Probing the early Universe with axion physics and gravitational waves

We show results for the expected reach of the network of experiments that is being set up globally with the aim of detecting the “invisible” axion, in light of a nonstandard thermal history of the universe. Assuming that the axion is the dark matter, we discuss the reach of a successful detection by a given experimental setup in a particular axion mass window for different modifications of the cosmological background before primordial nucleosynthesis occurred. Results are presented both in the case where the present energy budget in cold axions is produced through the vacuum realignment mechanism alone, or in the case in which axionic strings also provide with additional contributions to the axion energy density. We also show that in some cosmological models, the spectrum of gravitational waves from the axionic string network would be within reach of the future network of detectors like LISA and DECIGO-BBO. We conclude that some scenarios describing the early universe can be probed jointly by the experimental efforts on axion detection and by gravity wave multimessenger astronomy.

Figure 1

The value of the axion mass (in $\mu \mathrm{eV})$ that yields the observed dark matter abundance for different cosmological scenarios. The vertical axis reports the effective equation of state $w_{\mathrm{eff}}$, while the horizontal axis is the reheat temperature. The dashed vertical black line marks the reheat temperature $T_{\mathrm{RH}}^{*}$ that matches the temperature at which the axion acquires a mass in the standard scenario, $T_{\mathrm{RH}}^{*}=T_{\mathrm{osc}}$. We also show the sensitivity that is expected to be reached by ABRACADABRA (“ABRA”, orange dot-dashed line), KLASH (red dashed line), ADMX (blue dot-dashed line), MADMAX (green dashed line), and IAXO (magenta dot-dashed line). The black dashed line marks the region beyond which the axion decay constant violates the weak gravity conjecture, $f_A\gtrsim M_{\mathrm{Pl}}$, while the black solid line “ASTRO” gives the bound on $m_A\gtrsim 15\mathrm{meV}$ excluded by astrophysical considerations [170, 171, 172, 173].

Figure 2

The value of the axion mass (in $\mu \mathrm{eV})$ that yields the observed dark matter abundance for different cosmological scenarios. The vertical axis reports the effective equation of state $w_{\mathrm{eff}}$, while the horizontal axis is the reheat temperature. The dashed vertical black line marks the reheat temperature $T_{\mathrm{RH}}^{*}$ that matches the temperature at which the axion acquires a mass in the standard scenario, $T_{\mathrm{RH}}^{*}=T_{\mathrm{osc}}$. We also show the sensitivity that is expected to be reached by ABRACADABRA (“ABRA”, orange dot-dashed line), KLASH (red dashed line), ADMX (blue dot-dashed line), MADMAX (green dashed line), and IAXO (magenta dot-dashed line). The black dashed line marks the region beyond which the axion decay constant violates the weak gravity conjecture, $f_A\gtrsim M_{\mathrm{Pl}}$, while the black solid line “ASTRO” gives the bound on $m_A\gtrsim 15\mathrm{meV}$ excluded by astrophysical considerations [170, 171, 172, 173].

Figure 3

The fractional contribution to the GW energy density ${\mathrm{\Omega }}_{\mathrm{GW}}$ in Eq. (40) in units of ${\mathrm{\Omega }}_s(t_{\mathrm{osc}})$, as a function of the quantity $\nu =f{t}_{\mathrm{osc}}$, assuming that an early matter-dominated stage has taken place to time $t_{\mathrm{RH}}=x_{\mathrm{RH}}{t}_{\mathrm{osc}}$. We have plotted the results for $x_{\mathrm{RH}}={10}^{-32}$ (blue dashed line), $x_{\mathrm{RH}}={10}^{-12}$ (red dotted line), $x_{\mathrm{RH}}={10}^{-4}$ (green dot-dashed line), and $x_{\mathrm{RH}}>1$ (black solid line).

Figure 4

The fractional contribution to the GW energy density ${\mathrm{\Omega }}_{\mathrm{GW}}$ to the critical density at present time, as a function of the frequency of the GW corrected for the redshift. We have plotted results for $T_{\mathrm{RH}}=1\mathrm{MeV}$ (solid black line), $T_{\mathrm{RH}}=10\mathrm{MeV}$ (dashed black line), $T_{\mathrm{RH}}=100\mathrm{MeV}$ (dotted black line). Also shown are the sensitivities of current (solid) and planned (dashed) experiments that are undergoing in detecting GWs, see the text for additional information.