Detectable Data-driven Features in the Primordial Scalar Power Spectrum

Abstract

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 parametrize 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 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 constraints are tightest for CMB anisotropies and galaxy clustering, depending on the details of the specifications of the survey. 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.

Bayesian inference methodology for primordial power spectrum reconstructions from Large Scale Structure

“…Reconstruction, on the other hand, does not assume any model or template for P R (k), but rather infers its shape from the data. Several methods have been developed for model independent reconstruction of P R (k) based on different inference methods, such as Bayesian inference, linear interpolation methods [46,64], combination of top hat functions [65], wavelet expansion of P R (k) [66,67], smoothing splines [68][69][70], fixed wavenumber knots joined with cubic splines [60,62], the critical filter method [71], different spline techniques [72][73][74] or placement of N free knots in the {k,P R } plane [60,62,[72][73][74]; penalized likelihood, using function space generalization of the Fisher matrix formalism [75] or a P R (k) ansatz [60][61][62]; Principal Component Analysis, using expansion of a orthonormal set of basis functions [76]; and sparsity of the primordial power spectrum, using a sparsity-based linear inversion method [77]. These works have been applied to CMB and/or LSS data to reconstruct P R (k) and test for deviations from the standard power law form.…”

“…The most notable deviation, although not statistically significant, was a deficit in power at k ≈ 0.001 h Mpc −1 (ℓ ≈ 30) [60][61][62]. Some methods have also focused on detecting features at scales between k ≈ 0.01 h Mpc −1 and k ≈ 0.2 h Mpc −1 [66,67,71,74,76,77]. In [73], models that can account for a lack of power at k ≈ 0.001 h Mpc −1 and in k > 0.1 h Mpc −1 are slightly favoured against the power law parametrization in a Bayesian sense.…”