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We use Bayesian inference and nested sampling to develop a non-parametric method to reconstruct the primordial power spectrum $P_{\mathcal{R}}(k)$ from Large Scale Structure (LSS) data. The performance of the method is studied by applying it to simulations of the clustering of two different object catalogues, low-$z$ (ELGs) and high-$z$ (QSOs), and considering two different photometric errors. These object clusterings are derived from different templates of the primordial power spectrum motivated by models of inflation: the Standard Model power law characterized by the two parameters $A_s$ and $n_s$; a local feature template; and a global oscillatory template. Our reconstruction method involves sampling $N$ knots in the log $\{k,P_{\mathcal{R}}(k)\}$ plane. We use two statistical tests to examine the reconstructions for signs of primordial features: a global test comparing the evidences and a novel local test quantifying the power of the hypothesis test between the power law model and the marginalized probability over $N$ model. The method shows good performance in all scenarios considered. In particular, the tests show no feature detection for the SM. The method is able to detect power spectrum deviations at a level of $\approx 2\%$ for all considered features, combining either the low-$z$ or the high-$z$ redshift bins. Other scenarios with different redshift bins, photometric errors, feature amplitudes and detection levels are also discussed. In addition, we include a first application to real data from the Sloan Digital Sky Survey Luminous Red Galaxy Data Release 4 (SDSS LRG 04), finding no preference for deviations from the primordial power law. The method is flexible, model independent, and suitable for its application to existing and future LSS catalogues., Comment: 39 pages, 21 figures. Major changes. Updated to match the final version published in JCAP

One of the foundations of the Standard Model of Cosmology is statistical isotropy, which can be tested, among other probes, through the study of the Cosmic Microwave Background (CMB). However, a hemispherical power asymmetry on large scales has been reported for WMAP and Planck data by different works. The statistical significance is above 3${\sigma}$ for temperature, suggesting a directional dependence of the local power spectrum, and thus a feature beyond the ${\Lambda}$CDM model. With the third release of the Planck data (PR3), a new analysis was performed including the E-mode polarization maps, finding an asymmetry at a modest level of significance. In this work, we perform an asymmetry analysis in intensity and polarization maps for the latest Planck processing pipeline (PR4). We obtain similar results to those obtained with PR3, with a slightly lower significance (2.8% for the Sevem method) for the amplitude of the E-mode local variance dipole as well as a significant variability with the considered mask. In addition, a hint of a possible T-E alignment between the asymmetry axes is found at the level of $\sim$ 5%. For the analysis, we have implemented an alternative inpainting approach in order to get an accurate reconstruction of the E-modes. More sensitive all-sky CMB polarization data, such as those expected from the future LiteBIRD experiment, are needed to reach a more robust conclusion on the possible existence of deviations from statistical isotropy in the form of a hemispherical power asymmetry., Comment: 26 pages, 17 figure. Minor changes in the discussion, conclusions and results unchanged. Updated to match the final version published in JCAP