Gravitational tests of the Generalized Uncertainty Principle

We compute the corrections to the Schwarzschild metric necessary to reproduce the Hawking temperature derived from a Generalized Uncertainty Principle (GUP), so that the GUP deformation parameter is directly linked to the deformation of the metric. Using this modified Schwarzschild metric, we compute corrections to the standard General Relativistic predictions for the light deflection and perihelion precession, both for planets in the solar system and for binary pulsars. This analysis allows us to set bounds for the GUP deformation parameter from well-known astronomical measurements.Comment: 20 pages, 2 figure

Discovery and Characterization of Methylation of Arginine 42 on Histone H3: A Novel Histone Modification with Positive Transcriptional Effects

Eukaryotic genomic DNA is packaged in the form of chromatin, which contains repeating nucleosomal units consisting of roughly two super-helical turns of DNA wrapped around an octamer of core histone proteins composed of four histone species: one histone H3/H4 tetramer and two histone H2A/H2B dimers. Histones are basic globular proteins rich in lysine and arginine residues, with unstructured N-terminal “tail” regions protruding outside the nucleosome structure, and structured “core” domains in the DNA-associated portion. Several core residues, and in particular arginines in H3 and H4, mediate key interactions between the histone octamer and DNA in forming the nucleosomal particle. Histone post-translational modifications (PTMs) lead to downstream effects indirectly by allowing or preventing docking of effector molecules, or directly by changing the intrinsic biophysical properties of local chromatin. To date, little has been done to study PTMs that lie outside of the unstructured tail domains of histones. I describe here the identification by mass spectrometry of a novel methylation site on histone H3, the asymmetric dimethylation of arginine 42 (H3R42me2a). H3R42 is conserved through evolution and is at the DNA entry/ exit position within the nucleosome core, with likely interactions with the DNA backbone. I show that methyltransferases CARM1 and PRMT6 methylate this residue in vitro and in vivo. Using chemically-defined “designer” histones I also show that methylation of H3R42 stimulates transcription in vitro from chromatinized templates. Using peptide pull down experiments combined with enzymatic assays I demonstrate that H3R42me2a prevents the stimulation of the histone deacetylase activity of the N-CoR co-repressive complex by impeding its binding to H3. Thus, H3R42 is a new histone methylation site with stimulating effects on transcription. I propose that methylation of basic histone residues at the DNA interface may be a general mechanism to disrupt histone:DNA interactions, with effects on downstream processes, including transcription

Gravity coupling from micro-black holes

Recently much work has been done in lowering the Planck threshold of quantum gravitational effects (sub-millimeter dimension(s), Horava-Witten fifth dimension, strings or branes low energy effects, etc.). Working in the framework of 4-dim gravity, with semi-classical considerations based on Hawking evaporation of planckian micro-black holes, I shall show here as quantum gravity effects could occur also near GUT energies.Comment: LaTex file, 5 pages, no figure

Minimum length (scale) in Quantum Field Theory, Generalized Uncertainty Principle and the non-renormalisability of gravity

The notions of minimum geometrical length and minimum length scale are discussed with reference to correlation functions obtained from in-in and in-out amplitudes in quantum field theory. Whereas the in-in propagator for metric perturbations does not admit the former, the in-out Feynman propagator shows the emergence of the latter. A connection between the Feynman propagator of quantum field theories of gravity and the deformation parameter $\delta_0$ of the generalised uncertainty principle (GUP) is then exhibited, which allows to determine an exact expression for $\delta_0$ in terms of the residues of the causal propagator. A correspondence between the non-renormalisability of (some) theories (of gravity) and the existence of a minimum length scale is then conjectured to support the idea that non-renormalisable theories are self-complete and finite. The role played by the sign of the deformation parameter is further discussed by considering an implementation of the GUP on the lattice.Comment: LaTeX, 12 pages, no figures, final version to appear in PL

Higher Order Slow-Roll Predictions for Inflation

We study the WKB approximation beyond leading order for cosmological perturbations during inflation. To first order in the slow-roll parameters, we show that an improved WKB approximation leads to analytical results agreeing to within 0.1% with the standard slow-roll results. Moreover, the leading WKB approximation to second order in the slow-roll parameters leads to analytical predictions in qualitative agreement with those obtained by the Green's function method.Comment: Replaced to match published versio

Adiabatic Invariant Treatment of a Collapsing Sphere of Quantized Dust

The semiclassical collapse of a sphere of quantized dust is studied. A Born-Oppenheimer decomposition is performed for the wave function of the system and the semiclassical limit is considered for the gravitational part. The method of adiabatic invariants for time dependent Hamiltonians is then employed to find (approximate) solutions to the quantum dust equations of motions. This allows us to obtain corrections to the adiabatic approximation of the dust states associated with the time evolution of the metric. The diverse non-adiabatic corrections are generally associated with particle (dust) creation and related fluctuations. The back-reaction due to the dominant contribution to particle creation is estimated and seen to slow-down the collapse.Comment: LaTeX, 16 pages, no figures, final version to appear in Class. and Quantum Gravit

Point-like sources and the scale of quantum gravity

We review the General Relativistic model of a (quasi) point-like particle represented by a massive shell of neutral matter which has vanishing total energy in the small-volume limit. We then show that, by assuming a Generalised Uncertainty Principle, which implies the existence of a minimum length of the order of the Planck scale, the total energy instead remains finite and equal to the shell's proper mass both for very heavy and very light particles. This suggests that the quantum structure of space-time might be related to the classical Equivalence Principle and possible implications for the late stage of evaporating black holes are briefly mentioned.Comment: 5 pages, 3 figures, revtex4 styl

Improved WKB analysis of Slow-Roll Inflation

We extend the WKB method for the computation of cosmological perturbations during inflation beyond leading order and provide the power spectra of scalar and tensor perturbations to second order in the slow-roll parameters. Our method does not require that the slow-roll parameters be constant. Although leading and next-to-leading results in the slow-roll parameters depend on the approximation technique used in the computation, we find that the inflationary theoretical predictions obtained may reach the accuracy required by planned observations. In two technical appendices, we compare our techniques and results with previous findings.Comment: REVTeX 4, 13 pages, no figures, final version to appear in Phys. Rev.