The ultralight axion with mass around $10^{-22}$ eV is known as a candidate of dark matter. A peculiar feature of the ultralight axion is oscillating pressure in time, which produces oscillation of gravitational potentials. Since the solar system moves through the dark matter halo at the velocity of about $v \sim 300 \, \text{km} / \text{s} = 10^{-3}$, there exists axion wind, which looks like scalar gravitational waves for us. Hence, there is a chance to detect ultralight axion dark matter with a wide mass range by using laser interferometer detectors. We calculate the detector signal induced by the oscillating pressure of the ultralight axion field, which would be detected by future laser interferometer experiments. We also argue that the detector signal can be enhanced due to the resonance in modified gravity theory explaining the dark energy.Comment: 4 pages, 1 figure, published versio

We study the evolution of photon polarization during the photon-axion conversion process with focusing on the magnetic field configuration dependence. Most previous studies have been carried out in a conventional model where a network of magnetic domains is considered and each domain has a constant magnetic field. We investigate a more general model where a network of domains is still assumed, but each domain has a helical magnetic field. We find that the asymptotic behavior does not depend on the configuration of magnetic fields. Remarkably, we analytically obtain the asymptotic values of the variance of polarization in the conventional model. When the helicity is small, we show that there appears the damped oscillating behavior in the early stage of evolution.Moreover, we see that the constraints on the axion coupling and the cosmological magnetic fields using polarization observations are affected by the magnetic field configuration. This is because the different transient behavior of polarization dynamics is caused by the different magnetic field configuration. Recently, [C. Wang and D. Lai, J. Cosmol. Astropart. Phys. 06 (2016) 006.] claimed that the photon-axion conversion in helical model behaves peculiarly. However, our helical model gives much closer predictions to the conventional discontinuous magnetic field configuration model.

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.

It is known that a coherently oscillating axion field is a candidate of the dark matter. In the presence of the oscillating axion, the photon can be resonantly produced through the parametric amplification. In the universe, there also exist cosmological magnetic fields which are coherent electromagnetic fields. In the presence of magnetic fields, an axion can be converted into a photon, and vice versa. Thus, it is interesting to investigate what happens for the axion-photon system in the presence of both the axion dark matter and the magnetic fields. This system can be regarded as a coupled system of the axion and the photon whose equations contain the Mathieu type terms.We find that the instability condition is changed in the presence of magnetic fields in contrast to the conventional Mathieu equation. The positions of bifurcation points between stable and unstable are shifted and new instability bands appear. This is because the resonantly amplified axion can be converted to photon, and vice versa.

We discuss novel generalisations of Killing tensors, which are introduced by considering rational first integrals of geodesic equations. We introduce the notion of inconstructible generalised Killing tensors, which cannot be constructed from ordinary Killing tensors. Moreover, we introduce inconstructible rational first integrals, which are constructed from inconstructible generalised Killing tensors, and provide a method for checking the inconstructibility of a rational first integral. Using the method, we show that the rational first integral of the Collinson-O'Donnell solution is not inconstructible. We also provide several examples of metrics admitting an inconstructible rational first integral in two and four dimensions, by using the Maciejewski-Przybylska system. Furthermore, we attempt to generalise other hidden symmetries such as Killing-Yano tensors.PACS numbers: 02.40.Ky,04.20.-q ‡ It should be remarked that the idea of considering connections with totally skew-symmetric torsion was already proposed by Strominger [21] in the context of string theories, where such a torsion is identified with the 3-form flux livinging in the theories.