We present a model for the Universe in which quantum anomalies are argued to play an important dual rôle: they are responsible for generating matter-antimatter asymmetry in the Cosmos, but also provide time-dependent contributions to the vacuum energy density of "running-vacuum" type, which drive the Universe evolution. According to this scenario, during the inflationary phase of a string-inspired Universe, and its subsequent exit, the existence of primordial gravitational waves induce gravitational anomalies, which couple to the (Kalb-Ramond (KR)) axion field emerging from the antisymmetric tensor field of the massless gravitational multiplet of the string. Such anomalous CP violating interactions have two important effects: first, they lead to contributions to the vacuum energy density of the form appearing in the "running vacuum model" (RVM) framework, which are proportional to both, the square and the fourth power of the effective Hubble parameter, H 2 and H 4 respectively. The H 4 terms may lead to inflation, in a dynamical scenario whereby the rôle of the inflaton is played by the effective scalar-field ("vacuumon") representation of the RVM. Second, there is an undiluted KR axion at the end of inflation, which plays an important rôle in generating matter-antimatter asymmetry in the Cosmos, through baryogenesis via leptogenesis in models involving heavy right handed neutrinos. As the Universe exits inflation and enters a radiation dominated era, the generation of chiral fermionic matter is responsible for the cancellation of gravitational anomalies, thus restoring diffeomorphism invariance for the matter/radiation (quantum) theory, as required for consistency. Chiral U(1) anomalies may remain uncompensated, though, during matter/radiation dominance, providing RVM-like H 2 and H 4 contributions to the Universe energy density. Finally, in the current era, when the Universe enters a de Sitter phase again, and matter is no longer dominant, gravitational anomalies resurface, leading to RVM-like H 2 contributions to the vacuum energy density, which are however much more suppressed, as compared to their counterparts during inflation, due to the smallness of the present era's Hubble parameter H 0 . In turn, this feature endows the observed dark energy with a dynamical character that follows the RVM pattern, a fact which has been shown to improve the global fits to the current cosmological observations as compared to the concordance ΛCDM with its rigid cosmological constant , Λ > 0. Our model favours axionic Dark Matter, the source of which can be the KR axion. The uncompensated chiral anomalies in late epochs of the Universe are argued to play an important rôle in this, in the context of cosmological models characterised by the presence of large-scale cosmic magnetic fields at late eras.

We investigate the properties of the FLRW flat cosmological models in which the vacuum energy density evolves with time, Λ(t). Using different versions of the Λ(t) model, namely quantum field vacuum, power series vacuum and power law vacuum, we find that the main cosmological functions such as the scale factor of the universe, the Hubble expansion rate H and the energy densities are defined analytically. Performing a joint likelihood analysis of the recent supernovae type Ia data, the Cosmic Microwave Background (CMB) shift parameter and the Baryonic Acoustic Oscillations (BAOs) traced by the Sloan Digital Sky Survey (SDSS) galaxies, we put tight constraints on the main cosmological parameters of the Λ(t) scenarios. Furthermore, we study the linear matter fluctuation field of the above vacuum models. We find that the patterns of the power series vacuum Λ = n1 H + n2 H 2 predict stronger small scale dynamics, which implies a faster growth rate of perturbations with respect to the other two vacuum cases (quantum field and power law), despite the fact that all the cosmological models share the same equation of state (EOS) parameter. In the case of the quantum field vacuum Λ = n0 + n2 H 2 , the corresponding matter fluctuation field resembles that of the traditional Λ cosmology. The power law vacuum (Λ ∝ a −n ) mimics the classical quintessence cosmology, the best fit being tilted in the phantom phase. In this framework, we compare the observed growth rate of clustering measured from the optical galaxies with those predicted by the current Λ(t) models. Performing a Kolmogorov-Smirnov (KS) statistical test we show that the cosmological models which contain a constant vacuum (ΛCDM), quantum field vacuum and power law vacuum provide growth rates that match well with the observed growth rate. However, this is not the case for the power series vacuum models (in particular, the frequently adduced Λ ∝ H model) in which clusters form at significantly earlier times (z ≥ 4) with respect to all other models (z ∼ 2). Finally, we derived the theoretically predicted dark-matter halo mass function and the corresponding distribution of cluster-size halos for all the models studied. Their expected redshift distribution indicates that it will be difficult to distinguish the closely resembling models (constant vacuum, quantum field and power-law vacuum), using realistic future X-ray surveys of cluster abundances. However, cluster surveys based on the Sunayev-Zeldovich detection method give some hope to distinguish the closely resembling models at high redshifts.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

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

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