Minimum Length from First Principles

We show that no device or gedanken experiment is capable of measuring a distance less than the Planck length. By "measuring a distance less than the Planck length" we mean, technically, resolve the eigenvalues of the position operator to within that accuracy. The only assumptions in our argument are causality, the uncertainty principle from quantum mechanics and a dynamical criteria for gravitational collapse from classical general relativity called the hoop conjecture. The inability of any gedanken experiment to measure a sub-Planckian distance suggests the existence of a minimal length.Comment: 8 pages, Honorable Mention in the 2005 Gravity Research Foundation Essay Competitio

Grand unification and enhanced quantum gravitational effects

In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossible.Comment: 4 pages, 1 figure, revtex; minor changes in v2 (version published in Phys. Rev. Lett.

Cosmological Constant and Noncommutative Spacetime

We show that the cosmological constant appears as a Lagrange multiplier if nature is described by a canonical noncommutative spacetime. It is thus an arbitrary parameter unrelated to the action and thus to vacuum fluctuations. The noncommutative algebra restricts general coordinate transformations to four-volume preserving noncommutative coordinate transformations. The noncommutative gravitational action is thus an unimodular noncommutative gravity. We show that spacetime noncommutativity provides a very natural justification to an unimodular gravity solution to the cosmological problem. We obtain the right order of magnitude for the critical energy density of the universe if we assume that the scale for spacetime noncommutativity is the Planck scale.Comment: 7 page

Quantum gravity at a TeV and the renormalization of Newton's constant

We examine whether renormalization effects can cause Newton¿s constant to change dramatically with energy, perhaps even reducing the scale of quantum gravity to the TeV region without the introduction of extra dimensions. We examine a model that realizes this possibility and describe experimental signatures from the production of small black holes

Quantum Gravitational Effects and Grand Unification

In grand unified theories with large numbers of fields, renormalization effects significantly modify the scale at which quantum gravity becomes strong. This in turn can modify the boundary conditions for coupling constant unification, if higher dimensional operators induced by gravity are taken into consideration. We show that the generic size of, and the uncertainty in, these effects from gravity can be larger than the two-loop corrections typically considered in renormalization group analyses of unification. In some cases, gravitational effects of modest size can render unification impossible.Comment: 3 pages, to appear in the proceedings of 16th International Conference on Supersymmetry and Unification of Fundamental Interactions (SUSY08), Seoul, Korea, June 16-21 200

Invisible Higgs boson, continuous mass fields and unHiggs mechanism

We explore the consequences of an electroweak symmetry breaking sector which exhibits approximately scale invariant dynamics -- i.e., nontrivial fixed point behavior, as in unparticle models. One can think of an unHiggs as a composite Higgs boson with a continuous mass distribution. We find it convenient to represent the unHiggs in terms of a Kallen-Lehmann spectral function, from which it is simple to verify the generation of gauge boson and fermion masses, and unitarization of WW scattering. We show that a spectral function with broad support, which corresponds to approximate fixed point behavior over an extended range of energy, can lead to an effectively invisible Higgs particle, whose decays at LEP or LHC could be obscured by background.Comment: 8 page

Grand unification through gravitational effects

We systematically study the unification of gauge couplings in the presence of (one or more) effective dimension-5 operators cHGG/4MPl, induced into the grand unified theory by gravitational interactions at the Planck scale MPl. These operators alter the usual condition for gauge coupling unification, which can, depending on the Higgs content H and vacuum expectation value, result in unification at scales MX significantly different than naively expected. We find non-supersymmetric models of SU(5) and SO(10) unification, with natural Wilson coefficients c, that easily satisfy the constraints from proton decay. Furthermore, gauge coupling unification at scales as high as the Planck scale seems feasible, possibly hinting at simultaneous unification of gauge and gravitational interactions. In the Appendix we work out the group theoretical aspects of this scenario for SU(5) and SO(10) unified groups in detail; this material is also relevant in the analysis of non-universal gaugino masses obtained from supergravity.Comment: 27 pages, 5 figures, 8 tables, 1 appendix, revtex; v2: introduction and conclusion expanded, references added, minor changes, version published in PR

Three waves for quantum gravity

Using effective field theoretical methods, we show that besides the already observed gravitational waves, quantum gravity predicts two further massive classical fields leading to two new massive waves. We set a limit on the masses of these new modes using data from the E¨ot-Wash experiment. We point out that the existence of these new states is a model independent prediction of quantum gravity. We then explain how these new classical fields could impact astrophysical processes and in particular the binary inspirals of neutron stars or black holes. We calculate the emission rate of these new states in binary inspirals astrophysical processes

Bounds on the nonminimal coupling of the Higgs Boson to gravity

We derive the first bound on the value of the Higgs boson nonminimal coupling to the Ricci scalar. We show that the recent discovery of the Higgs boson at the Large Hadron Collider at CERN implies that the nonminimal coupling is smaller than 2.6×10^15

Quantum Black Holes from Cosmic Rays

We investigate the possibility for cosmic ray experiments to discover non-thermal small black holes with masses in the TeV range. Such black holes would result due to the impact between ultra high energy cosmic rays or neutrinos with nuclei from the upper atmosphere and decay instantaneously. They could be produced copiously if the Planck scale is in the few TeV region. As their masses are close to the Planck scale, these holes would typically decay into two particles emitted back-to-back. Depending on the angles between the emitted particles with respect to the center of mass direction of motion, it is possible for the simultaneous showers to be measured by the detectors.Comment: 6 pages, 3 figure