Emil Mottola

Cosmology with decaying vacuum energy

Abstract Motivated by recent attempts to solve the cosmological constant problem, we examine the observational consequences of a vacuum energy which decays in time. In both radiation and matter dominated eras, the ratio of the vacuum to the total energy density of the universe must be small. Although the vacuum cannot provide the “missing mass” required to close the universe today, its presence earlier in the history of the universe could have important consequences. Element abundances from primordial nucleosynthesis require the ratio x = ϱ vac /( ϱ vac + ϱ rad ) ⩽ 0.1 of neutrino (or equivalent light) species to exceed N ν > 4, a case ruled out in the standard cosmological model. If the vacuum decays into low energy photons, the lack of observed spectral distortions in the microwave background gives tighter bounds, x −4 . In the matter-dominated era, the presence of a vacuum term may allow more time for growth of protogalactic perturbations.

Gravitational vacuum condensate stars

A new final state of gravitational collapse is proposed. By extending the concept of Bose-Einstein condensation to gravitational systems, a cold, dark, compact object with an interior de Sitter condensate p(v) = -rho(v) and an exterior Schwarzschild geometry of arbitrary total mass M is constructed. These regions are separated by a shell with a small but finite proper thickness l of fluid with equation of state p = +rho, replacing both the Schwarzschild and de Sitter classical horizons. The new solution has no singularities, no event horizons, and a global time. Its entropy is maximized under small fluctuations and is given by the standard hydrodynamic entropy of the thin shell, which is of the order k(B)lMc/Plancks over 2 pi, instead of the Bekenstein-Hawking entropy formula, S(BH) = 4 pi k(B)GM(2)/Plancks over 2 pi c. Hence, unlike black holes, the new solution is thermodynamically stable and has no information paradox.

Weyl cohomology and the effective action for conformal anomalies

We present a general method of deriving the effective action for conformal anomalies in any even dimension, which satisfies the Wess-Zumino consistency condition by construction. The method relies on defining the coboundary operator of the local Weyl group,

The path integral measure, conformal factor problem and stability of the ground state of quantum gravity

{g}_{\mathrm{ab}}\ensuremath{\rightarrow}\mathrm{exp}(2\ensuremath{\sigma}{)g}_{\mathrm{ab}},

Graviton fluctuations in de Sitter space

and giving a cohomological interpretation to counterterms in the effective action in dimensional regularization with respect to this group. Nontrivial cocycles of the Weyl group arise from local functionals that are Weyl invariant in and only in the physical even integer dimension

Cosmological dark energy: prospects for a dynamical theory

d=2k.

Conformal Invariance, Dark Energy, and CMB Non-Gaussianity

In the physical dimension the nontrivial cocycles generate covariant nonlocal action functionals characterized by sensitivity to global Weyl rescalings. The nonlocal action so obtained is unique up to the addition of trivial cocycles and Weyl invariant terms, both of which are insensitive to global Weyl rescalings. These distinct behaviors under rigid dilations can be used to distinguish between infrared relevant and irrelevant operators in a generally covariant manner. Variation of the

Nonequilibrium quantum fields in the large-N expansion.

d=4

Conformal Invariance and Cosmic Background Radiation

nonlocal effective action yields two new conserved geometric stress tensors with local traces equal to the square of the Weyl tensor and the Gauss-Bonnet-Euler density, respectively. The second of these conserved tensors becomes

Conformal symmetry and central charges in 4 dimensions

{}^{(3)}{H}_{\mathrm{ab}}