Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In this paper, we review some fundamental concepts to understand Bayesian statistics and then introduce MCMC algorithms and samplers that allow us to perform the parameter inference procedure. We also introduce a general description of the standard cosmological model, known as the $\mathsf{\Lambda }$CDM model, along with several alternatives, and current datasets coming from astrophysical and cosmological observations. Finally, with the tools acquired, we use an MCMC algorithm implemented in python to test several cosmological models and find out the combination of parameters that best describes the Universe.

The main aim of this paper is to provide cosmological constraints on the multiscalar field dark matter model, in which we assume the dark matter is made up of different ultralight scalar fields. As a first approximation, we consider they are real and do not interact with each other. We study the equations for both the background and perturbations for $N$-fields and present the evolution of the density parameters, the mass power spectrum, and the cosmic microwave background spectrum. In particular, we focus on two scalar fields with several combinations for the potentials $V(\varphi )=1/2m_{\varphi }^2{\varphi }^2$, $V(\varphi )=m_{\varphi }^2{f}^2[1+\cos (\varphi /f)]$, and $V(\varphi )=m_{\varphi }^2{f}^2[\cosh (\varphi /f)-1]$, however, the work, along with the code, could be easily extended to more fields. We use the data from baryon acoustic oscillation, big bang nucleosynthesis, Lyman-$\alpha$ forest, and supernovae to find constraints on the sampling parameters for the cases of a single field and double field, along with the Bayesian evidence. We found that some combinations of the potentials get penalized through the evidence, however, for others there is a preference as good as for the cold dark matter.

In a previous work it was shown that by considering the quantum nature of the gravitational field mediator, it is possible to introduce the momentum energy of the graviton into the Einstein equations as an effective cosmological constant. The Compton Mass Dark Energy (CMaDE) model proposes that this momentum can be interpreted as dark energy, with a Compton wavelength given by the size of the observable universe $R_H$, implying that the dark energy varies depending on this size. The main result of this previous work is the existence of an effective cosmological constant $\Lambda=2\pi^2/\lambda^2$ that varies very slowly, being $\lambda=(c/H_0) R_H$ the graviton Compton wavelength. In the present work we use that the dark energy density parameter is given by $\Omega_\Lambda=2\pi^2/3/R_H^2$, it only has the curvature $\Omega_k$ as a free constant and depends exclusively on the radiation density parameter $\Omega_r$. Using $\Omega_{0r} = 9.54\times10^{- 5}$, the theoretical prediction for a flat universe of the dark energy density parameter is $\Omega_{0\Lambda} = 0.6922$. We perform a general study for a non-flat universe, using the Planck data and a modified version of the CLASS code we find an excellent concordance with the Cosmic Microwave Background and Mass Power Spectrum profiles, provided that the Hubble parameter today is $H_0 = 72.6$ km/s/Mpc for an universe with curvature $\Omega_{0k}=-0.003$. We conclude that the CMaDE model provides a natural explanation for the accelerated expansion and the coincidence problem of the universe.

En esta contribución, estudiamos las secciones de dispersión y absorción del agujero negro de Hayward rodeado por quintaesencia. Se muestra cómo se modifica el comportamiento de las secciones transversales de dispersión clásica y semiclásica al variar el valor de factor de normalización dependiente de la densidad de quintaescencia. Además, se estudia la sección de absorción con la aproximación sinc en el límite eikonal. En ambos casos se considera el parámetro de estado de quintaesencia en los casos particulares ω = −2/3 y ω = −4/9.

La Relatividad General (RG) de Einstein describe la gravedad como una manifestación de la curvatura del espacio-tiempo. Una de sus predicciones más fascinantes es la existencia de agujeros negros, objetos tan compactos que ni siquiera la luz puede escapar de su interior. Este artículo de revisión presenta un análisis introductorio de las geodésicas nulas (trayectorias de fotones) en el espacio-tiempo de Schwarzschild, la solución más elemental de las ecuaciones de Einstein en el vacío, que describe un agujero negro sin rotación ni carga. Se revisan los fundamentos de las ecuaciones de campo de Einstein y la métrica de Schwarzschild, destacando las propiedades del horizonte de eventos y la singularidad. El objetivo central es estudiar las trayectorias, o geodésicas, que sigue la luz en este entorno, el cual está determinado por el parámetro de impacto. Mediante el uso del método numérico de Runge-Kutta de cuarto orden aplicado a la ecuación de la órbita, se analizan y discuten los tres regímenes posibles para un fotón: la desviación gravitacional, las órbitas circulares inestables en la esfera de fotones y la captura definitiva por el agujero negro. Los resultados de las simulaciones se presentan y contrastan con las predicciones teóricas. Finalmente, se discuten las implicaciones de estos hallazgos para la astrofísica moderna, como la sombra de los agujeros negros, y se señalan posibles direcciones para investigaciones futuras.