We investigate the matter density fluctuations δρ M /ρ M for two dark energy (DE) models in the literature in which the cosmological term Λ is a running parameter.In the first model, the running ΛCDM model, matter and DE exchange energy, whereas in the second model, the ΛXCDM model, the total DE and matter components are conserved separately. The ΛXCDM model was proposed as an interesting solution to the cosmic coincidence problem. It includes an extra dynamical component, the "cosmon" X, which interacts with the running Λ, but not with matter. In our analysis we make use of the current value of the linear bias parameter, b2 is the present matter power spectrum and P GG is the galaxy fluctuation power spectrum. The former can be computed within a given model, and the latter is found from the observed LSS data (at small z) obtained by the 2dF galaxy redshift survey. It is found that b 2 Λ (z ≃ 0) = 1 within a 10% accuracy for the standard ΛCDM model. Adopting this limit for any DE model and using a method based on the effective equation of state for the DE, we can set a limit on the growth of matter density perturbations for the running ΛCDM model, the solution of which is known.This provides a good test of the procedure, which we then apply to the ΛXCDM model in order to determine the physical region of parameter space, compatible with the LSS data. In this region, the ΛXCDM model is consistent with known observations and provides at the same time a viable solution to the cosmic coincidence problem.

We investigate here models that suggest that the vacuum energy decays into cold dark matter (CDM) and show that the density fluctuation spectrum obtained from the cosmic microwave background (CMB) data together with large galaxy surveys (e.g., the Sloan Digital Sky Survey), puts strong limits on the rate of decay of the vacuum energy. CDM produced by a decaying vacuum energy would dilute the density fluctuation spectrum, created in the primordial universe and observed with large galaxy surveys at low redshifts. Our results indicate that the decay rate of the vacuum energy into CDM is extremely small. 95.35.+d, 98.70.Vc, 04.62.+v

We present a model which predicts inflation without the presence of inflaton fields, based on the ǫR 2 and Starobinsky models. It links the above models to the reheating epoch with conformally coupled massive particles created at the end of inflation. In the original Starobinsky model, the reheating era was created by massless non-conformally coupled particles. We assume here that non-conformal coupling to gravitation does not exist. In the ǫR 2 model, inflation is produced by the gravitational Lagrangian to which a term ǫR 2 is added, where ǫ is a constant and R is the Ricci scalar. Inflation is created by vacuum fluctuations in the Starobinsky model. Both models have the same late-inflation time-dependence, which is described by a characteristic mass M . There is a free parameter H0 on the order of the Planck mass M P l that determines the Hubble parameter near the Planck epoch and which depends upon the number and type of particles creating the vacuum fluctuations in the Starobinsky model. In our model, we assume the existence of particles with a mass m, on the order of M , conformally coupled to gravity, that have a long decay time.Taking m ≡ F M , we investigate values of F = 0.5 and 0.3. These particles, produced ∼ 60 e-folds before the end of inflation, created the nearly scale invariant scalar density fluctuations which are observed. Gravitational waves (tensor fluctuations) were also produced at this epoch. At t end , the Hubble parameter begins to oscillate rapidly, gravitationally producing the bulk of the m particles, which we identify as the origin of the matter content of the Universe today. The time required for the Universe to dissipate its vacuum energy into m particles is found to be t dis ≃ 6 M 2 P l /M 3 F . We assume that the reheating time tRH needed for the m particles to decay into relativistic particles, is very much greater than that necessary to create the m particles, t dis . A particle physics theory of m can, in principle, predict their decay rate Γmr ≡ t −1RH . From the ratio f ≡ t dis /tRH , F and g * (the total number of degrees of freedom of the relativistic particles) we can, then, evaluate the maximum temperature of the Universe Tmax and the reheat temperature TRH at tRH. From the observed scalar fluctuations at large scales, δρ/ρ ∼ 10 −5 , we have the prediction M ∼ = 1.15 × 10 −6 M Pl and the ratio of the tensor to scalar fluctuations, r ∼ = 6.8 × 10 −4 . Thus our model predicts M , t dis , t end , Tmax, TRH , tmax, and tRH as a function of f , F , and g * (and to a weaker extent the particle content of the vacuum near the Planck epoch). A measured value of r that is appreciably different from r = 6.8 × 10 −4 would discard our model (as well as the Starobinsky and ǫR 2 models).PACS numbers: 98.80.-k, 98.80.Es

Geodesic motion of test particles in van Stockum space-time, which represents the internal gravitational field produced by a rigidly rotating dust cylinder, is studied. In particular, it is found that confinement occurs quite generally in the radial direction, while the motion in the axial direction is free. The possible relevance of the confinement to the extragalactic jet formation is pointed out.

Magnetic fields of intensities similar to those in our galaxy are also observed in high redshift galaxies, where a mean field dynamo would not have had time to produce them. Therefore, a primordial origin is indicated. It has been suggested that magnetic fields were created at various primordial eras: during inflation, the electroweak phase transition, the quark-hadron phase transition (QHPT), during the formation of the first objects, and during reionization. We suggest here that the large scale fields ∼ µG, observed in galaxies at both high and low redshifts by Faraday Rotation Measurements (FRMs), have their origin in the electromagnetic fluctuations that naturally occurred in the dense hot plasma that existed just after the QHPT. We evolve the predicted fields to the present time. The size of the region containing a coherent magnetic field increased due to the fusion of smaller regions. Magnetic fields (MFs) ∼ 10µG over a comoving ∼ 1 pc region are predicted at redshift z ∼ 10. These fields are orders of magnitude greater than those predicted in previous scenarios for creating primordial magnetic fields. Line-of-sight average magnetic fields (MFs) ∼ 10 −2 µG, valid for FRMs, are obtained over a 1 Mpc comoving region at the redshift z ∼ 10. In the collapse to a galaxy (comoving size ∼ 30 kpc) at z ∼ 10, the fields are amplified to ∼ 10µG. This indicates that the MFs created immediately after the QHPT (10 −4 s), predicted by the Fluctuation-Dissipation Theorem, could be the origin of the ∼ µG fields observed by FRMs in galaxies at both high and low redshifts. Our predicted MFs are shown to be consistent with present observations. We discuss the possibility that the predicted MFs could cause non-negligible deflections of ultra-high energy cosmic rays and help create the observed isotropic distribution of their incoming directions. We also discuss the importance of the volume average magnetic field predicted by our model in producing the first stars and in reionizing the Universe.

A few years ago, Cornish, Spergel and Starkman ͑CSS͒ suggested that a multiply connected ''small'' universe could allow for classical chaotic mixing as a preinflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham ͑DHI͒ calculated the Casimir energy for static multiply connected flat space-times. Because of the interest in small volume hyperbolic universes ͑e.g., CSS͒, we generalize the DHI calculation by making a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static universe, whose spatial sections are the Weeks manifold, the smallest universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.

The classical 'Kirchhoff's theorem' (the energy density of the radiation at equilibrium at high temperature, T , is a function of T only) is used to obtain the Casimir energy at zero temperature without recourse to regularization. The validity of 'Kirchhoff's theorem' at the high-temperature limit for the case at hand is confirmed. The Casimir entropy is defined and its temperature dependence is displayed. The Casimir entropy at high temperatures is shown to approach a positive geometry-dependent but temperature-independent constant.

Kirchhoff's thermodynamically based classical theorem (the energy density of the radiation in equilibrium is a function of T only) is used to obtain a relation relevant to study of the Casimir effect. We use it to obtain the zero-temperature Casimir energy without recourse to regularizaion. The intimate connection between the zero-point energy and the thermal Bose occupancy expression noted by Einstein and Stern at the turn of the century is invoked to account for the results.