In this work we explore the power of future large-scale surveys to constrain possible deviations from the standard single-field slow-roll inflationary scenario. Specifically, we parameterize possible fluctuations around the almost scale-invariant primordial scalar power spectrum in a model-independent way. We then use their imprints on the simulated matter distribution, as observed by the galaxy clustering and weak lensing probes of Euclid and the Square Kilometer Array, to construct the best constrainable patterns of fluctuations. For comparison, we make similar forecasts for a futuristic CMB-S4-like survey. The modes are found to have similar, yet shifted, patterns, with increasing number of wiggles as the mode number increases. The forecasted constraints are tightest for cosmic microwave background anisotropies and galaxy clustering, depending on the details of the specifications of the survey. As case studies, we explore how two greatly different physically motivated patterns of primordial power spectrum are reconstructed by the proposed modes. We propose a figure of merit based on the amount of information delivered by the modes to truncate the mode hierarchy, which is automatically generated by the analysis.

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A geometrical phase transition in the very early Universe, from de Sitter to Gödel and back to de Sitter (dGd) spacetimes, can explain the universal phenomenon of rotation of many large scale structures. This phase transition is shown to induce fluctuations on the matter and radiation fields with possibly observable traces. In this work we simulate the dGd-induced inhomogeneities and use their power spectrum, parametrized by the parameter pair (p 1 , p 2 ), as possible seeds of CMB anisotropies along with the standard inflationary perturbations. With the Planck 2018 observations, we find p 1 = 0.008 +0.003 −0.008 and p 2 = 0.002 +0.001 −0.002 consistent with pure inflationary power spectrum and no hint for the dGd transition. Future large scale surveys can further tighten the constraints and probe the physics of the early Universe.

In this work we explore the possibility of variations in the primordial scalar power spectrum around the power-law shape, as predicted by single-field slow-roll inflationary scenarios. We search for a trace of these fluctuations in a semiblind, model-independent way in observations of the cosmic microwave background (CMB) sky. In particular, we use two sets of perturbation patterns, specific patterns with typical features such as oscillations, bumps, and transitions, as well as perturbation modes, constructed from eigenanalysis of the forecasted or measured covariance of perturbation parameters. These modes, in principle, span the parameter space of all possible perturbations to the primordial spectrum and, when rank ordered, the ones with the highest detectability would suffice to explore the constrainable features around the power-law spectrum in a data-driven (and not theoretically biased) manner. With Planck measurements of CMB anisotropies, the amplitudes of all perturbation patterns considered in this work are found to be consistent with zero. This finding confirms, in the absence of theoretical biases, the consistency of the Planck data with the assumption of a power-law inflationary pattern for the primordial spectrum.