Zeta-Functions for Non-Minimal Operators

We evaluate zeta-functions $\zeta(s)$ at $s=0$ for invariant non-minimal 2nd-order vector and tensor operators defined on maximally symmetric even dimensional spaces. We decompose the operators into their irreducible parts and obtain their corresponding eigenvalues. Using these eigenvalues, we are able to explicitly calculate $\zeta(0)$ for the cases of Euclidean spaces and $N$-spheres. In the $N$-sphere case, we make use of the Euler-Maclaurin formula to develop asymptotic expansions for the required sums. The resulting $\zeta(0)$ values for dimensions 2 to 10 are given in the Appendix.Comment: 26 pages, additional reference

Homogeneous magnetic fields in fully anisotropic string cosmological backgrounds

We present new solutions of the string cosmological effective action in the presence of a homogeneous Maxwell field with pure magnetic component. Exact solutions are derived in the case of space-independent dilaton and vanishing torsion background. In our examples the four dimensional metric is either of Bianchi-type III and VI$_{-1}$ or Kantowski-Sachs.Comment: 4 page

The Age-Redshift Relation for Standard Cosmology

We present compact, analytic expressions for the age-redshift relation $\tau(z)$ for standard Friedmann-Lema\^ \itre-Robertson-Walker (FLRW) cosmology. The new expressions are given in terms of incomplete Legendre elliptic integrals and evaluate much faster than by direct numerical integration.Comment: 13 pages, 3 figure

The renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime

The renormalization group (RG) is used to study the asymptotically free $\phi_6^3$-theory in curved spacetime. Several forms of the RG equations for the effective potential are formulated. By solving these equations we obtain the one-loop effective potential as well as its explicit forms in the case of strong gravitational fields and strong scalar fields. Using zeta function techniques, the one-loop and corresponding RG improved vacuum energies are found for the Kaluza-Klein backgrounds $R^4\times S^1\times S^1$ and $R^4\times S^2$. They are given in terms of exponentially convergent series, appropriate for numerical calculations. A study of these vacuum energies as a function of compactification lengths and other couplings shows that spontaneous compactification can be qualitatively different when the RG improved energy is used.Comment: LaTeX, 15 pages, 4 figure

Distance-redshift from an optical metric that includes absorption

We show that it is possible to equate the intensity reduction of a light wave caused by weak absorption with a geometrical reduction in intensity caused by a "transverse" conformal transformation of the spacetime metric in which the wave travels. We are consequently able to modify Gordon's optical metric to account for electromagnetic properties of ponderable material whose properties include both refraction and absorption. Unlike refraction alone however, including absorption requires a modification of the optical metric that depends on the eikonal of the wave itself. We derive the distance-redshift relation from the modified optical metric for Friedman-Lema\^itre-Robertson-Walker spacetimes whose cosmic fluid has associated refraction and absorption coefficients. We then fit the current supernovae data and provide an alternate explanation (other than dark energy) of the apparent acceleration of the universe.Comment: 2 figure

Quantum Cosmology of Kantowski-Sachs like Models

The Wheeler-DeWitt equation for a class of Kantowski-Sachs like models is completely solved. The generalized models include the Kantowski-Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski-Sachs cylinder inserted between two FRW half--spheres. The (second order) WKB approximation is exact for the wave functions of the complete set and this facilitates the product structure of the wave function for the joined model. In spite of the product structure the wave function can not be interpreted as admitting no correlations between the different regions. This problem is due to the joining procedure and may therefore be present for all joined models. Finally, the {s}ymmetric {i}nitial {c}ondition (SIC) for the wave function is analyzed and compared with the ``no bouindary'' condition. The consequences of the different boundary conditions for the arrow of time are briefly mentioned.Comment: 21 pages, uses LaTeX2e, epsf.sty and float.sty, three figures (50 kb); changes: one figure added, new interpretation of quantizing procedure for the joined model and many minor change

Bianchi Cosmological Models and Gauge Symmetries

We analyze carefully the problem of gauge symmetries for Bianchi models, from both the geometrical and dynamical points of view. Some of the geometrical definitions of gauge symmetries (=``homogeneity preserving diffeomorphisms'') given in the literature do not incorporate the crucial feature that local gauge transformations should be independent at each point of the manifold of the independent variables ( = time for Bianchi models), i.e, should be arbitrarily localizable ( in time). We give a geometrical definition of homogeneity preserving diffeomorphisms that does not possess this shortcoming. The proposed definition has the futher advantage of coinciding with the dynamical definition based on the invariance of the action ( in Lagrangian or Hamiltonian form). We explicitly verify the equivalence of the Lagrangian covariant phase space with the Hamiltonian reduced phase space. Remarks on the use of the Ashtekar variables in Bianchi models are also given.Comment: 16 pages, Latex file, ULB-PMIF-92/1

A Measure on a Subspace of FRW Solutions and ``The Flatness Problem" of Standard Cosmology

We use the metric on the space of gravity fields given by DeWitt to construct a unique kinematic measure on the space of FRW simple fluids and show that when the mass parameter $\Omega$ is used as a coordinate this measure is singular at $\Omega = 1$. This singularity, combined with the time evolution of $\Omega$, distorts distributions of $\Omega$ values to be concentrated in the neighborhood of 1 at early times. It is a distorted distribution of $\Omega$ values that sometimes misleads the casual observer to conclude that $\Omega$ must be exactly equal to 1.Comment: revtex 16 pages, 1 figure include

Cosmological black holes as voids progenitors. I. Simulations

Cosmological black holes (CBH), i.e. black holes with masses larger than $10^{14} solar masses, have been proposed as possible progenitors of galaxy voids (Stornaiolo 2002). The presence of a CBH in the central regions of a void should induce significant gravitational lensing effects and in this paper we discuss such gravitational signatures using simulated data. These signatures may be summarized as follows: i) a blind spot in the projected position of the CBH where no objects can be detected; ii) an excess of faint secondary images; iii) an excess of double images having a characteristic angular separation. All these signatures are shown to be detectable in future deep surveys.Comment: 5 pages, 5 figures, submitted to MNRA

Noncommutative Geometry and Cosmology

We study some consequences of noncommutativity to homogeneous cosmologies by introducing a deformation of the commutation relation between the minisuperspace variables. The investigation is carried out for the Kantowski-Sachs model by means of a comparative study of the universe evolution in four different scenarios: the classical commutative, classical noncommutative, quantum commutative, and quantum noncommutative. The comparison is rendered transparent by the use of the Bohmian formalism of quantum trajectories. As a result of our analysis, we found that noncommutativity can modify significantly the universe evolution, but cannot alter its singular behavior in the classical context. Quantum effects, on the other hand, can originate non-singular periodic universes in both commutative and noncommutative cases. The quantum noncommutative model is shown to present interesting properties, as the capability to give rise to non-trivial dynamics in situations where its commutative counterpart is necessarily static.Comment: 22 pages, 5 figures, substantial changes in the presentation, results are the same, to appear in Physical Review