Abstract: Despite the fact that the Lambda CDM model has been highly successful over the last few decades in providing an accurate fit to a broad range of cosmological and astrophysical observations, different intriguing tensions and anomalies emerged at various statistical levels. Given the fact that the dark energy and the dark matter sectors remain unexplored, the answer to some of the tensions may rely on modifications of these two dark sectors. This manuscript explores the important role of the growth of structure in constraining non-standard cosmologies. In particular, we focus on the interacting dark energy (IDE) scenario, where dark matter and dark energy interact non-gravitationally. We aim to place constraints on the phenomenological parameters of these alternative models, by considering different datasets related to a number of cosmological measurements, to achieve a complementary analysis. A special emphasis is devoted to redshift-space distortion measurements (RSD), whose role in constraining beyond the standard paradigm models has not been recently highlighted. These observations indeed have a strong constraining power, rendering all parameters to their Lambda CDM canonical values, and therefore leaving little room for the IDE models explored here.

Abstract: This study uses a nonsingular Yukawa-modified potential to obtain a static and spherically symmetric black hole solution with a cosmological constant. Such Yukawa-like corrections are encoded in two parameters, alpha and lambda, that modify Newton's law of gravity in large distances, and a deformation parameter l(0), which plays an essential role in short distances. The most significant effect is encoded in alpha, which modifies the total black hole mass with an extra mass proportional to alpha M, mimicking the dark matter effects at large distances from the black hole. On the other hand, the effect due to lambda is small for astrophysical values. We scrutinize the quasinormal frequencies and shadows associated with a spherically symmetric black hole and the thermodynamical behavior influenced by the Yukawa potential. In particular, the thermodynamics of this black hole displays a rich behavior, including possible phase transitions. We use the WKB method to probe the quasinormal modes of massless scalar, electromagnetic, and gravitational field perturbations. In order to check the influence of the parameters on the shadow radius, we consider astrophysical data to determine their values, incorporating information on an optically thin radiating and infalling gas surrounding a black hole to model the black hole shadow image. In particular, we consider Sgr A* black hole as an example and we find that its shadow radius changes by order of 10(-9), meaning that the shadow radius of a black hole with Yukawa potential practically gives rise to the same result encountered in the Schwarzschild black hole. Also, in the eikonal regime, using astrophysical data for Yukawa parameters, we show that the value of the real part of the QNMs frequencies changes by 10(-18). Such Yukawa-like corrections are, therefore, difficult to measure by observations of gravitational waves using the current technology.