*Euclid*: The search for primordial features

M. Ballardini, Y. Akrami, F. Finelli, D. Karagiannis, B. Li, Y. Li, Z. Sakr, D. Sapone, A. Achúcarro, M. Baldi, N. Bartolo, G. Cañas-Herrera, S. Casas, R. Murgia, H. A. Winther, M. Viel, A. Andrews, J. Jasche, G. Lavaux, D. K. Hazra, D. Paoletti, J. Valiviita, A. Amara, S. Andreon, N. Auricchio, P. Battaglia, D. Bonino, E. Branchini, M. Brescia, **J. Brinchmann**, S. Camera, V. Capobianco, C. Carbone, J. Carretero, M. Castellano, S. Cavuoti, A. Cimatti, G. Congedo, L. Conversi, Y. Copin, L. Corcione, F. Courbin, H. M. Courtois, **A. C. da Silva**, H. Degaudenzi, F. Dubath, X. Dupac, M. Farina, S. Farrens, M. Frailis, E. Franceschi, M. Fumana, S. Galeotta, B. R. Gillis, C. Giocoli, A. Grazian, F. Grupp, S. V. H. Haugan, W. A. Holmes, F. Hormuth, A. Hornstrup, P. Hudelot, K. Jahnke, S. Kermiche, A. Kiessling, M. Kunz, H. Kurki-Suonio, P. B. Lilje, V. Lindholm, I. Lloro, E. Maiorano, O. Mansutti, O. Marggraf, N. Martinet, F. Marulli, R. Massey, E. Medinaceli, S. Mei, Y. Mellier, M. Meneghetti, E. Merlin, G. Meylan, M. Moresco, L. Moscardini, E. Munari, S. -. 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, A. Renzi, J. D. Rhodes, G. Riccio, E. Romelli, M. Roncarelli, R. Saglia, B. Sartoris, T. Schrabback, A. Secroun, G. Seidel, S. Serrano, C. Sirignano, G. Sirri, L. Stanco, J. -. Starck, C. Surace, P. Tallada-Crespí, A. N. Taylor, **I. Tereno**, R. Toledo-Moreo, F. Torradeflot, I. Tutusaus, E. A. Valentijn, L. Valenziano, T. Vassallo, A. Veropalumbo, Y. Wang, J. Weller, G. Zamorani, J. Zoubian, V. Scottez

**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_{X }Ξ_{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 *σ*_{8}, 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_{+}), 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}).

**Keywords**

gravitation / gravitational lensing: weak / cosmological parameters / early Universe / large-scale structure of Universe

**Notes**

- This paper is published on behalf of the Euclid Consortium.

**Astronomy & Astrophysics**

Volume 683, Article Number A220, Number of pages 22

2024 March