Small field models with gravitational wave signature supported by CMB data

Abstract

We study scale dependence of the cosmic microwave background (CMB) power spectrum in a class of small, single-field models of inflation which lead to a high value of the tensor to scalar ratio. The inflaton potentials that we consider are degree 5 polynomials, for which we precisely calculate the power spectrum, and extract the cosmological parameters: the scalar index ns, the running of the scalar index nrun and the tensor to scalar ratio r. We find that for non-vanishing nrun and for r as small as r = 0.001, the precisely calculated values of ns and nrun deviate significantly from what the standard analytic treatment predicts. We study in detail, and discuss the probable reasons for such deviations. As such, all previously considered models (of this kind) are based upon inaccurate assumptions. We scan the possible values of potential parameters for which the cosmological parameters are within the allowed range by observations. The 5 parameter class is able to reproduce all of the allowed values of ns and nrun for values of r that are as high as 0.001. Subsequently this study at once refutes previous such models built using the analytical Stewart-Lyth term, and revives the small field brand, by building models that do yield an appreciable r while conforming to known CMB observables.

Small field models of inflation that predict a tensor-to-scalar ratio r=0.03

“…We continue our investigations [11,12] of a class of inflationary models that were proposed by Ben-Dayan and Brustein [13] and were followed by [14][15][16]. This class of models is compatible with several fundamental physics considerations.…”

“…3. This enables us to assign likelihood to each simulated model, as discussed in detail in [11,12]. Consequently, it is possible to perform a likelihood analysis of models.…”

“…The metric is of the FRW form and the potential given by Previously, in [11,13] this class of models was discussed from a phenomenological and theoretical points of view. In [11], the technical details of model building and simulation methods were discussed, while in [12], the analysis and the extraction of the most probable model were discussed. Additionally, in [12], the most likely model which yields r = 0.01 was identified.…”

The Swampland: Introduction and Review

“…Of course, such bounds may be evaded in models where the magnitude of r is not bounded by the field excursion, see for example [].…”

Constraints on scalar and tensor spectra from Neff

“…Step amplitude Region of constraints Δ N eff > S i Figure 6: The step function is located at k i = 20k 0 , and what is shown are the constraints for different experimental stages (S1-S4), at the step amplitude vs. underlying n s . The bend parameterization provides a reasonable approximation to models with non-monotonic slow-roll parameter , such that r 0.01 while the field excursion is still small, ∆φ ≤ 1 [31][32][33].…”