4 research outputs found
Instantons and unitarity in quantum cosmology with fixed four-volume
We find a number of complex solutions of the Einstein equations in the
so-called unimodular version of general relativity, and we interpret them as
saddle points yielding estimates of a gravitational path integral over a space
of almost everywhere Lorentzian metrics on a spacetime manifold with topology
of the "no-boundary" type. In this setting, the compatibility of the
no-boundary initial condition with the definability of the quantum measure
reduces reduces to the normalizability and unitary evolution of the no-boundary
wave function \psi. We consider the spacetime topologies R^4 and RP^4 # R^4
within a Taub minisuperspace model with spatial topology S^3, and the spacetime
topology R^2 x T^2 within a Bianchi type I minisuperspace model with spatial
topology T^3. In each case there exists exactly one complex saddle point (or
combination of saddle points) that yields a wave function compatible with
normalizability and unitary evolution. The existence of such saddle points
tends to bear out the suggestion that the unimodular theory is less divergent
than traditional Einstein gravity. In the Bianchi type I case, the
distinguished complex solution is approximately real and Lorentzian at late
times, and appears to describe an explosive expansion from zero size at T=0.
(In the Taub cases, in contrast, the only complex solution with nearly
Lorentzian late-time behavior yields a wave function that is normalizable but
evolves nonunitarily, with the total probability increasing exponentially in
the unimodular "time" in a manner that suggests a continuous creation of new
universes at zero volume.) The issue of the stability of these results upon the
inclusion of more degrees of freedom is raised.Comment: 32 pages, REVTeX v3.1 with amsfonts. (v2: minor typos etc corrected.
Complex actions in two-dimensional topology change
We investigate topology change in (1+1) dimensions by analyzing the
scalar-curvature action at the points of metric-degeneration
that (with minor exceptions) any nontrivial Lorentzian cobordism necessarily
possesses. In two dimensions any cobordism can be built up as a combination of
only two elementary types, the ``yarmulke'' and the ``trousers.'' For each of
these elementary cobordisms, we consider a family of Morse-theory inspired
Lorentzian metrics that vanish smoothly at a single point, resulting in a
conical-type singularity there. In the yarmulke case, the distinguished point
is analogous to a cosmological initial (or final) singularity, with the
spacetime as a whole being obtained from one causal region of Misner space by
adjoining a single point. In the trousers case, the distinguished point is a
``crotch singularity'' that signals a change in the spacetime topology (this
being also the fundamental vertex of string theory, if one makes that
interpretation). We regularize the metrics by adding a small imaginary part
whose sign is fixed to be positive by the condition that it lead to a
convergent scalar field path integral on the regularized spacetime. As the
regulator is removed, the scalar density approaches a
delta-function whose strength is complex: for the yarmulke family the strength
is , where is the rapidity parameter of the associated
Misner space; for the trousers family it is simply . This implies that
in the path integral over spacetime metrics for Einstein gravity in three or
more spacetime dimensions, topology change via a crotch singularity is
exponentially suppressed, whereas appearance or disappearance of a universe via
a yarmulke singularity is exponentially enhanced.Comment: 34 pages, REVTeX v3.0. (Presentational reorganization; core results
unchanged.
Cosmological Implications of a Scale Invariant Standard Model
We generalize the standard model of particle physics such it displays global
scale invariance. The gravitational action is also suitably modified such that
it respects this symmetry. This model is interesting since the cosmological
constant term is absent in the action. We find that the scale symmetry is
broken by the recently introduced cosmological symmetry breaking mechanism.
This simultaneously generates all the dimensionful parameters such as the
Newton's gravitational constant, the particle masses and the vacuum or dark
energy. We find that in its simplest version the model predicts the Higgs mass
to be very small, which is ruled out experimentally. We further generalize the
model such that it displays local scale invariance. In this case the Higgs
particle disappears from the particle spectrum and instead we find a very
massive vector boson. Hence the model gives a consistent description of
particle physics phenomenology as well as fits the cosmological dark energy.Comment: 12 pages, no figure