Observable gravitational waves from inflation with small field excursions

TL;DR

This work shows that single-field small-field inflation can produce observable tensor modes if the slow-roll parameter ε evolves non-monotonically, circumventing the Lyth bound. It presents a concrete mechanism and a well-motivated potential that achieve r ≥ 0.05 with Δφ ≤ $M_{ m P}$, while predicting a non-power-law scalar spectrum with scale-dependent running and small-scale power enhancement. Full numerical treatment beyond slow-roll reveals significant deviations from simple power-law predictions, implying distinct observational signatures and potential primordial black hole production. The authors also sketch a supergravity MSSM-based embedding, illustrating that such small-field models can be consistent with fundamental theory, albeit with tight parameter constraints.

Abstract

The detection of primordial gravitational waves, or tensor perturbations, would be regarded as compelling evidence for inflation. The canonical measure of this is the ratio of tensor to scalar perturbations, r. For single-field slow-roll models of inflation with small field excursions, the Lyth bound dictates that if the evolution of the slow-roll parameter epsilon is monotonic, the tensor-to-scalar ratio must be below observationally detectable levels. We describe how non-monotonic evolution of epsilon can evade the Lyth bound and generate observationally large r, even with small field excursions. This has consequences for the scalar power spectrum as it necessarily predicts an enhancement in the spectrum at very small scales and significant scale-dependent running at CMB scales. This effect has not been appropriately accounted for in previous analyses. We describe a mechanism that will generically produce the required behaviour in epsilon and give an example of this mechanism arising in a well-motivated small-field model. This model can produce r\geq0.05 while satisfying all current observational constraints.

Figures (4)

• Figure 1: Left panel: The behaviour of the slow-roll parameters as a function of inflaton field value $\phi$, measured in units of $M_{\rm P}$, for the model parameters given in equation (\ref{['sample']}). Right panel: $\epsilon$ as a function of $\phi$ for the same parameters, shown with a magnified scale.
• Figure 2: Power $P(k)$ for the model parameters of equation \ref{['sample']} for the entire range of scales $k$ that cross the horizon during the $N_\mathrm{req}$$e$-folds of inflation. The solid blue curve is obtained from the slow-roll approximation and the red dashed curve from a full numerical calculation. Inset: The fractional difference $(P_\mathrm{num}-P_\mathrm{s.r.})/P_\mathrm{num}$ between the numerical calculation and the slow-roll approximation at large scales corresponding to the current observational window.
• Figure 3: The fractional difference between the numerically evaluated power spectrum $P(k)$ for parameters in equation \ref{['sample']} and the assumed power-law form with the values of $A_k=2.3\times10^{-9}$ and $n_s=0.98$ at the pivot scale $k_{\rm piv}=0.002$ Mpc$^{-1}$ to which the model was matched as described in the text.
• Figure 4: The fractional difference between the numerically evaluated power spectrum $P(k)$ and the assumed power-law form to which the values of $A_k$, $n_s$ and $\alpha$ are matched at the pivot scale $k_{\rm piv}=0.002$ Mpc$^{-1}$. The green dash-dot curve is for model 1, the blue dashed curve for model 2 and the red solid curve for model 3. The various models are described in section \ref{['sec:beyondSR']}. Model 1 is taken from BenDayan:2009kv and model 2 from Rehman:2010. Note that although the power spectra are matched to the power-law form at the pivot scale, they all necessarily deviate from this form at other scales within the observational window. Only model 3 matches the power-law to within current observational accuracy.