R. Kantowski

Constraints on Extra Dimensions From Cosmological and Terrestrial Measurements

If quantum fields exist in extra compact dimensions, they will give rise to a quantum vacuum or Casimir energy. That vacuum energy will manifest itself as a cosmological constant. The fact that supernova and cosmic microwave background data indicate that the cosmological constant is of the same order as the critical mass density to close the universe supplies a lower bound on the size of the extra dimensions. Recent laboratory constraints on deviations from Newtons law place an upper limit. The allowed region is so small as to suggest that either extra compact dimensions do not exist, or their properties are about to be tightly constrained by experimental data.

Age-redshift relation for standard cosmology

We present compact, analytic expressions for the age-redshift relation

Vilkovisky-DeWitt effective action for Einstein gravity on Kaluza-Klein space-times M**4 x S**N

\tau(z)

Gauge-independent trace anomaly for gravitons.

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.

Operator phases in BF-type topological field theories

We evaluate the divergent part of the Vilkovisky-DeWitt effective action for Einstein gravity on even-dimensional Kaluza-Klein spacetimes of the form

Renormalization group and spontaneous compactification of a higher-dimensional scalar field theory in curved spacetime.

M^{4}\times S^{N}

The Vilkovisky-De Witt effective action in BF-type topological field theories

. Explicit results are given for

Casimir energies of fields on even dimensional Kaluza-Klein Spaces of the form M4 × SN1 × SN2 × …,

N

Casimir Energies in M(4) X S(

=2, 4, and 6. Trace anomalies for gravitons are also given for these cases. Stable Kaluza-Klein configurations are sought, unsuccessfully, assuming the divergent part of the effective action dominates the dynamics.

N

We show that the trace anomaly for gravitons calculated using the usual effective action formalism depends on the choice of gauge when the background spacetime is not a solution of the classical equation of motion, that is, when off shell. We then use the gauge-independent Vilkovisky-DeWitt effective action to restore gauge independence to the off-shell case. Additionally we explicitly evaluate trace anomalies for some {ital N}-sphere background spacetimes.