Edouard Belin, 31400 Toulouse, France
¹² Institut für Theoretische Physik, University of Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany
¹³ Departamento de Física, FCFM, Universidad de Chile, Blanco Encalada 2008, Santiago, Chile
¹⁴ Institute Lorentz, Leiden University, PO Box 9506, Leiden 2300 RA, The Netherlands
¹⁵ Departamento de Física, Universidad del País Vasco UPV-EHU, 48940 Leioa, Spain
¹⁶ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
¹⁷ INFN –Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹⁸ Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
¹⁹ INFN – Padova, Via Marzolo 8, 35131 Padova, Italy
²⁰ INAF – Osservatorio Astronomico di Padova, Via dell’Osservatorio 5, 35122 Padova, Italy
²¹ European Space Agency/ESTEC, Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
²² Institute for Theoretical Particle Physics and Cosmology (TTK), RWTH Aachen University, 52056 Aachen, Germany
²³ Gran Sasso Science Institute (GSSI), Viale F. Crispi 7, L’Aquila, (AQ) 67100, Italy
²⁴ INFN – Laboratori Nazionali del Gran Sasso (LNGS), L’Aquila, (AQ) 67100, Italy
²⁵ Institute of Theoretical Astrophysics, University of Oslo, PO Box 1029, Blindern, 0315 Oslo, Norway
²⁶ IFPU, Institute for Fundamental Physics of the Universe, Via Beirut 2, 34151 Trieste, Italy
²⁷ INAF – Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, 34143 Trieste, Italy
²⁸ SISSA, International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, TS, Italy
²⁹ INFN, Sezione di Trieste, Via Valerio 2, 34127 Trieste, TS, Italy
³⁰ Department of Astronomy, Stockholm University, Albanova, 10691 Stockholm, Sweden
³¹ Institut d’Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
³² Institut d’Astrophysique de Paris, UMR 7095, CNRS, and Sorbonne Université, 98 bis boulevard Arago, 75014 Paris, France
³³ The Institute of Mathematical Sciences, HBNI, CIT Campus, Chennai 600113, India
³⁴ Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400085, India
³⁵ Department of Physics, PO Box 64, 00014 University of Helsinki, Finland
³⁶ Helsinki Institute of Physics, Gustaf Hällströmin katu 2, University of Helsinki, Helsinki, Finland
³⁷ Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX, UK
³⁸ INAF – Osservatorio Astronomico di Brera, Via Brera 28, 20122 Milano, Italy
³⁹ INAF – Osservatorio Astrofisico di Torino, Via Osservatorio 20, 10025 Pino Torinese, (TO), Italy
⁴⁰ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁴¹ INFN – Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
⁴² Department of Physics “E. Pancini”, University Federico II, Via Cinthia 6, 80126 Napoli, Italy
⁴³ INAF – Osservatorio Astronomico di Capodimonte, Via Moiariello 16, 80131 Napoli, Italy
⁴⁴ INFN section of Naples, Via Cinthia 6, 80126 Napoli, Italy
⁴⁵ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
⁴⁶ Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁴⁷ INFN – Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁴⁸ INAF – IASF Milano, Via Alfonso Corti 12, 20133 Milano, Italy
⁴⁹ Institut de Física d'Altes Energies (IFAE), The Barcelona Institute of Science and Technology, Campus UAB, 08193 Bellaterra, (Barcelona), Spain
⁵⁰ Port d’Informació Científica, Campus UAB, C. Albareda s/n, 08193 Bellaterra, (Barcelona), Spain
⁵¹ INAF – Osservatorio Astronomico di Roma, Via Frascati 33, 00078 Monteporzio Catone, Italy
⁵² Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
⁵³ Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh EH9 3HJ, UK
⁵⁴ European Space Agency/ESRIN, Largo Galileo Galilei 1, 00044 Frascati, Roma, Italy
⁵⁵ ESAC/ESA, Camino Bajo del Castillo s/n., Urb. Villafranca del Castillo, 28692 Villanueva de la Cañada, Madrid, Spain
⁵⁶ University of Lyon, Univ Claude Bernard Lyon 1, CNRS/IN2P3, IP2I Lyon, UMR 5822, 69622 Villeurbanne, France
⁵⁷ Institute of Physics, Laboratory of Astrophysics, Ecole Polytechnique Fédérale de Lausanne (EPFL), Observatoire de Sauverny, 1290 Versoix, Switzerland
⁵⁸ UCB Lyon 1, CNRS/IN2P3, IUF, IP2I Lyon, 4 rue Enrico Fermi, 69622 Villeurbanne, France
⁵⁹ Departamento de Física, Faculdade de Ciências, Universidade de Lisboa, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal
⁶⁰ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal
⁶¹ Department of Astronomy, University of Geneva, ch. d’Ecogia 16, 1290 Versoix, Switzerland
⁶² INAF – Istituto di Astrofisica e Planetologia Spaziali, via del Fosso del Cavaliere, 100, 00100 Roma, Italy
⁶³ Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France
⁶⁴ Max Planck Institute for Extraterrestrial Physics, Giessenbachstr. 1, 85748 Garching, Germany
⁶⁵ University Observatory, Faculty of Physics, Ludwig-Maximilians-Universität, Scheinerstr. 1, 81679 Munich, Germany
⁶⁶ Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA
⁶⁷ von Hoerner & Sulger GmbH, SchloßPlatz 8, 68723 Schwetzingen, Germany
⁶⁸ Technical University of Denmark, Elektrovej 327, 2800 Kgs., Lyngby, Denmark
⁶⁹ Cosmic Dawn Center (DAWN), Copenhagen, Denmark
⁷⁰ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
⁷¹ Aix-Marseille Université, CNRS/IN2P3, CPPM, Marseille, France
⁷² Université de Genève, Département de Physique Théorique and Centre for Astroparticle Physics, 24 quai Ernest-Ansermet, 1211 Genève 4, Switzerland
⁷³ NOVA optical infrared instrumentation group at ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo, The Netherlands
⁷⁴ Universität Bonn, Argelander-Institut für Astronomie, Auf dem Hügel 71, 53121 Bonn, Germany
⁷⁵ Aix-Marseille Université, CNRS, CNES, LAM, Marseille, France
⁷⁶ Dipartimento di Fisica e Astronomia “Augusto Righi” – Alma Mater Studiorum Università di Bologna, Via Piero Gobetti 93/2, 40129 Bologna, Italy
⁷⁷ Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75013 Paris, France
⁷⁸ Department of Physics and Astronomy, University of Aarhus, Ny Munkegade 120, 8000 Aarhus C, Denmark
⁷⁹ Centre for Astrophysics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸⁰ Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
⁸¹ Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
⁸² Université Paris-Saclay, Université Paris Cité, CEA, CNRS, Astrophysique, Instrumentation et Modélisation Paris-Saclay, 91191 Gif-sur-Yvette, France
⁸³ Space Science Data Center, Italian Space Agency, Via del Politecnico snc, 00133 Roma, Italy
⁸⁴ Centre National d’Etudes Spatiales – Centre spatial de Toulouse, 18 avenue Edouard Belin, 31401 Toulouse Cedex 9, France
⁸⁵ Institute of Space Science, Str. Atomistilor, nr. 409 Măgurele, Ilfov 077125, Romania
⁸⁶ Universitäts-Sternwarte München, Fakultät für Physik, Ludwig-Maximilians-Universität München, Scheinerstrasse 1, 81679 München, Germany
⁸⁷ Universität Innsbruck, Institut für Astro- und Teilchenphysik, Technikerstr. 25/8, 6020 Innsbruck, Austria
⁸⁸ Institut d’Estudis Espacials de Catalunya (IEEC), Carrer Gran Capitá 2-4, 08034 Barcelona, Spain
⁸⁹ Institute of Space Sciences (ICE, CSIC), Campus UAB, Carrer de Can Magrans, s/n, 08193 Barcelona, Spain
⁹⁰ Satlantis, University Science Park, Sede Bld 48940, Leioa-Bilbao, Spain
⁹¹ AIM, CEA, CNRS, Université Paris-Saclay, Université de Paris, 91191 Gif-sur-Yvette, France
⁹² Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Avenida Complutense 40, 28040 Madrid, Spain
⁹³ Instituto de Astrofísica e Ciências do Espaço, Faculdade de Ciências, Universidade de Lisboa, Tapada da Ajuda, 1349-018 Lisboa, Portugal
⁹⁴ Universidad Politécnica de Cartagena, Departamento de Electrónica y Tecnología de Computadoras, Plaza del Hospital 1, 30202 Cartagena, Spain
⁹⁵ Kapteyn Astronomical Institute, University of Groningen, PO Box 800, 9700 AV Groningen, The Netherlands
⁹⁶ Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125, USA
⁹⁷ Junia, EPA department, 41 Bd Vauban, 59800 Lille, France

Received: 5 October 2023
Accepted: 21 December 2023

Abstract

Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and photometric measurements from the Euclid space mission will provide unique constraints on the primordial power spectrum, thanks to the redshift coverage and high-accuracy measurement of nonlinear scales, thus allowing us to investigate deviations from the standard power-law primordial power spectrum. We consider two models with primordial undamped oscillations superimposed on the matter power spectrum described by 1 + 𝒜_X sin (ω_XΞ_X + 2 πϕ_X), one linearly spaced in k space with Ξ_lin ≡ k/k_* where k_* = 0.05 Mpc⁻¹ and the other logarithmically spaced in k space with Ξ_log ≡ ln(k/k_*). We note that 𝒜_X is the amplitude of the primordial feature, ω_X is the dimensionless frequency, and ϕ_X is the normalised phase, where X = {lin, log}. We provide forecasts from spectroscopic and photometric primary Euclid probes on the standard cosmological parameters Ω_m, 0, Ω_b, 0, h, n_s, and σ₈, and the primordial feature parameters 𝒜_X, ω_X, and ϕ_X. We focus on the uncertainties of the primordial feature amplitude 𝒜_X and on the capability of Euclid to detect primordial features at a given frequency. We also study a nonlinear density reconstruction method in order to retrieve the oscillatory signals in the primordial power spectrum, which are damped on small scales in the late-time Universe due to cosmic structure formation. Finally, we also include the expected measurements from Euclid’s galaxy-clustering bispectrum and from observations of the cosmic microwave background (CMB). We forecast uncertainties in estimated values of the cosmological parameters with a Fisher matrix method applied to spectroscopic galaxy clustering (GC_sp), weak lensing (WL), photometric galaxy clustering (GC_ph), the cross correlation (XC) between GC_ph and WL, the spectroscopic galaxy clustering bispectrum, the CMB temperature and E-mode polarisation, the temperature-polarisation cross correlation, and CMB weak lensing. We consider two sets of specifications for the Euclid probes (pessimistic and optimistic) and three different CMB experiment configurations, that is, Planck, Simons Observatory (SO), and CMB Stage-4 (CMB-S4). We find the following percentage relative errors in the feature amplitude with Euclid primary probes: for the linear (logarithmic) feature model, with a fiducial value of 𝒜_X = 0.01, ω_X = 10, and ϕ_X = 0: 21% (22%) in the pessimistic settings and 18% (18%) in the optimistic settings at a 68.3% confidence level (CL) using GC_sp+WL+GC_ph+XC. While the uncertainties on the feature amplitude are strongly dependent on the frequency value when single Euclid probes are considered, we find robust constraints on 𝒜_X from the combination of spectroscopic and photometric measurements over the frequency range of (1,  10^2.1). Due to the inclusion of numerical reconstruction, the GC_sp bispectrum, SO-like CMB reduces the uncertainty on the primordial feature amplitude by 32%–48%, 50%–65%, and 15%–50%, respectively. Combining all the sources of information explored expected from Euclid in combination with the future SO-like CMB experiment, we forecast 𝒜_lin ≃ 0.010 ± 0.001 at a 68.3% CL and 𝒜_log ≃ 0.010 ± 0.001 for GC_sp(PS rec + BS)+WL+GC_ph+XC+SO-like for both the optimistic and pessimistic settings over the frequency range (1,  10^2.1).