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-$\alpha$ observations, and the consequences in the stability of self-gravitating objects made of axions.

In this work, we study tracker phantom dark energy models with a general parametrization of the scalar potentials. Our analysis also considers the scenario of having both phantom field and the cosmological constant as the dark energy components. A detailed statistical analysis with current cosmological observations shows an increase in the value of the Hubble parameter due to the presence of phantom dark energy but it cannot alleviate the Hubble tension completely. Our results using Bayesian methods suggest a decisive evidence in favor of a phantom field over a positive cosmological constant, although the possibility of a negative cosmological constant cannot be ruled out, hidden in the dark sector.

We consider here a full study of stellar dynamics from the brane-world point of view in the case of constant density and of a polytropic fluid. We start our study cataloguing the minimal requirements to obtain a compact object with a Schwarzschild exterior, highlighting the low and high energy limit, the boundary conditions, and the appropriate behavior of Weyl contributions inside and outside of the star. Under the previous requirements we show an extensive study of stellar behavior, starting with stars of constant density and its extended cases with the presence of nonlocal contributions. Finally, we focus our attention to more realistic stars with a polytropic equation of state, especially in the case of white dwarfs, and study their static configurations numerically. One of the main results is that the inclusion of the Weyl functions from brane-world models allows the existence of more compact configurations than within general relativity.