How well can we really determine the scale of inflation?

A detection of primordial B modes has been heralded not only as a smoking gun for the existence of inflation, but also as a way to establish the scale at which inflation took place. In this paper we critically reinvestigate the connection between a detection of primordial gravity waves and the scale of inflation. We consider whether the presence of additional fields and nonadiabaticity during inflation may have provided an additional source of primordial B modes competitive with those of the quasi–de Sitter vacuum. In particular, we examine whether the additional sources could provide the dominant signal, which could lead to a misinterpretation of the scale of inflation. In light of constraints on the level of non-Gaussianity coming from Planck we find that only hidden sectors with strictly gravitationally strong couplings provide a feasible mechanism. The required model building is somewhat elaborate, and so we discuss possible UV completions in the context of type IIB orientifold compactifications with Ramond-Ramond axions. We find that an embedding is possible and that dangerous sinusoidal corrections can be suppressed through the compactification geometry. Our main result is that even when additional sources of primordial gravity waves are competitive with the inflaton, a positive B-mode detection would still be a relatively good indicator of the scale of inflation. This conclusion will be strengthened by future constraints on both non-Gaussianity and cosmic microwave background polarization.

Figure 1

Change in the tensor power spectrum due to particle production $\mathrm{\Delta }{P}_t\equiv ({\mathrm{\Delta }}_t^2-{\mathrm{\Delta }}_{\text{std}}^2)/{\mathrm{\Delta }}_{\text{std}}^2$ with ${\mathrm{\Delta }}_{\text{std}}^2$ being the contribution from vacuum fluctuations during inflation for both the single ($N_{\text{events}}=1$) and multiple production cases ($N_{\text{events}}>1$). The lightly shaded region (gray) represents a tension with the Planck upperbound on equilateral-type non-Gaussianity ($|f_{\mathrm{NL}}^{\mathrm{equil}}|<42$), whereas in the dark shaded region particle production is clearly not competitive with the vacuum contribution. We note that even in cases where the signal is competitive, this does not necessarily imply a dominant contribution. Thus, we see that in both cases (single or multiple production) non-Gaussianity puts strong constraints on the tensor contribution. The multiple production case is rather insensitive to the coupling, but in both cases we have plotted results for $g=10^{-2}$ and $|f_{\mathrm{NL}}^{\mathrm{equil}}|=42$.

Figure 2

Change in the tensor power spectrum $\mathrm{\Delta }{P}_t\equiv ({\mathrm{\Delta }}_t^2-{\mathrm{\Delta }}_{\text{std}}^2)/{\mathrm{\Delta }}_{\text{std}}^2$ due to (gravitationally coupled) gauge field production as discussed in the text, with ${\mathrm{\Delta }}_{\text{std}}^2$ being the contribution from vacuum fluctuations during inflation. The medium gray region represents a tension with the Planck upperbound on equilateral-type non-Gaussianity ($|f_{\mathrm{NL}}^{\text{equil}}|<42$), whereas in the darkest shaded region gauge field production is not competitive with the vacuum contribution. The light gray region corresponds to the constraint coming from the backreaction of the produced gauge fields on the spectator scalar $\chi$. As plotted, the above graph is actually conservative as the real constraint requires the kinetic energy to be much greater than the gauge field energy ${\dot{\chi }}^2\gg {\overrightarrow{E}}^2+⟨{\overrightarrow{B}}^2⟩$. Given this caveat, the two white regions represent the available parameter space for the choices ${\epsilon }_{\chi }=\epsilon$ and the more realistic value ${\epsilon }_{\chi }<0.1\epsilon$ (${\epsilon }_{\chi }<\epsilon <1$ is required for $\chi$ to remain a spectator field).

Figure 3

A cartoon of the model for gauge field production from a sector $\chi$ that is gravitationally coupled to the inflaton $\varphi$.