Possible relationship between initial conditions for inflation and past geodesic incompleteness of the inflationary spacetime

According to the Borde-Guth-Vilenkin (BGV) theorem an expanding region of spacetime cannot be extended to the past beyond some boundary \mathcal{B}. Therefore, the inflationary universe must have had some kind of beginning. However, the BGW theorem says nothing about the boundary conditions on \mathcal{B}, or even about its location. Here we present a single-scalar field model of the Two-Measure Theory, where the non-Riemannian volume element $\Upsilon d^4x$ is present in the action. As a result of the model dynamics, an upper bound \varphi_0 of admissible values of the scalar field \varphi appears, which sets the position of \mathcal{B} in the form of a spacelike hypersurface \Upsilon(x)=0 with a boundary condition: \Upsilon\to 0^+ as \varphi\to\varphi_0^-. A detailed study has established that if the initial kinetic energy density \rho_{kin}^{(in)} prevails over initial gradient energy density \rho_{grad}^{(in)} then there is an interval of initial values \varphi_{in}^{(min)}\leq\varphi_{in}<\varphi_0, where \rho_{kin}^{(in)} and \rho_{grad}^{(in)} cannot exceed the potential energy density and hence the initial conditions necessary for the onset of inflation are satisfied. It is shown that under almost all possible left-handed boundary conditions on \mathcal{B}, that is where \Upsilon\to 0^-, the metric tensor in the Einstein frame has a jump discontinuity on \mathcal{B}, so the Christoffel connection coefficients are not defined on the spacelike hypersurface \Upsilon=0. Thus, if \varphi_{in}^{(min)}\leq \varphi_{in}<\varphi_0 and \rho_{kin}^{(in)}>\rho_{grad}^{(in)}, then there was an inflationary stage in the history of our Universe and the congruence of timelike geodesics cannot be extended to the past beyond the hypersurface \Upsilon=0.Comment: 44 pages; 4 figures; fixed a few typos; to appear in JCA

f(R)-Gravity: "Einstein Frame" Lagrangian Formulation, Non-Standard Black Holes and QCD-like Confinement/Deconfinement

We consider f(R) = R + R^2 gravity interacting with a dilaton and a special non-standard form of nonlinear electrodynamics containing a square-root of ordinary Maxwell Lagrangian. In flat spacetime the latter arises due to a spontaneous breakdown of scale symmetry and produces an effective charge-confining potential. In the R + R^2 gravity case, upon deriving the explicit form of the equivalent local "Einstein frame" Lagrangian action, we find several physically relevant features due to the combined effect of the gauge field and gravity nonlinearities such as: appearance of dynamical effective gauge couplings and confinement-deconfinement transition effect as functions of the dilaton vacuum expectation value; new mechanism for dynamical generation of cosmological constant; deriving non-standard black hole solutions carrying additional constant vacuum radial electric field and with non-asymptotically flat "hedge-hog"-type spacetime asymptotics.Comment: 10 pages, to appear in "Springer Proceedings of Mathematics and Statistics" (proceedings of Xth International Workshop "Lie Theory and Its Applications in Physics", Varna, 2013

Asymmetric Wormholes via Electrically Charged Lightlike Branes

We consider a self-consistent Einstein-Maxwell-Kalb-Ramond system in the bulk D=4 space-time interacting with a variable-tension electrically charged lightlike brane. The latter serves both as a material and charge source for gravity and electromagnetism, as well as it dynamically generates a bulk space varying cosmological constant. We find an asymmetric wormhole solution describing two "universes" with different spherically symmetric black-hole-type geometries connected through a "throat" occupied by the lightlike brane. The electrically neutral "left universe" comprises the exterior region of Schwarzschild-de-Sitter (or pure Schwarzschild) space-time above the inner (Schwarzschild-type) horizon, whereas the electrically charged "right universe" consists of the exterior Reissner-Nordstroem (or Reissner-Nordstroem-de-Sitter) black hole region beyond the outer Reissner-Nordstroem horizon. All physical parameters of the wormhole are uniquely determined by two free parameters - the electric charge and Kalb-Ramond coupling of the lightlike brane.Comment: 17 pages, to appear in the proceedings "Lie Theory and Its Applications in Physics 08" (Varna, June 2009), eds. V. Dobrev and H. Doebner (Heron Press, Sofia, 2010