Glimpsing at the primordial perturbation field
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In this thesis I will focus on ``non-minimal'' properties of the primordial perturbation field;
\nboth analysing data, and assessing the constraining power of novel probes.
\nIn particular, I will address the problem of finding deviations from a power-law primordial power spectrum, the possibility of better constraining compensated isocurvature perturbations, and detect primordial non-Gaussianity in an ample range of scales.
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\nI present a minimally parametric, model independent reconstruction of the shape of the primordial power spectrum. 
\nWe use a comprehensive set of the state-of the art cosmological data:
\n\\Planck observations of the temperature and polarisation anisotropies of the cosmic microwave background (CMB),
\nWiggleZ and Sloan Digital Sky Survey Data Release 7 galaxy power spectra,
\nand the Canada-France-Hawaii Lensing Survey correlation function.
\nThis reconstruction strongly supports the evidence for a power law primordial power spectrum with a red tilt and disfavours deviations from a power law power spectrum including small-scale power suppression such as that induced by significantly massive neutrinos.
\nThis offers a powerful confirmation of the inflationary paradigm, justifying the adoption of the inflationary prior in cosmological analyses.
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\nWe develop a linear perturbation theory for the spectral $y$-distortions of the CMB.
\nThe $y$-distortions generated during the recombination epoch are usually negligible because the energy transfer due to the Compton scattering is strongly suppressed at that time, but they can be significant if there is are compensated isocurvature perturbations with large amplitude.
\nSince $y$-distortions explicitly depend on the baryon density fluctuations, they can be used to detect and constrain compensated isocurvature perturbations (CIPs) models.
\nWe compute the cross correlation functions of the $y$-distortions with the CMB temperature and the $E$-mode polarization anisotropies ($T$, $E$ respectively).
\nWe investigate how well measurements of $y$-anisotropies provided by a 
\nPIXIE-like and a PRISM-like survey,
\nLiteBIRD, and a cosmic variance limited (CVL) survey, will constrain $f'=\\Delta^2_{\\zeta \\text{CIP}}/\\Delta^2_{\\zeta \\zeta}$,
\nand find that the degradation in constraining power due to the presence of Sunyaev Zel’dovich effect from galaxy clusters
\nwill prevent detections unless the amplitude of CIP is unnaturally high, with forecasted upper limits of, \\eg
\n$f'<2 \\times 10^5$ (68\\% C.L.) with LiteBIRD, and $f'<2 \\times 10^4$ (68\\% C.L.) with CVL observations.
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\nCross-correlations between CMB temperature and $y$-distortions anisotropies have been previously proposed as a way to measure the local bispectrum parameter $\\fnl^\\text{loc}$ in a range of scales much smaller than those accessible to CMB primary anisotropies.
\nUnfortunately, the primordial $y$-$T$ signal is strongly contaminated by the late-time correlation between the Integrated Sachs Wolfe and \\SZ (SZ) effects.
\nMoreover, SZ itself generates a large noise contribution in the $y$-parameter map. 
\nWe consider two original ways to address these issues:
\nTo remove the bias due to the SZ-CMB temperature coupling, while also adding new signal, we include in the analysis the $y$-$E$ cross-correlation.
\nIn order to reduce the noise, we propose to clean the $y$-map by subtracting a SZ template, reconstructed via cross-correlation with external tracers.
\nWe combine this SZ template subtraction with the previously adopted solution of directly masking detected clusters.
\nOur forecasts show that, using $y$-distortions, a PRISM-like survey can achieve $\\fnl^\\text{loc} < 300$ (68\\% C.L.), while an ideal experiment will achieve $\\fnl^\\text{loc} < 130$, with improvements of a factor $\\sim 3$ from adding the $y$-$E$ signal, and a further $20 \\sim 30 \\%$ from template cleaning.
\nThese forecasts are much worse than current $\\fnl^\\text{loc}$ boundaries from Planck, but we stress again that they refer to completely different scales.

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