On the finiteness of the BRS modulo-d cocycles

Ladders of field polynomial differential forms obeying systems of descent equations and corresponding to observables and anomalies of gauge theories are renormalized. They obey renormalized descent equations. Moreover they are shown to have vanishing anomalous dimensions. As an application a simple proof of the nonrenormalization theorem for the nonabelian gauge anomaly is given.Comment: 21 p., UGVA-DPT 1992/03-759, Publ. in Nucl Phys. B381 (1992) 37

Inflationary potentials in DBI models

We study DBI inflation based upon a general model characterized by a power-law flow parameter $\epsilon(\phi)\propto\phi^{\alpha}$ and speed of sound $c_s(\phi)\propto\phi^{\beta}$, where $\alpha$ and $\beta$ are constants. We show that in the slow-roll limit this general model gives rise to distinct inflationary classes according to the relation between $\alpha$ and $\beta$ and to the time evolution of the inflaton field, each one corresponding to a specific potential; in particular, we find that the well-known canonical polynomial (large- and small-field), hybrid and exponential potentials also arise in this non-canonical model. We find that these non-canonical classes have the same physical features as their canonical analogs, except for the fact that the inflaton field evolves with varying speed of sound; also, we show that a broad class of canonical and D-brane inflation models are particular cases of this general non-canonical model. Next, we compare the predictions of large-field polynomial models with the current observational data, showing that models with low speed of sound have red-tilted scalar spectrum with low tensor-to-scalar ratio, in good agreement with the observed values. These models also show a correlation between large non-gaussianity with low tensor amplitudes, which is a distinct signature of DBI inflation with large-field polynomial potentials.Comment: Minor changes, reference added. Version submitted to JCA

N=1 SYM Action and BRST Cohomology

The relation between BRST cohomology and the N=1 supersymmetric Yang-Mills action in 4 dimensions is discussed. In particular, it is shown that both off and on shell N=1 SYM actions are related to a lower dimensional field polynomial by solving the descent equations, which is obtained from the cohomological analysis of linearized Slavnov-Taylor operator \B, in the framework of Algebraic Renormalization. Furthermore we show that off and on shell solutions differ only by a \B- exact term, which is a consequence of the fact that the cohomology of both cases are same.Comment: 14 Pages, LaTex. Revised version. To be published in MPL

N=2 Super Yang Mills Action and BRST Cohomology

The extended BRST cohomology of N=2 super Yang-Mills theory is discussed in the framework of Algebraic Renormalization. In particular, N=2 supersymmetric descent equations are derived from the cohomological analysis of linearized Slavnov-Taylor operator \B. It is then shown that both off- and on-shell N=2 super Yang-Mills actions are related to a lower-dimensional gauge invariant field polynomial Tr\f^2 by solving these descent equations. Moreover, it is found that these off- and on-shell solutions differ only by a \B-exact term, which can be interprated as a consequence of the fact that the cohomology of both cases are the same.Comment: Latex, 1+13 page

Braneworld inflation from an effective field theory after WMAP three-year data

In light of the results from the WMAP three-year sky survey, we study an inflationary model based on a single-field polynomial potential, with up to quartic terms in the inflaton field. Our analysis is performed in the context of the Randall-Sundrum II braneworld theory, and we consider both the high-energy and low-energy (i.e. the standard cosmology case) limits of the theory. We examine the parameter space of the model, which leads to both large-field and small-field inflationary type solutions. We conclude that small field inflation, for a potential with a negative mass square term, is in general favored by current bounds on the tensor-to-scalar perturbation ratio rs.Comment: 11 pages, 5 figures; references updated and a few comments added; final version to appear in Phys. Rev.

Large Field Polynomial Inflation: Parameter Space, Predictions and (Double) Eternal Nature

Simple monomial inflationary scenarios have been ruled out by recent observations. In this work we revisit the next simplest scenario, a single--field model where the scalar potential is a polynomial of degree four which features a concave ``almost'' saddle point. We focus on trans--Planckian field values. We reparametrize the potential, which greatly simplifies the procedure for finding acceptbale model parameters. This allows for the first comprehensive scan of parameter space consistent with recent Planck and BICEP/Keck 2018 measurements. Even for trans--Planckian field values the tensor--to--scalar ratio $r$ can be as small as $\mathcal{O}(10^{-8})$, but the model can also saturate the current upper bound. In contrast to the small--field version of this model, radiative stability does not lead to strong constraints on the parameters of the inflaton potential. For very large field values the potential can be approximated by the quartic term; as well known, this allows eternal inflation even for field energy well below the reduced Planck mass $M_{\rm Pl}$, with Hubble parameter $H \sim 10^{-2} M_{\rm Pl}$. More interestingly, we find a region of parameter space that even supports {\em two phases of eternal inflation}. The second epoch only occurs if the slope at the would--be saddle point is very small, and has $H \sim 10^{-5} M_{\rm Pl}$; it can only be realized if $r \sim 10^{-2}$, within the sensitivity range of next--generation CMB observations.Comment: 25 pages, 5 figures; analysis for the small field model was presented in arXiv:2104.0397