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 $n_s$, the running of the scalar index $n_{\mathrm{run}}$ and the tensor to scalar ratio $r$. We find that for non-vanishing $n_{\mathrm{run}}$ and for $r$ as small as $r=0.001$, the precisely calculated values of $n_s$ and $n_{\mathrm{run}}$ 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 $n_s$ and $n_{\mathrm{run}}$ 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.

30 pages, 11 figures

References in corpus (10)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Cosmology and Fundamental Physics with the Euclid Satellite
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• Inflation and String Theory
• BICEP3: a 95 GHz refracting telescope for degree-scale CMB polarization
• The Lyth Bound of Inflation with a Tilt
• Compatibility of Planck and BICEP2 in the Light of Inflation
• BICEP2 implications for single-field slow-roll inflation revisited
• New constraints on the observable inflaton potential from WMAP and SDSS

Cited by in corpus (10)

• The Swampland: Introduction and Review
• The abundance of primordial black holes depends on the shape of the inflationary power spectrum
• Constraints on Scalar and Tensor spectra from $N_{eff}$
• Draining the Swampland
• Likelihood analysis of small field polynomial models of inflation yielding a high Tensor-to-Scalar ratio
• Small field models of inflation that predict a tensor-to-scalar ratio $r=0.03$
• On primordial black holes from an inflection point
• The Upper Bound on the Tensor-to-Scalar Ratio Consistent with Quantum Gravity
• Analytic Correlation of Inflationary Potential to Power Spectrum Shape: Limits of Validity, and `No-Go' for Small Field Model Analytics
• Numerical Analysis of the Primordial Power Spectrum for (Small Field) Inflationary Potentials