Natural inflation with multiple sub-Planckian axions

Abstract: We extend the Kim-Nilles-Peloso (KNP) alignment mechanism for natural inflation to models with $N>2$ axions, which obtains a super-Planckian effective axion decay constant $f_{\textrm{eff}}\gg M_{Pl}$ through an alignment of the anomaly coefficients of multiple axions having sub-Planckian fundamental decay constants $f_0\ll M_{Pl}$. The original version of the KNP mechanism realized with two axions requires that some of the anomaly coefficients should be of the order of $f_{\textrm{eff}}/f_0$, which would be uncomfortably large if $f_{\rm eff}/f_0 \gtrsim {\cal O}(100)$ as suggested by the recent BICEP2 results. We note that the KNP mechanism can be realized with the anomaly coefficients of $\mathcal{O}(1)$ if the number of axions $N$ is large as $N\ln N\gtrsim 2\ln (f_{\textrm{eff}}/f_0)$, in which case the effective decay constant can be enhanced as $f_{\rm eff}/f_0 \sim \sqrt{N !}\,n^{N-1}$ for $n$ denoting the typical size of the integer-valued anomaly coefficients. Comparing to the other multiple axion scenario, the N-flation scenario which requires $N \sim f_{\textrm{eff}}^2/f_0^2$, the KNP mechanism has a virtue of not invoking to a too large number of axions, although it requires a specific alignment of the anomaly coefficients, which can be achieved with a probability of ${\cal O}(f_0/f_{\rm eff})$ under a random choice of the anomaly coefficients. We also present a simple model realizing a multiple axion monodromy along the inflaton direction.

• The paper extends the KNP mechanism to model natural inflation with more than two axions, enabling a super-Planckian effective decay constant.
• It employs the alignment of integer-valued anomaly coefficients to enhance decay constants without requiring individual axion scales above the Planck mass.
• This methodology offers a viable framework for reconciling string theory constraints with high-energy inflationary observations such as those from BICEP2.

Analysis of "Natural inflation with multiple sub-Planckian axions"

In this paper, Choi, Kim, and Yun extend the Kim-Nilles-Peloso (KNP) alignment mechanism employed in models of natural inflation to configurations involving more than two axion fields. The primary goal is to achieve a super-Planckian effective axion decay constant, $f_{\text{eff}}$, without recourse to axion decay constants that individually exceed the Planck scale, $M_{Pl}$. This extension seeks to address the implications of the BICEP2 results, which indicate a high inflation scale, inferring the necessity of a super-Planckian field excursion.

Context and Motivation

Natural inflation is predicated on the hypothesis that the inflaton, typically an axion, experiences a periodic potential characterized by a decay constant. For successful slow-roll inflation, particularly to match the recent BICEP2 observations, the effective decay constant must significantly exceed the Planck mass. Traditional models faced challenges in providing such large decay constants from realistic theoretical frameworks, including string theory, which typically predicts sub-Planckian axion scales.

Extending the KNP Mechanism

The original KNP mechanism leveraged the alignment of anomaly coefficients between two axions to realize a large $f_{\text{eff}}$. However, the requirement that the coefficients were large posed practical issues. This study proposes a generalization to $N > 2$ axion fields, enabling large $f_{\text{eff}}$ without the necessity for unreasonably large individual coefficients.

The authors propose that when $N$ axions are considered, and if the relative alignment of integer-valued anomaly coefficients is chosen appropriately, the effective decay constant can increase significantly as $f_{\text{eff}}/f_i \sim \sqrt{N!} n^{N-1}$, where $f_i$ represents the fundamental decay constants, and $n$ symbolizes the characteristic magnitude of these coefficients. The implication is that only moderately large numbers of axions, with suitably aligned coefficients, are needed to achieve super-Planckian values.

This extended framework is beneficial as it mitigates against requiring high individual coefficients, which would otherwise conflict with constraints from fundamental theories. The authors identify that a probability of $\mathcal{O}(f_i/f_{\text{eff}})$ exists for achieving effective alignment, thus improving the likelihood of naturally occurring such conditions in theoretical constructs.

Implications and Future Directions

From a theoretical standpoint, the study advances our understanding of how enhanced axionic decay constants may naturally arise, potentially alleviating some of the pressures to reconsider effective field theory models in light of quantum gravitational constraints. It offers a feasible workaround to the constraints imposed by string theory, thus presenting a viable path to unify high-energy inflationary models with a more grounded theoretical base.

Practically, these findings could augment the range of models available to explain early-universe phenomena that align with recent observations like those from BICEP2. Researchers could further optimize the balance between the number of axions and the stringency of coefficient alignment, maximizing $f_{\text{eff}}$ while minimizing model complexity.

Conclusion

This work signifies a methodical advancement in the framework of natural inflation models. By employing $N$-axion concepts, it demonstrates a more substantial potential for resolving the high decay constant prerequisite inferred from contemporary cosmic observations. Future research could explore the application of these models to broader classes of string-theory-derived potentials, further cementing their compatibility with high energy-scale phenomena. This strategic direction might also inspire new approaches within inflationary cosmology, offering deeper insights into the interplay between cosmological observations and foundational physics.