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We investigate the dynamical features of a large family of running vacuum cosmologies for which $Lambda$ evolves as a polynomial in the Hubble parameter. Specifically, using the critical point analysis we study the existence and the stability of singular solutions which describe de-Sitter, radiation and matter dominated eras. We find several classes of $Lambda(H)$ cosmologies for which new analytical solutions are given in terms of Laurent expansions. Finally, we show that the Milne universe and the $R_{h}=ct$ model can be seen as perturbations around a specific $Lambda(H)$ model, but this model is unstable.
Current astronomical observations are successfully explained by the present cosmological paradigm based on the concordance model ($Lambda_0$CDM + Inflation). However, such a scenario is composed of a heterogeneous mix of ingredients for describing th
Although the standard cosmological model explains most of the observed phenomena it still struggles with the problem of initial singularity. An interesting scenario in which the problem of the initial singularity is somehow circumvented was proposed
Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration constant. Recent
Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann-Lemaitre-Robertson-Walker metrics. The
In this paper we consider a specific type of the bimetric theory of gravitation with the two different metrics introduced in the cosmological frame. Both metrics respect all the symmetries of the standard FLRW solution and contain conformally related