Euclid Collaboration, F. Finelli, Y. Akrami, A. Andrews, M. Ballardini, S. Casas, D. Karagiannis, Z. Sakr, J. Valiviita, G. Alestas, N. Bartolo, J. R. Bermejo-Climent, S. Nesseris, D. Paoletti, D. Sapone, I. Tutusaus, A. Achúcarro, G. Canas-Herrera, J. Jasche, G. Lavaux, N. Aghanim, B. Altieri, A. Amara, L. Amendola, S. Andreon, N. Auricchio, C. Baccigalupi, D. Bagot, M. Baldi, S. Bardelli, P. Battaglia, A. Biviano, E. Branchini, M. Brescia, S. Camera, V. Capobianco, C. Carbone, J. Carretero, M. Castellano, G. Castignani, S. Cavuoti, K. C. Chambers, A. Cimatti, C. Colodro-Conde, G. Congedo, C. J. Conselice, L. Conversi, Y. Copin, F. Courbin, H. M. Courtois, M. Cropper, A. C. da Silva, H. Degaudenzi, S. de la Torre, G. De Lucia, A. M. Di Giorgio, H. Dole, M. Douspis, F. Dubath, C. A. J. Duncan, X. Dupac, S. Dusini, S. Escoffier, M. Farina, R. Farinelli, F. Faustini, S. Ferriol, P. Fosalba, M. Frailis, E. Franceschi, M. Fumana, S. Galeotta, K. George, B. R. Gillis, C. Giocoli, J. Gracia-Carpio, A. Grazian, F. Grupp, S. V. H. Haugan, W. A. Holmes, I. M. Hook, F. Hormuth, A. Hornstrup, K. Jahnke, M. Jhabvala, B. Joachimi, E. Keihanen, S. Kermiche, A. Kiessling, B. Kubik, M. Kümmel, M. Kunz, H. Kurki-Suonio, A. M. C. Le Brun, S. Ligori, P. B. Lilje, V. Lindholm, I. Lloro, G. Mainetti, D. Maino, E. Maiorano, O. Mansutti, S. Marcin, O. Marggraf, M. Martinelli, N. Martinet, F. Marulli, R. Massey, E. Medinaceli, S. Mei, Y. Mellier, M. Meneghetti, E. Merlin, G. Meylan, A. Mora, M. Moresco, L. Moscardini, C. Neissner, S. M. Niemi, C. Padilla, S. Paltani, F. Pasian, K. Pedersen, W. J. Percival, V. Pettorino, S. Pires, G. Polenta, M. Poncet, L. A. Popa, L. Pozzetti, F. Raison, R. Rebolo, A. Renzi, J. D. Rhodes, G. Riccio, E. Romelli, M. Roncarelli, C. Rosset, R. Saglia, B. Sartoris, M. Schirmer, T. Schrabback, A. Secroun, E. Sefusatti, G. Seidel, M. D. Seiffert, S. Serrano, P. Simon, C. Sirignano, G. Sirri, A. Spurio Mancini, L. Stanco, J. Steinwagner, P. Tallada-Crespí, D. Tavagnacco, A. N. Taylor, I. Tereno, N. Tessore, S. Toft, R. Toledo-Moreo, F. Torradeflot, L. Valenziano, T. Vassallo, G. A. Verdoes Kleijn, A. Veropalumbo, Y. Wang, J. Weller, A. Zacchei, G. Zamorani, F. M. Zerbi, E. Zucca, V. Allevato, E. Bozzo, C. Burigana, R. Cabanac, M. Calabrese, A. Cappi, D. Di Ferdinando, J. A. Escartin Vigo, L. Gabarra, J. Martin-Fleitas, S. Matthew, N. Mauri, R. B. Metcalf, A. A. Nucita, A. Pezzotta, M. Pöntinen, C. Porciani, I. Risso, V. Scottez, M. Sereno, M. Tenti, M. Viel, M. Wiesmann, I. T. Andika, M. Archidiacono, F. Atrio-Barandela, S. Avila, A. Balaguera-Antolinez, D. Bertacca, M. Bethermin, A. Blanchard, L. Blot, H. Böhringer, S. Borgani, M. L. Brown, S. Bruton, A. Calabro, B. Camacho Quevedo, F. Caro, C. S. Carvalho, T. Castro, F. Cogato, S. Conseil, A. Cooray, S. Davini, F. De Paolis, G. Desprez, A. Diaz-Sanchez, J. J. Diaz, S. Di Domizio, J. M. Diego, P. Dimauro, A. Enia, Y. Fang, A. G. Ferrari, A. Finoguenov, A. Fontana, A. Franco, K. Ganga, J. Garcia-Bellido, T. Gasparetto, V. Gautard, E. Gaztanaga, F. Giacomini, F. Gianotti, G. Gozaliasl, A. Gruppuso, M. Guidi, C. M. Gutierrez, S. Hemmati, C. Hernandez-Monteagudo, H. Hildebrandt, J. Hjorth, S. Joudaki, J. J. E. Kajava, Y. Kang, V. Kansal, K. Kiiveri, C. C. Kirkpatrick, S. J. Kruk, M. Lattanzi, V. Le Brun, J. Le Graet, L. Legrand, M. Lembo, F. Lepori, G. Leroy, G. F. Lesci, J. Lesgourgues, L. Leuzzi, T. I. Liaudat, J. F. Macias-Perez, G. Maggio, M. Magliocchetti, F. Mannucci, R. Maoli, C. J. A. P. Martins, L. Maurin, M. Migliaccio, M. Miluzio, P. Monaco, C. Moretti, G. Morgante, S. Nadathur, K. Naidoo, A. Navarro-Alsina, L. Pagano, F. Passalacqua, K. Paterson, L. Patrizii, A. Pisani, D. Potter, S. Quai, M. Radovich, P. Flose-Reimberg, P. F. Rocci, G. Rodighiero, S. Sacquegna, M. Sahlen, D. B. Sanders, E. Sarpa, A. Schneider, D. Sciotti, E. Sellentin, L. C. Smith, K. Tanidis, C. Tao, G. Testera, R. Teyssier, S. Tosi, A. Troja, M. Tucci, C. Valieri, A. Venhola, D. Vergani, F. Vernizzi, G. Verza, P. E. Vielzeuf, N. A. Walton

Abstract
Context. The Euclid mission of the European Space Agency will deliver galaxy and cosmic shear surveys, which will be used to constrain initial conditions and statistics of primordial fluctuations. Aims. We present highlights for the Euclid scientific capability to test initial conditions beyond Λ cold dark matter with the three-dimensional galaxy clustering from the spectroscopic survey, the tomographic approach to 3 × 2pt statistics from photometric galaxy survey, and their combination. We then present how these Euclid results can be enhanced when combined with current and future measurements of the cosmic microwave background (CMB) anisotropies. Methods. We provide Fisher forecasts from the combination of Euclid spectroscopic and photometric surveys for spatial curvature, running of the spectral index of the power spectrum of curvature perturbations, isocurvature perturbations, and primordial features. For the parameters of these models, we also provide the combination of Euclid forecasts (pessimistic and optimistic) with three different CMB specifications, i.e. Planck, the Simons Observatory (SO), and CMB-S4. We provide Fisher forecasts for how the power spectrum and bispectrum from the Euclid spectroscopic survey will constrain the local, equilateral, and orthogonal shapes of primordial non-Gaussianity. We also review how Bayesian field-level inference of primordial non-Gaussianity can constrain local primordial non-Gaussianity. Results. We find that the combination of the Euclid main probes will provide an uncertainty of σ(Ω_K) = 0.0044 (0.003) at a 68% confidence level (CL) in pessimistic (optimistic) settings, assuming flat spatial sections as fiducial cosmology. We also find that the combination of the Euclid main probes can detect the running of the scalar spectral index for the fiducial value α_s = -0.01 with approximately 2σ (4σ) uncertainty and provide the uncertainty of σ(α_s) = 0.004 (0.0015) for the fiducial value α_s = -0.001 at a 68% CL, always with pessimistic (optimistic) settings. We show how Euclid will have the capability to provide constraints on isocurvature perturbations with a blue spectral index that are one order of magnitude tighter than current bounds. For primordial non-Gaussianity, the combined power spectrum and bispectrum Fisher forecast for the Euclid spectroscopic survey leads to σ(f_NL^local) = 2.2 σ ( f NL local ) = 2.2 , σ(f_NL^equil) = 108 σ ( f NL equil ) = 108 , and σ(f_NL^ortho) = 33 σ ( f NL ortho ) = 33 by assuming k_max = 0.15 h Mpc^-1 and universality for the halo mass function. We show how Bayesian field-level inference can reach the combined power spectrum and bispectrum Fisher forecast uncertainty on f_NL^local f NL local at these large scales, although it is more conservative as it is based on more realistic three-dimensional mock data and masks. For the Euclid main probes, we find relative errors on the amplitude of primordial oscillations (with a fiducial value of 0.01), of 21% (18%) for linear frequency and of 22% (18%) for logarithmic frequency at a 68% CL in the pessimistic (optimistic) case. These uncertainties can be further improved by adding the information from the bispectrum and the non-linear reconstruction. Conclusions. We show how Euclid, with its unique combination of three-dimensional galaxy clustering from the spectroscopic survey and 3 × 2pt statistics from the photometric survey, will provide the tightest constraints on low redshift to date. By targeting a markedly different range in redshift and scale, Euclid's expected uncertainties are complementary to those obtained by CMB primary anisotropy, returning the tightest combined constraints on the physics of the early Universe.

Keywords
cosmological parameters / early Universe / large-scale structure of Universe / inflation

Astronomy & Astrophysics
Volume 712, Article Number A166, Number of pages 27
2026 August

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