Based on a dispersive approach, we apply the inverse amplitude method to unitarize one-loop SU(2) and SU(3) chiral perturbation theory. Numerically, we find that this unitarization technique yields the correct complex analytic structure in terms of cuts and poles. Indeed, using the chiral parameter estimates obtained from low-energy experiments we obtain the poles associated with the $\rho \mathrm{}\left(770\right)\mathrm{}$ and $K^{*}\mathrm{}\left(982\right)\mathrm{}$ resonances. Just by fixing their actual masses we obtain a parametrization of the $\pi \pi$ and $\pi K$ phase shifts in eight different channels. With this fit we have then calculated several low-energy phenomenological parameters estimating their errors. Among others, we have obtained the chiral parameters and scattering lengths, which can be relevant for future experiments.

In the context of $f(R)$ theories of gravity, we address the problem of finding static and spherically symmetric black hole solutions. Several aspects of constant curvature solutions with and without electric charge are discussed. We also study the general case (without imposing constant curvature). Following a perturbative approach around the Einstein-Hilbert action, it is found that only solutions of the Schwarzschild-(anti) de Sitter type are present up to second order in perturbations. Explicit expressions for the effective cosmological constant are obtained in terms of the $f(R)$ function. Finally, we have considered the thermodynamics of black holes in anti-de Sitter space-time and found that this kind of solution can only exist provided the theory satisfies $R_0+f(R_0)<0$. Interestingly, this expression is related to the condition which guarantees the positivity of the effective Newton’s constant in this type of theories. In addition, it also ensures that the thermodynamical properties in $f(R)$ gravities are qualitatively similar to those of standard general relativity.

In this work we consider the possibility of describing the current evolution of the universe, without the introduction of any cosmological constant or dark energy (DE), by modifying the Einstein-Hilbert (EH) action. In the context of the $f(R)$ gravities within the metric formalism, we show that it is possible to find an action without cosmological constant which exactly reproduces the behavior of the EH action with cosmological constant. In addition the $f(R)$ action is analytical at the origin having Minkowski and Schwarzschild solutions as vacuum solutions. The found $f(R)$ action is highly nontrivial and must be written in terms of hypergeometric functions but, in spite of looking somewhat artificial, it shows that the cosmological constant, or more generally the DE, is not a logical necessity.

We apply the one-loop results of the $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_R$ chiral perturbation theory supplemented with the inverse-amplitude method to fit the available experimental data on $\pi \pi$ and $\pi K$ scattering. With essentially only three parameters we describe accurately data corresponding to six different channels: namely, $(I, J)=(0, 0), (2, 0), (1, 1), (\frac{1}{2}, 0), (\frac{3}{2}, 0), \mathrm{and} (\frac{1}{2}, 1)$. In addition we reproduce the first resonances of the (1,1) and (½,1) channel with the right mass corresponding to the $\rho$ and the $K^{*} \mathrm{}\left(892\right)\mathrm{}$ particles.