Abstract
Reconstructions of the primordial power spectrum (PPS) of curvature perturbations from cosmic microwave background anisotropies and large-scale structure data suggest that the usually assumed power-law PPS has localised features (up to \sim 10\%∼10% in amplitude), although of only marginal significance in the framework of \LambdaΛCDM cosmology. On the other hand if the cosmology is taken to be Einstein-de Sitter, larger features in the PPS (up to \sim 20\%∼20% in amplitude) are required to accurately fit the observed acoustic peaks. Within the context of single clock inflation, we show that any given reconstruction of the PPS can be mapped on to functional parameters of the underlying effective theory of the adiabatic mode within a 2nd-order formalism, provided the best fit fractional change of the PPS, \Delta{P}_{R}/{P}_{R}ΔPR/PR is such that (\Delta{P}_{R}/{P}_{R})^3(ΔPR/PR)3 falls within the 1\,\sigma1σ confidence interval of the reconstruction for features induced by variations of either the sound speed c_\mathrm{s}cs or the slow-roll parameter \epsilonϵ. Although there is a degeneracy amongst these functional parameters (and the models that project onto them), we can identify simple representative inflationary models that yield such features in the PPS. Thus we provide a dictionary (more accurately, a thesaurus) to go from observational data, via the reconstructed PPS, to models that reproduce them to per cent level precision.
Highlights
The outline of this paper is as follows – in § II, we review the effective theory of the adiabatic mode, detailing the method by which one can reproduce the scale dependence of a given reconstructed ∆PR/PR by a time dependence in cs keeping ε fixed, or vice-versa, within a 2nd-order formalism
The primordial power spectrum (PPS) estimated from Planck Release 2 data assuming a ΛCDM model consistent with the best-fit Planck Release 2 parameters is shown in Fig. 5 including estimated Bayesian and frequentist uncertainties and a fiducial power-law PPS with spectral index ns = 0.968
The reconstruction of ε(τ) shown in Fig. 6 derived from this PPS is normalised such that the pivot scale k∗ = 2×10−3 Mpc−1 exits the horizon at N = 0 e-folds
Summary
All observations of the cosmic microwave background (CMB) are consistent with scale invariant, adiabatic, Gaussian initial conditions [1] – widely accepted as evidence of an epoch of early universe inflation, processed by an intervening ΛCDM cosmology [2]. Attempts to match CMB observations with an Einstein-de Sitter (EdS) cosmology (which has ΩΛ = 0) requires a PPS with larger departures from scale invariance in order to reproduce the observed acoustic peaks in the CMB power spectrum [36] This begs the question – what underlying model of inflation could have produced the requisite features? It is possible to convert any given scale dependence for the primordial power spectrum into a time dependence for the parameters of the underlying effective theory (EFT) of the adiabatic mode [39] in the context of single clock inflation. Various details not covered in the main body of the paper are elaborated on in the appendices
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