Nonlinearities in a realistic axion field potential may play an important role in the cosmological dynamics. In this paper we use the Boltzmann code CLASS to solve the background and linear perturbations evolution of an axion field and contrast our results with those of CDM and the free axion case. We conclude that there is a slight delay in the onset of the axion field oscillations when nonlinearities in the axion potential are taken into account. Besides, we identify a tachyonic instability of linear modes resulting in the presence of a bump in the power spectrum at small scales. Some comments are in turn about the true source of the tachyonic instability, how the parameters of the axionlike potential can be constrained by Ly-α observations, and the consequences in the stability of self-gravitating objects made of axions.
INTRODUCTIONModern cosmological observations have brought about a large amount of data [1,2], making it possible to constrain, with high accuracy, theoretical models describing the Universe at large scales. The so-called Lambda Cold Dark Matter (ΛCDM) paradigm is very successful at reproducing cosmological observations [1] but it requires a dark matter (DM) component (≈ 26%), effectively described by collisionless particles that interacts mostly gravitationally with other matter components [3][4][5]. However, there are longstanding discussions about how well the ΛCDM model describes the Universe at galactic and sub-galactic scales [6,7]. The solution to these problems may come from the specific properties of the DM, or from an interplay between the DM properties and kinematic effects with baryons, but still the incompleteness of galactic observations may impair our ability to infer the DM distribution properties from them. Given the current status, the further development of theoretical models still is very much desirable if one is to elucidate the properties of this matter component of the Universe.According to recent studies, axion DM has become a compelling candidate to replace CDM [8][9][10], and even some experiments have been already set up to have a direct detection of this elusive particle [11][12][13][14][15][16]. In particular, there are several proposals for detection of ultralight axions (ULA) using laser interferometers [17], analyzing the frequency and dynamics of pulsars [18,19], and also in gravitational wave detectors [20]. Nonetheless, there are still many open questions such as what is the right axion mass limits one can place by using, for instance, galactic kinematics [21][22][23][24][25], and Lyman-α observations [26,27]. At the cosmological level, axion models have been studied considering it as a free scalar field, i.e., as a scalar field endowed with a quadratic potential V (φ) = m 2 φ 2 /2 [28-33]. However, a more realistic form of the axion potential is the trigonometric one,where m φ is the axion mass and f is the decay constant of the axion. The axion potential (1) originally arose in QCD with the aim to solve the strong CP problem [34][35][36][37], and the poten...
