Potential reconstruction from general power spectrum in single-field inflation

We suggest a new method to reconstruct, within canonical single-field inflation, the inflaton potential directly from the primordial power spectrum which may deviate significantly from near scale-invariance. Our approach relies on a more generalized slow-roll approximation than the standard one, and can probe the properties of the inflaton potential reliably. We give a few examples for reconstructing potential and discuss the validity of our method.

Inflation story: slow-roll and beyond

We present constraints on inflationary dynamics and features in the primordial power spectrum of scalar perturbations using the Cosmic Microwave Background temperature, polarization data from Planck 2018 data release and updated likelihoods. We constrain the slow-roll dynamics using Hilltop Quartic Potential and Starobinsky R + R 2 model in the Einstein frame using the Planck 2018 binned Plik likelihood. Using the Hilltop as base potential, we construct Whipped Inflation potential to introduce suppression in the scalar power spectrum at large angular scales. We notice marginal (68% C.L.) preference of suppression from the large scale temperature angular power spectrum. However, large-scale E-mode likelihood based on high frequency instrument cross spectrum, does not support this suppression and in the combined data the preference towards the suppression becomes negligible. Based on the Hilltop and Starobinsky model, we construct the Wiggly Whipped Inflation potentials to introduce oscillatory features along with the suppression. We use unbinned data from the recently released CamSpec v12.5 likelihood which updates Planck 2018 results. We compare the Bayesian evidences of the feature models with their baseline slow-roll potentials. We find that the complete slow-roll baseline potential is moderately preferred against potentials which generate features. Compared to Planck 2015 PlikHM bin1 likelihood, we find that the significance of sharp features has decreased owing to the updates in the data analysis pipeline. We also compute the bispectra for the best fit candidates obtained from our analysis.

Quantization ambiguities and the robustness of effective descriptions of primordial perturbations in hybrid Loop Quantum Cosmology

We study the imprint that certain quantization ambiguities may leave in effective regimes of the hybrid loop quantum description of cosmological perturbations. More specifically, in the case of scalar perturbations we investigate how to reconstruct the Mukhanov-Sasaki field in the effective regime of Loop Quantum Cosmology, taking as starting point for the quantization a canonical formulation in terms of other perturbative gauge invariants that possess different dynamics. This formulation of the quantum theory, in terms of variables other than the Mukhanov-Sasaki ones, is crucial to arrive at a quantum Hamiltonian with a good behavior, elluding the problems with ill defined Hamiltonian operators typical of quantum field theories. In the reconstruction of the Mukhanov-Sasaki field, we ask that the effective Mukhanov-Sasaki equations adopt a similar form and display the same Hamiltonian structure as the classical ones, a property that has been widely assumed in Loop Quantum Cosmology studies over the last decade. This condition actually restricts the freedom inherent to certain quantization ambiguities. Once these ambiguities are removed, the reconstruction of the Mukhanov-Sasaki field naturally identifies a set of positive-frequency solutions to the effective equations, and hence a choice of initial conditions for the perturbations. Our analysis constitutes an important and necessary test of the robustness of standard effective descriptions in Loop Quantum Cosmology, along with their observational predictions on the primordial power spectrum, taking into account that they should be the consequence of a more fundamental quantum theory with a well-defined Hamiltonian, in the spirit of Dirac’s long-standing ideas.

Classicalization of Quantum Fluctuations at the Planck Scale in the Rh=ct Universe

The quantum to classical transition of fluctuations in the early universe is still not completely understood. Some headway has been made incorporating the effects of decoherence and the squeezing of states, though the methods and procedures continue to be challenged. But new developments in the analysis of the most recent Planck data suggest that the primordial power spectrum has a cutoff associated with the very first quantum fluctuation to have emerged into the semi-classical universe from the Planck domain at about the Planck time. In this paper, we examine the implications of this result on the question of classicalization, and demonstrate that the birth of quantum fluctuations at the Planck scale would have been a `process' supplanting the need for a `measurement' in quantum mechanics. Emerging with a single wavenumber, these fluctuations would have avoided the interference between different degrees of freedom in a superposed state. Moreover, the implied scalar field potential had an equation-of-state consistent with the zero active mass condition in general relativity, allowing the quantum fluctuations to emerge in their ground state with a time-independent frequency. They were therefore effectively quantum harmonic oscillators with classical correlations in phase space from the very beginning.

Role of trans-Planckian modes in cosmology

Motivated by the old trans-Planckian (TP) problem of inflationary cosmology, it has been conjectured that any consistent effective field theory should keep TP modes ‘hidden’ behind the Hubble horizon, so as to prevent them from turning classical and thereby affecting macroscopic observations. In this paper we present two arguments against the Hubble horizon being a scale of singular significance as has been put forward in the TP Censorship Conjecture (TCC). First, refinements of TCC are presented that allow for the TP modes to grow beyond the horizon while still keeping the de-Sitter conjecture valid. Second, we show that TP modes can turn classical even well within the Hubble horizon, which, as such, negates this rationale behind keeping them from crossing it. The role of TP modes is known to be less of a problem in warm inflation, because fluctuations start out usually as classical. This allows warm inflation to be more resilient to the TP problem compared to cold inflation. To understand how robust this is, we identity limits where quantum modes can affect the primordial power spectrum in one specific case.