Quantum Gravity Constraints on Inflation

We study quantum gravity constraints on inflationary model building. Our approach is based on requiring the entropy associated to a given inflationary model to be less than that of the de Sitter entropy. We give two prescriptions for determining the inflationary entropy, based on either `bits per unit area' or entanglement entropy. The existence of transPlanckian flat directions, necessary for large tensor modes in the CMB, correlates with an inflationary entropy greater than that allowed by de Sitter space. Independently these techniques also constrain or exclude de Sitter models with large-rank gauge groups and high UV cutoffs, such as racetrack inflation or the KKLT construction.Comment: 22 pages; v2 references adde

Inflation with racetrack superpotential and matter field

Several models of inflation with the racetrack superpotential for the volume modulus coupled to a matter field are investigated. In particular, it is shown that two classes of racetrack inflation models, saddle point and inflection point ones, can be constructed in a fully supersymmetric framework with the matter field F-term as a source of supersymmetry breaking and uplifting. Two models of F-term supersymmetry breaking are considered: the Polonyi model and the quantum corrected O'Raifeartaigh model. In the former case, both classes of racetrack inflation models differ significantly from the corresponding models with non-supersymmetric uplifting. The main difference is a quite strong dominance of the inflaton by the matter field. In addition, fine-tuning of the parameters is relaxed as compared to the original racetrack models. In the case of the racetrack inflation models coupled to the O'Raifeartaigh model, the matter field is approximately decoupled from the inflationary dynamics. In all of the above models the gravitino mass is larger than the Hubble scale during inflation. The possibility of having the gravitino much lighter than the Hubble scale is also investigated. It is very hard to construct models with light gravitino in which the volume modulus dominates inflation. On the other hand, models in which the inflationary dynamics is dominated by the matter field are relatively simple and seem to be more natural.Comment: 40 pages, 13 figures, references added, typos corrected, version to be publishe

Biogenic nano-magnetite and nano-zero valent iron treatment of alkaline Cr(VI) leachate and chromite ore processing residue

Highly reactive nano-scale biogenic magnetite (BnM), synthesized by the Fe(III)-reducing bacterium Geobacter sulfurreducens, was tested for the potential to remediate alkaline Cr(VI) contaminated waters associated with chromite ore processing residue (COPR). The performance of this biomaterial, targeting aqueous Cr(VI) removal, was compared to a synthetic alternative, nano-scale zero valent iron (nZVI). Samples of highly contaminated alkaline groundwater and COPR solid waste were obtained from a contaminated site in Glasgow, UK. During batch reactivity tests, Cr(VI) removal from groundwater was inhibited by ~25% (BnM) and ~50% (nZVI) when compared to the treatment of less chemically complex model pH 12 Cr(VI) solutions. In both the model Cr(VI) solutions and contaminated groundwater experiments the surface of the nanoparticles became passivated, preventing complete coupling of their available electrons to Cr(VI) reduction. To investigate this process, the surfaces of the reacted samples were analyzed by TEM-EDX, XAS and XPS, confirming Cr(VI) reduction to the less soluble Cr(III) on the nanoparticle surface. In groundwater reacted samples the presence of Ca, Si and S was also noted on the surface of the nanoparticles, and is likely responsible for earlier onset of passivation. Treatment of the solid COPR material in contact with water, by addition of increasing weight % of the nanoparticles, resulted in a decrease in aqueous Cr(VI) concentrations to below detection limits, via the addition of ≥5% w/w BnM or ≥1% w/w nZVI. XANES analysis of the Cr K edge, showed that the % Cr(VI) in the COPR dropped from 26% to a minimum of 4-7% by the addition of 5% w/w BnM or 2% w/w nZVI, with higher additions unable to reduce the remaining Cr(VI). The treated materials exhibited minimal re-mobilization of soluble Cr(VI) by re-equilibration with atmospheric oxygen, with the bulk of the Cr remaining in the solid fraction. Both nanoparticles exhibited a considerable capacity for the remediation of COPR related Cr(VI) contamination, with the synthetic nZVI demonstrating greater reactivity than the BnM. However, the biosynthesized BnM was also capable of significant Cr(VI) reduction and demonstrated a greater efficiency for the coupling of its electrons towards Cr(VI) reduction than the nZVI