Reconciling inflation with openness

It is already understood that the increasing observational evidence for an open Universe can be reconciled with inflation if our horizon is contained inside one single huge bubble nucleated during the inflationary phase transition. In this frame of ideas, we show here that the probability of living in a bubble with the right $\Omega_0$ (now the observations require $\Omega_0 \approx .2$) can be comparable with unity, rather than infinitesimally small. For this purpose we modify both quantitatively and qualitatively an intuitive toy model based upon fourth order gravity. As this scheme can be implemented in canonical General Relativity as well (although then the inflation driving potential must be designed entirely ad hoc), inferring from the observations that $\Omega_0 < 1$ not only does not conflict with the inflationary paradigm, but rather supports therein the occurrence of a primordial phase transition.Comment: 4 pages, one postscript figure, to be published on Physical Review D PACS: 98.80. C

Limits on the gravity wave contribution to microwave anisotropies

We present limits on the fraction of large angle microwave anisotropies which could come from tensor perturbations. We use the COBE results as well as smaller scale CMB observations, measurements of galaxy correlations, abundances of galaxy clusters, and Lyman alpha absorption cloud statistics. Our aim is to provide conservative limits on the tensor-to-scalar ratio for standard inflationary models. For power-law inflation, for example, we find T/S<0.52 at 95% confidence, with a similar constraint for phi^p potentials. However, for models with tensor amplitude unrelated to the scalar spectral index it is still currently possible to have T/S>1.Comment: 23 pages, 7 figures, accepted for publication in Phys. Rev. D. Calculations extended to blue spectral index, Fig. 6 added, discussion of results expande

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199

Newtonian and Post Newtonian Expansionfree Fluid Evolution in f(R) Gravity

We consider a collapsing sphere and discuss its evolution under the vanishing expansion scalar in the framework of $f(R)$ gravity. The fluid is assumed to be locally anisotropic which evolves adiabatically. To study the dynamics of the collapsing fluid, Newtonian and post Newtonian regimes are taken into account. The field equations are investigated for a well-known $f(R)$ model of the form $R+\delta R^2$ admitting Schwarzschild solution. The perturbation scheme is used on the dynamical equations to explore the instability conditions of expansionfree fluid evolution. We conclude that instability conditions depend upon pressure anisotropy, energy density and some constraints arising from this theory.Comment: 20 pages, accepted for publication in Astrophys. Space Sc

The asymptotic variance rate of the output process of finite capacity birth-death queues

We analyze the output process of finite capacity birth-death Markovian queues. We develop a formula for the asymptotic variance rate of the form &#0955; *+&#0963;vi where &#0955; * is the rate of outputs and v i are functions of the birth and death rates. We show that if the birth rates are non-increasing and the death rates are non-decreasing (as is common in many queueing systems) then the values of v i are strictly negative and thus the limiting index of dispersion of counts of the output process is less than unity. In the M/M/1/K case, our formula evaluates to a closed form expression that shows the following phenomenon: When the system is balanced, i.e. the arrival and service rates are equal, &#0963;vi\&#0955;* is minimal. The situation is similar for the M/M/c/K queue, the Erlang loss system and some PH/PH/1/K queues: In all these systems there is a pronounced decrease in the asymptotic variance rate when the system parameters are balanced