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In recent years, a Gaussian process regression (GPR)-based framework has been developed for foreground mitigation from data collected by the LOw-Frequency ARray (LOFAR), to measure the 21-cm signal power spectrum from the Epoch of Reionization (EoR) and cosmic dawn. However, it has been noted that through this method there can be a significant amount of signal loss if the EoR signal covariance is misestimated. To obtain better covariance models, we propose to use a kernel trained on the grizzly simulations using a Variational Auto-Encoder (VAE)-based algorithm. In this work, we explore the abilities of this machine learning-based kernel (VAE kernel) used with GPR, by testing it on mock signals from a variety of simulations, exploring noise levels corresponding to ≈10 nights (≈141 h) and ≈100 nights (≈1410 h) of observations with LOFAR. Our work suggests the possibility of successful extraction of the 21-cm signal within 2σ uncertainty in most cases using the VAE kernel, with better recovery of both shape and power than with previously used covariance models. We also explore the role of the excess noise component identified in past applications of GPR and additionally analyse the possibility of redshift dependence on the performance of the VAE kernel. The latter allows us to prepare for future LOFAR observations at a range of redshifts, as well as compare with results from other telescopes. [ABSTRACT FROM AUTHOR]

Direct detection of the Cosmic Dawn and Epoch of Reionization via the redshifted 21-cm line of neutral Hydrogen will have unprecedented implications for studying structure formation in the early Universe. This exciting goal is challenged by the difficulty of extracting the faint 21-cm signal buried beneath bright astrophysical foregrounds and contaminated by numerous systematics. Here, we focus on improving the Gaussian Process Regression (GPR) signal separation method originally developed for LOFAR observations. We address a key limitation of the current approach by incorporating covariance prior models learnt from 21-cm signal simulations using variational autoencoder (VAE) and interpolatory autoencoder (IAE). Extensive tests are conducted to evaluate GPR, VAE–GPR, and IAE–GPR in different scenarios. Our findings reveal that the new method outperforms standard GPR in component separation tasks. Moreover, the improved method demonstrates robustness when applied to signals not represented in the training set. It also presents a certain degree of resilience to data systematics, highlighting its ability to effectively mitigate their impact on the signal recovery process. However, our findings also underscore the importance of accurately characterizing and understanding these systematics to achieve successful detection. Our generative approaches provide good results even with limited training data, offering a valuable advantage when a large training set is not feasible. Comparing the two algorithms, IAE–GPR shows slightly higher fidelity in recovering power spectra compared to VAE–GPR. These advancements highlight the strength of generative approaches and optimize the analysis techniques for future 21-cm signal detection at high redshifts. [ABSTRACT FROM AUTHOR]

The light-cone (LC) anisotropy arises due to cosmic evolution of the cosmic dawn (CD) 21-cm signal along the line-of-sight (LoS) axis of the observation volume. The LC effect makes the signal statistically non-ergodic along the LoS axis. The multifrequency angular power spectrum (MAPS) provides an unbiased alternative to the popular three-dimensional (3D) power spectrum as it does not assume statistical ergodicity along every direction in the signal volume. Unlike the 3D power spectrum which mixes the cosmic evolution of the 21-cm signal along the LoS k modes, MAPS keeps the evolution information disentangled. Here, we first study the impact of different underlying physical processes during CD on the behaviour of the 21-cm MAPS using simulations of various different scenarios and models. We also make error predictions in 21-cm MAPS measurements considering only the system noise and cosmic variance for mock observations of Hydrogen Epoch of Reionization Array (HERA), NenuFAR , and SKA-Low. We find that 100 h of HERA observations will be able to measure 21-cm MAPS at ≥3σ for ℓ ≲ 1000 with |$0.1\, {\rm MHz}$| channel-width. The better sensitivity of SKA-Low allows reaching this sensitivity up to ℓ ≲ 3000. Note that due to the difference in the frequency coverage of the various experiments, the CD–epoch of reionization model considered for NenuFAR is different than those used for the HERA and SKA-Low predictions. Considering NenuFAR with the new model, measurements ≥2σ are possible only for ℓ ≲ 600 with |$0.2\, {\rm MHz}$| channel-width and for a 10 times longer observation time of t obs = 1000 h. However, for the range 300 ≲ ℓ ≲ 600 and t obs = 1000 h more than 3σ measurements are still possible for NenuFAR when combining consecutive frequency channels within a 5 MHz band. [ABSTRACT FROM AUTHOR]