Axion Cosmology and the Energy Scale of Inflation

TL;DR

The paper investigates how combining inflationary physics with QCD axion cosmology constrains the fundamental parameters $E_I$ and $f_a$. By computing the axion abundance $\xi_a$, axion-induced isocurvature $\alpha_a$, and primordial tensor amplitude $Q_t$ as functions of $E_I$, $f_a$, and the misalignment angle $\theta_i$, and applying current bounds from WMAP5/Planck-like data, it identifies two viable regimes: a classic window and an inflationary anthropic window. A key result is that a large PQ scale $f_a\sim 10^{16}$ GeV implies an upper limit on the inflation scale, $E_I\lesssim 3.8\times 10^{14}$ GeV (roughly $r\lesssim 2\times 10^{-9}$), which disfavors many high-scale inflation models while predicting detectable isocurvature fluctuations if axions contribute a non-negligible fraction of dark matter. The work highlights the complementary role of isocurvature and tensor modes in constraining fundamental physics and guides future axion searches (e.g., ADMX) and cosmological probes for isocurvature signals.

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.

Figures (3)

• Figure 1: Naive expectations for the energy scale of inflation $E_I$ and the axion PQ scale $f_a$. For $E_I\gtrsim2.4\times10^{16}$ GeV, the inflaton must undergo super-Planckian excursions in field space (in single field models). For $E_I\lesssim6.7\times10^{15}$ GeV, generic inflation potentials fail to reproduce the observed nearly scale invariant power spectrum. For $f_a\gtrsim2.4\times10^{18}$ GeV, the PQ breaking scale is super-Planckian. For $f_a\lesssim10^{15}$ GeV (and $f_a\gg$ TeV), the PQ breaking is in the "desert" of particle physics and non-trivial to achieve in string theory. This leaves the region labeled "naive window".
• Figure 2: Observational constraints on the energy scale of inflation $E_I$ and the axion PQ scale $f_a$ are shown in the top (bottom) panel for inefficient (efficient) thermalization at the end of inflation. The thick red diagonal line is $f_a=\hbox{Max}\{T_{\hbox{\tiny{GH}}}=H_I/2\pi,T_{\hbox{\tiny{max}}}=\epsilon_{\hbox{\tiny{eff}}}\,E_I\}$, ($\epsilon_{\hbox{\tiny{eff}}}\approx0$ in top, $\epsilon_{\hbox{\tiny{eff}}}=10^{-3}$ in bottom, with $\epsilon_{\hbox{\tiny{eff}}}=10^{-1.5}$, 1 indicated). Above this line is the inflationary anthropic scenario and below this line is the classic scenario. The region in which there is too much isocurvature, $\alpha_a>0.072$, depends on the axion fraction $R_a\equiv\xi_a/\xi_{\hbox{\tiny{CDM}}}$ of the CDM; the purple region applies for any $R_a$, the blue region is for $R_a>0.25\%$ (which is expected at 95% confidence), and the cyan region is for $R_a=100\%$. The green region has too much axion CDM: $\xi_a>2.9$ eV. Each constraint is divided into two parts: the darker part is for a conservative value $\chi=1/20$ and the lighter part is for a moderate value $\chi=1$. The orange region has excessive GWs amplitude: $Q_t>9.3\times 10^{-6}$. The yellow region has too much axion interaction in stars (darker is firmly ruled out, lighter is for some analyzes). The brown region is excluded by the laboratory ADMX search. The dashed cyan, orange, and brown lines are future targets for isocurvature, GWs, and ADMX searches, respectively.
• Figure 3: Axion mass $m_a$ (solid) and axion energy density $\rho_a$ (dashed), as a function of temperature $T$ (or time $t$). The red and blue curves are for PQ breaking scales $f_a=10^{12}$ GeV and $f_a=10^{15}$ GeV, respectively. The arrow indicates the effect of increasing $f_a$. The decreasing orange curve is the Hubble parameter $3H$. We have taken $\langle\theta^2\rangle=\pi^2/3$, although this is modified by the intervention of inflation, as explained in the text. For simplicity, we have here only kept track of the variation with temperature in the number of relativistic degrees of freedom before ($g_*=g_{*S}=61.75$) and after ($g_*=g_{*S}=10.75$) the QCD phase transition, and taken $\chi=1$.