The IR-Completion of Gravity: What happens at Hubble Scales?

We have recently proposed an "Ultra-Strong" version of the Equivalence Principle (EP) that is not satisfied by standard semiclassical gravity. In the theory that we are conjecturing, the vacuum expectation value of the (bare) energy momentum tensor is exactly the same as in flat space: quartically divergent with the cut-off and with no spacetime dependent (subleading) ter ms. The presence of such terms seems in fact related to some known difficulties, such as the black hole information loss and the cosmological constant problem. Since the terms that we want to get rid of are subleading in the high-momentum expansion, we attempt to explore the conjectured theory by "IR-completing" GR. We consider a scalar field in a flat FRW Universe and isolate the first IR-correction to its Fourier modes operators that kills the quadratic (next to leading) time dependent divergence of the stress energy tensor VEV. Analogously to other modifications of field operators that have been proposed in the literature (typically in the UV), the present approach seems to suggest a breakdown (here, in the IR, at large distances) of the metric manifold description. We show that corrections to GR are in fact very tiny, become effective at distances comparable to the inverse curvature and do not contain any adjustable parameter. Finally, we derive some cosmological implications. By studying the consistency of the canonical commutation relations, we infer a correction to the distance between two comoving observers, which grows as the scale factor only when small compared to the Hubble length, but gets relevant corrections otherwise. The corrections to cosmological distance measures are also calculable and, for a spatially flat matter dominated Universe, go in the direction of an effective positive acceleration.Comment: 27 pages, 2 figures. Final version, references adde

Minimal Scales from an Extended Hilbert Space

We consider an extension of the conventional quantum Heisenberg algebra, assuming that coordinates as well as momenta fulfil nontrivial commutation relations. As a consequence, a minimal length and a minimal mass scale are implemented. Our commutators do not depend on positions and momenta and we provide an extension of the coordinate coherent state approach to Noncommutative Geometry. We explore, as toy model, the corresponding quantum field theory in a (2+1)-dimensional spacetime. Then we investigate the more realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative planes. As a result, we obtain propagators, which are finite in the ultraviolet as well as the infrared regime.Comment: 16 pages, version which matches that published on CQ

UV stable, Lorentz-violating dark energy with transient phantom era

Phantom fields with negative kinetic energy are often plagued by the vacuum quantum instability in the ultraviolet region. We present a Lorentz-violating dark energy model free from this problem and show that the crossing of the cosmological constant boundary w=-1 to the phantom equation of state is realized before reaching a de Sitter attractor. Another interesting feature is a peculiar time-dependence of the effective Newton's constant; the magnitude of this effect is naturally small but may be close to experimental limits. We also derive momentum scales of instabilities at which tachyons or ghosts appear in the infrared region around the present Hubble scale and clarify the conditions under which tachyonic instabilities do not spoil homogeneity of the present/future Universe.Comment: 22 pages, 7 figures; Presentation modified substantially, results and conclusions unchanged. Journal versio

Crossing the Phantom Divide Line in a DGP-Inspired F(R,ϕ)F(R,\phi)-Gravity

We study possible crossing of the phantom divide line in a DGP-inspired $F(R,\phi)$ braneworld scenario where scalar field and curvature quintessence are treated in a unified framework. With some specific form of $F(R,\phi)$ and by adopting a suitable ansatz, we show that there are appropriate regions of the parameters space which account for late-time acceleration and admit crossing of the phantom divide line.Comment: 23 Pages, 10 figs, Submitted to JCA

A Braneworld Dark Energy Model with Induced Gravity and the Gauss-Bonnet Effect

We construct a holographic dark energy model with a non-minimally coupled scalar field on the brane where Gauss-Bonnet and Induced Gravity effects are taken into account. This model provides a wide parameter space with several interesting cosmological implications. Especially, the equation of state parameter of the model crosses the phantom divide line and it is possible to realize bouncing solutions in this setup.Comment: 20 pages, 3 eps figures, to appear in IJT