Observational constraints on the second-order primordial power spectrum: Exploring a Continuous Spontaneous Localization inspired inflationary model

Abstract: Inflation, a period of exponential expansion in the early Universe, is considered an important part of the standard $\Lambda$CDM cosmological model, and plays a crucial role in explaining a wide range of current observations. The standard inflationary model predicts a primordial spectrum of fluctuations that is nearly scale-independent, fitting remarkably well the latest observational data. Nevertheless, there is an ongoing discussion surrounding the transition from an initial homogeneous and isotropic quantum state, characterizing the matter fields during inflation, to a classical inhomogeneous/anisotropic one, which gives rise to large-scale structure in the Universe. To tackle this issue, in the present work we explore an inflationary scenario where quantum ``collapse'' (or reduction) occurs naturally during the evolution of the system; this model is inspired in the so called Continuous Spontaneous Localization (CSL) model. Our present work builds upon previous results by considering the primordial power spectrum up to the second order in the Hubble Flow Functions, where we perform an estimation of the model free parameters. By validating the predictions of the model against observational data, we investigate whether this second-order calculation can explain the slight departure from the power law observed in the scalar spectral running index. We hope this research contributes to the understanding of the quantum-to-classical transition and its implications for cosmology.