Hubble expansion and structure formation in time varying vacuum models

Abstract

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

Notes on ghost dark energy

“…But χ 2 min is larger than the one for the ΛCDM model, χ 2 ΛCDM = 554.264. A similar conclusion is also reached by other authors using different data set [33]. It is not hard to understand why in this model, χ 2 min is large, compared to the ΛCDM model.…”

Solving the main cosmological puzzles with a generalized time varying vacuum energy

“…Finally, in order to confirm the above results, we need to define a robust cosmological probe at high redshifts (z ≥ 3). In Basilakos et al (2009) we propose that the future cluster surveys based on the Sunayev-Zeldovich detection method will possibly distinguish the closely resembling vacuum models at high redshifts. the renormalization group from the quantum field theory introduces only even powers of H out of which the H 2 is the leading term (Grande et al 2006;Solá 2008, and references therein).…”

“…It becomes 1 Note that from a theoretical viewpoint the predicted value of the γ parameter is |γ| = 1 12π M 2 M 2 P , where M P is the Planck mass and M is an effective mass parameter representing the average mass of the heavy particles of the Grand Unified Theory (GUT) near the Planck scale, after taking into account their multiplicities. In the case of M ∼ M P we can derive an upper limit of |γ| ≤ 1/12π (for more details see Basilakos et al 2009). clear is that for 0.1 ≤ a ≤ 0.34 (or 2 ≤ z ≤ 10) the vacuum density is low enough (r ∼ 0) to allow galaxies and galaxy clusters to form (Garriga et al 1999;Basilakos et al 2009).…”

“…In the case of M ∼ M P we can derive an upper limit of |γ| ≤ 1/12π (for more details see Basilakos et al 2009). clear is that for 0.1 ≤ a ≤ 0.34 (or 2 ≤ z ≤ 10) the vacuum density is low enough (r ∼ 0) to allow galaxies and galaxy clusters to form (Garriga et al 1999;Basilakos et al 2009). From now on, we will utilize γ 0.004 that corresponds to the best fit parameter.…”

“…Of course, the weak point in this theory is the unknown functional form of the Λ(t) parameter. Also, in the Λ(t) cosmological model there is a coupling between the time-dependent vacuum and matter (Wang & Meng 2005;Alcaniz & Lima 2005;Carneiro et al 2008;Basilakos 2009;Basilakos et al 2009). Indeed, using the combination of the conservation of the total energy with the variation of the vacuum energy, one can prove that the Λ(t) model provides either a particle production process or that the mass of the dark matter particles increases (Basilakos 2009, and references therein).…”