Pulsar timing signal from ultralight axion in f ( R ) theory
Arata Aoki, Jiro Soda · 2016 · 20 citationsRead the paper
An ultralight axion around $1{0}^{\ensuremath{-}23}\text{ }\mathrm{eV}$ is known as a viable dark matter candidate. A distinguished feature of such a dark matter is the oscillating pressure which produces the oscillation of the gravitational potential with frequency in the nano-Hz range. Recently, Khmelnitsky and Rubakov pointed out that this time dependent potential induces the pulse arrival residual and could be observed by the Square Kilometre Array (SKA) experiment. In this paper, we study the detectability of the oscillating pressure of the axion in the framework of $f(R)$ theory, and show that the amplitude of the gravitational potential can be enhanced or suppressed compared to that in Einstein's theory depending on the parameters of the $f(R)$ model and mass of the axion. In particular, we investigate the Hu-Sawicki model and find the condition that the Hu-Sawicki model is excluded.
What the full text shows
Theory or simulation- The amplitude of the gravitational potential induced by ultralight axions in the $R^2$ model is enhanced or suppressed relative to Einstein's theory depending on the mass scale $M$. — $ rac{ ext{amplitude}}{ ext{Einstein amplitude}} = rac{1}{1 - (2m/M)^2}$ ($f(R) = R^2/6M^2$ model)
- The gravitational potential amplitude is dramatically amplified due to resonance when the mass scale $M$ approaches twice the axion mass $2m$. ($M o 2m$)
- The Hu-Sawicki model is excluded if the observed mass scale $M$ is below a specific minimum value. — $M < 0.76 imes 10^{-23} ext{ eV}$ (Hu-Sawicki model)
- The Hu-Sawicki model is incompatible with ultralight axion dark matter for certain parameters due to instability caused by non-linear terms. ($M o 2m$ or $M ext{ in the Einstein limit } (M ext{ is large})$)
- Setup
- Theoretical analysis using a dark matter halo energy density of $0.3 ext{ GeV/cm}^3$ and axion mass $m ext{ around } 10^{-23} ext{ eV}$.
- How
- The authors derived the time-dependent gravitational potential $\delta ext{Phi}$ by solving the trace of the $f(R)$ field equations using the oscillating pressure of an ultralight axion field as the source. They compared the results of the $R^2$ and Hu-Sawicki models against Einstein's general relativity.
- Limitations
- The analysis assumes the spatial derivative of $f_R$ is much smaller than its time derivative. · The $R^2$ model results ignore homogeneous solutions that oscillate freely with frequency $M$.
Summarized by Gemma 4 from the open-access full text · 8 Oct 2026. Read it