Despite the many efforts, our theoretical understanding of the ultimate nature of the dark energy component of the universe still lags well behind the astounding experimental evidence achieved from the increasingly sophisticated observational tools at our disposal. While the canonical possibility is a strict cosmological constant, or rigid vacuum energy density ρ Λ =const., the exceeding simplicity of this possibility lies also at the root of its unconvincing theoretical status, as there is no explanation for the existence of such constant for the entire cosmic history. Herein we explore general models of the vacuum energy density slowly evolving with the Hubble function H and/or its time derivative, ρ Λ = ρ Λ (H,Ḣ). Some of these models are actually well-motivated from the theoretical point of view and may provide a rich phenomenology that could be explored in future observations, whereas some others have more limitations. In this work, we put them to the test and elucidate which ones are still compatible with the present observations and which ones are already ruled out. We consider their implications on structure formation, in combination with data on type Ia supernovae, the Cosmic Microwave Background, the Baryonic Acoustic Oscillations, and the predicted redshift distribution of cluster-size collapsed structures. The relation of these vacuum models on possible evidence of dynamical dark energy recently pointed out in the literature is also briefly addressed. Keywords: dynamical dark energy, cosmological constant, structure formation. arXiv:1409.7048v3 [astro-ph.CO] 27 Nov 2014 7.1 Generalized Press-Schechter formalism 40 7.2 Numerical results: number counts of the dynamical vacuum models 45 8. Discussion and conclusions 48 A. Understanding how the cluster number counts method works 51 B. Computing the collapse density threshold δ c for the dynamical vacuum models 53 B.1 Type-A models 54 B.2 Type-B models 55 B.3 Numerical procedure to determine δ c 55 -1 -1 The linear terms also appear if nonperturbative infrared effects would be possible in the cosmological

Despite the fact that a rigid Λ-term is a fundamental building block of the concordance ΛCDM model, we show that a large class of cosmological scenarios with dynamical vacuum energy density ρ Λ and/or gravitational coupling G, together with a possible non-conservation of matter, are capable of seriously challenging the traditional phenomenological success of the ΛCDM. In this paper, we discuss these "running vacuum models" (RVM's), in which ρ Λ = ρ Λ (H) consists of a nonvanishing constant term and a series of powers of the Hubble rate. Such generic structure is potentially linked to the quantum field theoretical description of the expanding Universe. By performing an overall fit to the cosmological observables SNIa+BAO+H(z)+LSS+BBN+CMB (in which the WMAP9, Planck 2013 and Planck 2015 data are taken into account), we find that the class of RVM's appears significantly more favored than the ΛCDM, namely at an unprecedented level of 4.2σ. Furthermore, the Akaike and Bayesian information criteria confirm that the dynamical RVM's are strongly preferred as compared to the conventional rigid Λ-picture of the cosmic evolution. Subject headings: dark energy-dark matter-large-scale structure of universe

No abstract

Perhaps the deepest mystery of our accelerating universe in expansion is the existence of a tiny and rigid cosmological constant, Λ. Its size is many orders of magnitude below the expected one in the standard model of particle physics. This is a very welcome fact, namely if we care at all about our own existence and fate. However, we do not have a minimally satisfactory explanation for our good fortune and for the failing of the SM at that crucial point. To start with, an expanding universe is not expected to have a static vacuum energy density. We should rather observe a mildly dynamical behavior δΛ(t) ~ R ~ H2(t) with the expansion rate H. At the same time, it is natural to think that the huge value of the primeval vacuum energy (presumably connected to some GUT) was responsible for the initial inflationary phase. In the traditional inflaton models such phase is inserted by hand in the early epoch of the cosmic evolution, and it is assumed to match the standard ΛCDM regime during the radiation epoch. Here, instead, we consider a class of dynamical vacuum models which incorporate in a single vacuum structure [Formula: see text] the rapid stage of inflation, followed by the radiation and cold matter epochs, until achieving our dark energy universe. The early behavior of such "running vacuum model" [Formula: see text] bares resemblance with Starobinsky's inflation in the early universe and is very close to the concordance model for the entire post-inflationary history. Most remarkably, the inflationary period in the [Formula: see text] terminates with "graceful exit" and the large entropy problem can be solved. The model is compatible with the latest cosmological data on Hubble expansion and structure formation, and at the same time presents distinctive observational features that can be tested in the near future.

Recently there have been claims on model-independent evidence of dynamical dark energy. Herein we consider a fairly general class of cosmological models with a time-evolving cosmological term of the form Λ(H) = C 0 + C H H 2 + CḢḢ, where H is the Hubble rate. These models are well motivated from the theoretical point of view since they can be related to the general form of the effective action of quantum field theory in curved spacetime. Consistency with matter conservation can be achieved by letting the Newtonian coupling G change very slowly with the expansion. We solve these dynamical vacuum models and fit them to the wealth of expansion history and linear structure formation data. The results of our analysis indicate a significantly better agreement as compared to the concordance ΛCDM model, thus supporting the possibility of a dynamical cosmic vacuum.