Axion Cosmology and the Energy Scale of Inflation (0807.1726v3)

Abstract: We survey observational constraints on the parameter space of inflation and axions and map out two allowed windows: the classic window and the inflationary anthropic window. The cosmology of the latter is particularly interesting; inflationary axion cosmology predicts the existence of isocurvature fluctuations in the CMB, with an amplitude that grows with both the energy scale of inflation and the fraction of dark matter in axions. Statistical arguments favor a substantial value for the latter, and so current bounds on isocurvature fluctuations imply tight constraints on inflation. For example, an axion Peccei-Quinn scale of 10^16 GeV excludes any inflation model with energy scale > 3.8*10^14 GeV (r > 2*10^-9) at 95% confidence, and so implies negligible gravitational waves from inflation, but suggests appreciable isocurvature fluctuations.

• The paper revisits Peccei-Quinn symmetry to show that axion physics imposes crucial constraints on the inflation energy scale.
• It demonstrates that isocurvature fluctuations in the CMB significantly limit high-energy inflation models, especially in axion dark matter scenarios.
• The study suggests that future CMB measurements could unveil axion-induced isocurvature perturbations, refining our understanding of inflation.

Axion Cosmology and the Energy Scale of Inflation: A Critical Overview

The paper by Hertzberg, Tegmark, and Wilczek presents an intricate analysis of the constraints imposed by axion physics and inflationary cosmology. By exploring the intersections of these areas, the authors provide a comprehensive survey of the parameter space concerning the energy scale of inflation ($E_I$) and the Peccei-Quinn (PQ) scale ($f_a$) associated with axions.

Key Findings

The paper meticulously delineates two specific regions within the parameter space, termed as the "classic" and the "inflationary anthropic" windows. The paper's analytical framework indicates significant constraints that these windows impose on both models of inflation and axion cosmology. The research highlights the existence of isocurvature fluctuations in the Cosmic Microwave Background (CMB), whose amplitude is influenced by $E_I$ and the fraction of dark matter composed of axions. Notably, the isocurvature constraints restrict inflation models with high energy scales.

First, in the context of axion physics, the paper revisits the PQ symmetry and its spontaneous breaking, which leads to the axion as a potential answer to the strong CP problem in QCD. The research underscores the significance of the PQ scale $f_a$, noting theoretical arguments favoring its association with unification scales. Statistical considerations further imply that a substantial portion of dark matter in the universe has a high probability of being axion dark matter.

In terms of inflation, the authors articulate that high values of $E_I$ are compelling due to their ability to predict the observed spectral index $n_s\sim0.96$. The paper argues for constraints on $E_I$ with optimistic interpretations suggesting that gravitational wave signals from primordial processes might be negligible unless isocurvature fluctuations are adequately explored. It posits a pivotal role for isocurvature constraints in future studies, which could provide insights beyond the detection capabilities of gravitational wave probes.

Implications and Future Directions

Practically, the work challenges several established inflationary models, asserting that high-scale inflation, where $E_I\gtrsim2.6\times10^{14}$\,GeV, encounters theoretical and observational hurdles. This carries significant ramifications for models predicting substantial gravity wave signatures, compelling the cosmology community to explore lower values of $E_I$ further.

Theoretically, this research marks a substantial step in understanding the potential multiverse implications and the selection effects on anthropic grounds, particularly in the exploration of axion-induced isocurvature fluctuations. It nudges towards a paradigm shift, where low-energy inflationary models and axion-driven isocurvature perturbations become increasingly relevant areas of investigation.

Speculative projections in the paper suggest that forthcoming advancements in CMB measurements, such as those from the Planck satellite and other future missions, should aim for enhanced sensitivity to isocurvature modes, potentially uncovering axion evidence and offering indirect probes into the inflationary epoch.

Conclusion

This robust intersectional paper signifies substantial progress in simultaneously constraining inflationary and axion models. As these fields continue to mature, the interplay between isocurvature constraints, gravitational wave limits, and axion physics has the potential to not only refine the existing theoretical models but also guide the development of new physics beyond the standard cosmological paradigm. Future work should build on these findings by pursuing refined observational capabilities and deeper theoretical insights into the axion field's role in the early universe dynamics.