Quantum modes in DBI inflation: exact solutions and constraints from vacuum selection

We study a two-parameter family of exactly solvable inflation models with variable sound speed, and derive a corresponding exact expression for the spectrum of curvature perturbations. We generalize this expression to the slow roll case, and derive an approximate expression for the scalar spectral index valid to second order in slow roll. We apply the result to the case of DBI inflation, and show that for certain choices of slow roll parameters, the Bunch-Davies limit (a) does not exist, or (b) is sensitive to stringy physics in the bulk, which in principle can have observable signatures in the primordial power spectrum.Comment: 10 pages, LaTeX; V2: version submitted to PRD. References added, minor error in text correcte

Inflation over the hill

We calculate the power spectrum of curvature perturbations when the inflaton field is rolling over the top of a local maximum of a potential. We show that the evolution of the field can be decomposed into a late-time attractor, which is identified as the slow roll solution, plus a rapidly decaying non-slow roll solution, corresponding to the field rolling ``up the hill'' to the maximum of the potential. The exponentially decaying transient solution can map to an observationally relevant range of scales because the universe is also expanding exponentially. We consider the two branches separately and we find that they are related through a simple transformation of the slow roll parameter $\eta$ and they predict identical power spectra. We generalize this approach to the case where the inflaton field is described by both branches simultaneously and find that the mode equation can be solved exactly at all times. Even though the slow roll parameter $\eta$ is evolving rapidly during the transition from the transient solution to the late-time attractor solution, the resultant power spectrum is an exact power-law spectrum. Such solutions may be useful for model-building on the string landscape.Comment: 11 pages, 1 figure (V3: Version accepted by PRD, title changed by journal

Asymptotic behavior of small solutions for the discrete nonlinear Schr\"odinger and Klein-Gordon equations

We show decay estimates for the propagator of the discrete Schr\"odinger and Klein-Gordon equations in the form \norm{U(t)f}{l^\infty}\leq C (1+|t|)^{-d/3}\norm{f}{l^1}. This implies a corresponding (restricted) set of Strichartz estimates. Applications of the latter include the existence of excitation thresholds for certain regimes of the parameters and the decay of small initial data for relevant $l^p$ norms. The analytical decay estimates are corroborated with numerical results.Comment: 13 pages, 4 figure

FRW Cosmology with Non-positively Defined Higgs Potentials

We discuss the classical aspects of dynamics of scalar models with non-positive Higgs potentials in the FRW cosmology. These models appear as effective local models in non-local models related with string field theories. After a suitable field redefinition these models have the form of local Higgs models with a negative extra cosmological term and the total Higgs potential is non-positively defined and has rather small coupling constant. The non-positivity of the potential leads to the fact that on some stage of evolution the expansion mode gives place to the mode of contraction, due to that the stage of reheating is absent. In these models the hard regime of inflation gives place to inflation near the hill top and the area of the slow roll inflation is very small. Meanwhile one can obtain enough e-foldings before the contraction to make the model under consideration admissible to describe inflation.Comment: 40 pages, 20 figures, typos correcte

Single-field inflation constraints from CMB and SDSS data

We present constraints on canonical single-field inflation derived from WMAP five year, ACBAR, QUAD, BICEP data combined with the halo power spectrum from SDSS LRG7. Models with a non-scale-invariant spectrum and a red tilt n_s < 1 are now preferred over the Harrison-Zel'dovich model (n_s = 1, tensor-to-scalar ratio r = 0) at high significance. Assuming no running of the spectral indices, we derive constraints on the parameters (n_s, r) and compare our results with the predictions of simple inflationary models. The marginalised credible intervals read n_s = 0.962^{+0.028}_{-0.026} and r < 0.17 (at 95% confidence level). Interestingly, the 68% c.l. contours favour mainly models with a convex potential in the observable region, but the quadratic potential model remains inside the 95% c.l. contours. We demonstrate that these results are robust to changes in the datasets considered and in the theoretical assumptions made. We then consider a non-vanishing running of the spectral indices by employing different methods, non-parametric but approximate, or parametric but exact. With our combination of CMB and LSS data, running models are preferred over power-law models only by a Delta chi^2 ~ 5.8, allowing inflationary stages producing a sizable negative running -0.063^{+0.061}_{-0.049} and larger tensor-scalar ratio r < 0.33 at the 95% c.l. This requires large values of the third derivative of the inflaton potential within the observable range. We derive bounds on this derivative under the assumption that the inflaton potential can be approximated as a third order polynomial within the observable range.Comment: 32 pages, 7 figures. v2: additional references, some typos corrected, passed to JCAP style. v3: minor changes, matches published versio

A predictive group-contribution framework for the thermodynamic modelling of CO absorption in cyclic amines, alkyl polyamines, alkanolamines and phase-change amines: New data and SAFT- Mie parameters

A significant effort is under way to identify improved solvents for carbon dioxide (CO ) capture by chemisorption. We develop a predictive framework that is applicable to aqueous solvent + CO mixtures containing cyclic amines, alkyl polyamines, and alkanolamines. A number of the mixtures studied exhibit liquid–liquid phase separation, a behaviour that has shown promise in reducing the energetic cost of CO capture. The proposed framework is based on the SAFT- Mie group-contribution (GC) approach, in which chemical reactions are described via physical association models that allow a simpler, implicit, treatment of the chemical speciation characteristic of these mixtures. We use previously optimized group interaction parameters between some amine groups and water (Perdomo et al., 2021), and develop new group interactions for the cNH, cN, NH2, NH, N, cCHNH, and cCHN groups with CO2; a set of second-order group parameters are also developed to account for proximity effects in some alkanolamines. A combination of literature data and new experimental measurements for the absorption of CO2 in aqueous cyclohexylamine systems obtained in our current work, are used to develop and test the proposed models. The SAFT- Mie GC approach is used to predict the thermodynamics of selected mixtures, including ternary phase diagrams and mixing properties relevant in the context of CO2 capture. The current work constitutes a substantial extension of the range of aqueous amine-based solvents that can be modelled and thus offers the most comprehensive thermodynamically consistent platform to date to screen novel candidate solvents for CO2 capture

Cosmological observations in non-local F(R)F(R) cosmology

In this article in a generalization of our previous work, we investigate the dynamics of the non-local $F(R)$ gravity after casting it into local form. The non-singular bouncing behavior and quintom model of dark energy are achieved without involving negative kinetic energy fields. Two cosmological tests are performed to constrain the model parameters. In case of phantom crossing the distance modulus predicted by the model best-fits the observational data. In comparison with the CPL parametrization for drift velocity, the model in some redshift intervals is in good agreement with the data.Comment: 12 pages, 7 figures, will be published in Astrophysics and space scienc

Non-relativistic Matrix Inflation

We reconsider a string theoretic inflationary model, where inflation is driven by $n$ multiple coincident $D3$-branes in the finite $n$ limit. We show that the finite $n$ action can be continued to the limit of large $n$, where it converges to the action for a wrapped $D5$-brane with $n$ units of U(1) flux. This provides an important consistency check of the scenario and allows for more control over certain back-reaction effects. We determine the most general form of the action for a specific sub-class of models and examine the non-relativistic limits of the theory where the branes move at speeds much less than the speed of light. The non-Abelian nature of the world-volume theory implies that the inflaton field is matrix valued and this results in modifications to the slow-roll parameters and Hubble-flow equations. A specific small field model of inflation is investigated where the branes move out of an AdS throat, and observational constraints are employed to place bounds on the background fluxes.Comment: 25 page