Pulsar timing signal from ultralight axion inf(R)theory

Abstract

An ultralight axion around 10 −23 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.

Nonlinear resonant oscillation of gravitational potential induced by ultralight axion in f(R) gravity

“…We first consider the f (R) ∝ R 2 model, which can be solved analytically. We have already studied this model in the previous paper in the framework of f (R) gravity [30]. However, since the model is useful for qualitative understanding of general f (R) models, here we again discuss the same model in the scalar-tensor theory.…”

“…In this section, we will summarize our previous work [30] and derive the formula (15). Then, we move on to the scalar-tensor formulation of f (R) gravity and derive the main formula (30) for calculating the timedependent part of the gravitational potential in f (R) gravity.…”

“…Therefore, in order to obtain the time-dependent part of the gravitational potential in the scalar-tensor formulation, we first calculate the effective potential from a function f (R) by using Eq. ( 28), solve the equation of motion (29), and then substitute the solution into the formula (30).…”

“…In our previous paper [30], we have discussed the detectability of the ultralight axion dark matter in the framework of f (R) gravity, which is the simplest modified gravity. We derived the gravitational potential sourced by the axion oscillation in the f (R) ∝ R 2 model.…”

Exploring String Axions with Gravitational Waves

“…Remarkably, the mass of string axions can take values in the broad range from 10 −33 eV to 10 3 eV [1,2]. In order to explore the string axiverse, we can use the cosmic microwave background radiations (CMB) [3], the large scale structure of the universe [4], pulsar timing arrays [5][6][7], interferometer detectors [8,9], the dynamics of binary system [10], cosmological gravitational waves (GWs) [11], black hole physics [12], electromagnetic waves propagating in the axion background [13,14], and nuclear spin precession [15]. On top of these methods, we proposed a novel way to explore the string axions with gravitational waves [16].…”