Reheating the Universe After Multi-Field Inflation

We study in detail (p)reheating after multi-field inflation models with a particular focus on N-flation. We consider a variety of different couplings between the inflatons and the matter sector, including both quartic and trilinear interactions with a light scalar field. We show that the presence of multiple oscillating inflatons makes parametric resonance inefficient in the case of the quartic interactions. Moreover, perturbative processes do not permit a complete decay of the inflaton for this coupling. In order to recover the hot big bang, we must instead consider trilinear couplings. In this case we show that strong nonperturbative preheating is possible via multi-field tachyonic resonance. In addition, late-time perturbative effects do permit a complete decay of the condensate. We also study the production of gauge fields for several prototype couplings, finding similar results to the trilinear scalar coupling. During the course of our analysis we develop the mathematical theory of the quasi-periodic Mathieu equation, the multi-field generalization of the Floquet theory familiar from preheating after single field inflation. We also elaborate on the theory of perturbative decays of a classical inflaton condensate, which is applicable in single-field models also.Comment: 46+1 pages, 19 figure

Quantified Constraints and Containment Problems

The quantified constraint satisfaction problem $\mathrm{QCSP}(\mathcal{A})$ is the problem to decide whether a positive Horn sentence, involving nothing more than the two quantifiers and conjunction, is true on some fixed structure $\mathcal{A}$. We study two containment problems related to the QCSP. Firstly, we give a combinatorial condition on finite structures $\mathcal{A}$ and $\mathcal{B}$ that is necessary and sufficient to render $\mathrm{QCSP}(\mathcal{A}) \subseteq \mathrm{QCSP}(\mathcal{B})$. We prove that $\mathrm{QCSP}(\mathcal{A}) \subseteq \mathrm{QCSP}(\mathcal{B})$, that is all sentences of positive Horn logic true on $\mathcal{A}$ are true on $\mathcal{B}$, iff there is a surjective homomorphism from $\mathcal{A}^{|A|^{|B|}}$ to $\mathcal{B}$. This can be seen as improving an old result of Keisler that shows the former equivalent to there being a surjective homomorphism from $\mathcal{A}^\omega$ to $\mathcal{B}$. We note that this condition is already necessary to guarantee containment of the $\Pi_2$ restriction of the QCSP, that is $\Pi_2$-$\mathrm{CSP}(\mathcal{A}) \subseteq \Pi_2$-$\mathrm{CSP}(\mathcal{B})$. The exponent's bound of ${|A|^{|B|}}$ places the decision procedure for the model containment problem in non-deterministic double-exponential time complexity. We further show the exponent's bound $|A|^{|B|}$ to be close to tight by giving a sequence of structures $\mathcal{A}$ together with a fixed $\mathcal{B}$, $|B|=2$, such that there is a surjective homomorphism from $\mathcal{A}^r$ to $\mathcal{B}$ only when $r \geq |A|$. Secondly, we prove that the entailment problem for positive Horn fragment of first-order logic is decidable. That is, given two sentences $\varphi$ and $\psi$ of positive Horn, we give an algorithm that determines whether $\varphi \rightarrow \psi$ is true in all structures (models). Our result is in some sense tight, since we show that the entailment problem for positive first-order logic (i.e. positive Horn plus disjunction) is undecidable. In the final part of the paper we ponder a notion of Q-core that is some canonical representative among the class of templates that engender the same QCSP. Although the Q-core is not as well-behaved as its better known cousin the core, we demonstrate that it is still a useful notion in the realm of QCSP complexity classifications.Comment: This paper is a considerably expanded journal version of a LICS 2008 paper of the same title together with the most significant parts of a CP 2012 paper from the latter two author

Phenomenology of a Pseudo-Scalar Inflaton: Naturally Large Nongaussianity

Many controlled realizations of chaotic inflation employ pseudo-scalar axions. Pseudo-scalars \phi are naturally coupled to gauge fields through c \phi F \tilde{F}. In the presence of this coupling, gauge field quanta are copiously produced by the rolling inflaton. The produced gauge quanta, in turn, source inflaton fluctuations via inverse decay. These new cosmological perturbations add incoherently with the "vacuum" perturbations, and are highly nongaussian. This provides a natural mechanism to generate large nongaussianity in single or multi field slow-roll inflation. The resulting phenomenological signatures are highly distinctive: large nongaussianity of (nearly) equilateral shape, in addition to detectably large values of both the scalar spectral tilt and tensor-to-scalar ratio (both being typical of large field inflation). The WMAP bound on nongaussianity implies that the coupling, c, of the pseudo-scalar inflaton to any gauge field must be smaller than about 10^{2} M_p^{-1}.Comment: 45 pages, 7 figure

Effect of off-pump coronary surgery with right ventricular assist device on organ function and inflammatory response: a randomized controlled trial.

BACKGROUND: Right ventricular assist devices (RVADs) have been proposed to improve exposure of the coronary arteries in off-pump surgery. In this study we investigated the impact of the A-Med RVAD on inflammatory response and organ function in patients undergoing coronary artery bypass grafting. METHODS: Sixty patients were prospectively randomized to conventional surgery with cardiopulmonary bypass (CPB) and cardioplegic arrest, beating heart surgery (off-pump), or beating heart surgery with the RVAD. Serial blood samples were collected postoperatively, for analysis of inflammatory markers, troponin I, protein S100, and free hemoglobin. Renal tubular function was assessed by measuring urine N-acetyl-glucosaminidase activity. RESULTS: No hospital deaths or major postoperative complications occurred in the study population. Interleukin-6, interleukin-8, C3a, and troponin I levels after surgery were significantly higher in the CPB group compared with the off-pump and RVAD groups. Free hemoglobin levels immediately after the operation, peak and total S100 levels, and N-acetyl-glucosaminidase activity were also significantly higher in the CPB group. CONCLUSIONS: Off-pump coronary revascularization, with or without RVAD, reduces inflammatory response, myocardial, neurologic, and renal injury, and decreases hemolysis when compared with conventional surgery with CPB and cardioplegic arrest

On Tunnelling In Two-Throat Warped Reheating

We revisit the energy transfer necessary for the warped reheating scenario in a two-throat geometry. We study KK mode wavefunctions of the full two-throat system in the Randall--Sundrum (RS) approximation and find an interesting subtlety in the calculation of the KK mode tunnelling rate. While wavepacket tunnelling is suppressed unless the Standard Model throat is very long, wavefunctions of modes localized in different throats have a non-zero overlap and energy can be transferred between the throats by interactions between such KK modes. The corresponding decay rates are calculated and found to be faster than the tunnelling rates found in previously published works. However, it turns out that the imaginary parts of the mode frequencies, induced by the decay, slow the decay rates themselves down. The self-consistent decay rate turns out to be given by the plane wave tunnelling rate considered previously in the literature. We then discuss mechanisms that may enhance the energy transfer between the throats over the RS rates. In particular, we study models in which the warp factor changes in the UV region less abruptly than in the RS model, and find that it is easy to build phenomenological models in which the plane wave tunnelling rate, and hence the KK mode interaction rates, are enhanced compared to the standard RS setup.Comment: 27 pages + appendices, 5 figures, latex. v2: Discussion of decay in Section 4 changed: the most dangerous graviton amplitudes are zero, the results are now more positive for the warped reheating scenario; typos fixed, discussion cleaned up. v3:corrections in Section 5 (decay rates slowed down), mild changes of overall conclusion

MATHEMATICAL FORMULAS FOR CALCULATING NET RETURNS FROM PARTICIPATION IN GOVERNMENT PROGRAMS, CRP, AND CROP INSURANCE ALTERNATIVES

The purpose of this report is to provide a revised version of the publication, "Mathematical Formulas for Calculating Net Returns from Participation in Government Commodity Programs including Marketing Loans" (Williams and Barnaby, 1994). The change in design of the government commodity programs and development of several crop insurance alternatives has been significant since the previous paper was published. The formulas for calculating net returns incorporate provisions from the Farm Security and Rural Investment Act of 2002 and several crop insurance designs developed in the 1990s. Individuals conducting research or education programs will be able to use this revision for reference when estimating net returns for producers under current commodity program and crop insurance plan provisions.Agricultural Finance,

Inhomogeneous tachyon condensation

We investigate the spacetime-dependent condensation of the tachyon in effective field theories. Previous work identified singularities in the field which appear in finite time: infinite gradients at the kinks, and (in the eikonal approximation) caustics near local minima. By performing a perturbation analysis, and with numerical simulations, we demonstrate and explain key features of the condensation process: perturbations generically freeze, and minima develop singular second derivatives in finite time (caustics). This last has previously been understood in terms of the eikonal approximation to the dynamics. We show explicitly from the field equations how this approximation emerges, and how the caustics develop, both in the DBI and BSFT effective actions. We also investigate the equation of state parameter of tachyon matter showing that it is small, but generically non-zero. The energy density tends to infinity near field minima with a charateristic profile. A proposal to regulate infinities by modifying the effective action is also studied. We find that although the infinities at the kinks are successfully regularised in the time-dependent case, caustics still present.Comment: 4 figures,19p

Experimental Analysis of Proton-Induced Displacement and Ionization Damage Using Gate-Controlled Lateral PNP Bipolar Transistors

The electrical characteristics of proton-irradiated bipolar transistors are affected by ionization damage to the insulating oxide and displacement damage to the semiconductor bulk. While both types of damage degrade the transistor, it is important to understand the mechanisms individually and to be able to analyze them separately. In this paper, a method for analyzing the effects of ionization and displacement damage using gate-controlled lateral PNP bipolar junction transistors is described. This technique allows the effects of oxide charge, surface recombination velocity, and bulk traps to be measured independently

Analysis of scalar perturbations in cosmological models with a non-local scalar field

We develop the cosmological perturbations formalism in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field in the presence of the arbitrary potential and formulate the local system of equations for perturbations in the linearized model when both simple and double roots of the characteristic equation are present. We carry out the general analysis related to the curvature and entropy perturbations and consider the most specific example of perturbations when important quantities in the model become complex.Comment: LaTeX, 25 pages, 1 figure, v2: Subsection 3.2 and Section 5 added, references added, accepted for publication in Class. Quant. Grav. arXiv admin note: text overlap with arXiv:0903.517

Brane Bremsstrahlung in DBI Inflation

We consider the effect of trapped branes on the evolution of a test brane whose motion generates DBI inflation along a warped throat. The coupling between the inflationary brane and a trapped brane leads to the radiation of non-thermal particles on the trapped brane. We calculate the Gaussian spectrum of the radiated particles and their backreaction on the DBI motion of the inflationary brane. Radiation occurs for momenta lower than the speed of the test brane when crossing the trapped brane. The slowing down effect is either due to a parametric resonance when the interaction time is small compared to the Hubble time or a tachyonic resonance when the interaction time is large. In both cases the motion of the inflationary brane after the interaction is governed by a chameleonic potential,which tends to slow it down. We find that a single trapped brane can hardly slow down a DBI inflaton whose fluctuations lead to the Cosmic Microwave Background spectrum. A more drastic effect is obtained when the DBI brane encounters a tightly spaced stack of trapped branes.Comment: 20 pages, 1 figur