arXiv subjects

Yeinzon Rodriguez

Publications and source records attributed to Yeinzon Rodriguez.

At least 37 records · Page 2Linked to original sources

arXiv2016

On the 4D generalized Proca action for an Abelian vector field

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated Stückelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the Stückelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field $A_μ$, the Faraday tensor $F_{μν}$ and its Hodge dual $\tilde{F}_{μν}$.

hep-th↗

arXiv2016

A New Pedagogical Way of Finding Out the Gauge Field Strength Tensor in Abelian and Non-Abelian Local Gauge Field Theories

The gauge field strength tensor $F_{μν}$ in Abelian and non-Abelian local gauge field theories is a key object in the construction of the Lagrangian since it provides the kinetic term(s) of the gauge field(s) $A_μ$. When introducing this object, most of textbooks employ as a tool the commutator of the gauge covariant derivatives $D_μψ$ of a fermion field $ψ$: $F_{μν} ψ= (i/g)[D_μ,D_ν]ψ$. I argue that such a construction, although completely correct and valid, is not pedagogical enough for many students that approach the gauge field theories for the first time. Another construction, based on the object $D_μA_ν$: $F_{μν} = D_{[μ} A_{ν]}$, which avoids the introduction of additional and, for the case in consideration, spurious degrees of freedom such as the fermion one, simpler, more pedagogical in many cases, and suitable for first-time students, is presented.

physics.gen-ph↗

arXiv2016

Massive Gauge-flation

Gauge-flation model at zeroth order in cosmological perturbation theory offers an interesting scenario for realizing inflation within a particle physics context, allowing us to investigate interesting possible connections between inflation and the subsequent evolution of the Universe. Difficulties, however, arise at the perturbative level, thus motivating a modification of the original model. In order to agree with the latest Planck observations, we modify the model such that the new dynamics can produce a relation between the spectral index $n_{s}$ and the tensor-to-scalar ratio $r$ allowed by the data. By including an identical mass term for each of the fields of the system, we find interesting dynamics leading to slow-roll inflation of the right length. The presence of the mass term has the potential to modify the $n_{s}$ vs. $r$ relation so as to agree with the data. As a first step, we study the model at zeroth order in cosmological perturbation theory, finding the conditions required for slow-roll inflation and the number of e-foldings of inflation. Numerical solutions are used to explore the impact of the mass term. We conclude that the massive version of Gauge-flation offers a viable inflationary model.

gr-qc↗

arXiv2016

Generalized Proca action for an Abelian vector field

We revisit the most general theory for a massive vector field with derivative self-interactions, extending previous works on the subject to account for terms having trivial total derivative interactions for the longitudinal mode. In the flat spacetime (Minkowski) case, we obtain all the possible terms containing products of up to five first-order derivatives of the vector field, and provide a conjecture about higher-order terms. Rendering the metric dynamical, we covariantize the results and add all possible terms implying curvature.

hep-th↗

arXiv2015

Towards a proof of the equivalence between FRW background expansion and statistical isotropy

We will expose in this paper our advances towards a proof of the equivalence between FRW background expansion, during some period of time that contains primordial inflation, and the statistical isotropy of the primordial curvature perturbation $ζ$ at the end of this period of time. Our motivation rests on the growing interest in the existence of a preferred direction in the Universe hinted by the continuous presence of anomalies in the CMB data.

astro-ph.CO↗

arXiv2015

Moment transport equations and their application to the perturbed universe

There are many inflationary models that allow the formation of the large-scale structure of the observable universe. The non-gaussianity parameter $f_{NL}$ is a useful tool to discriminate among these cosmological models when comparing the theoretical predictions with the satellite survey results like those from WMAP and Planck. The goal of this proceeding contribution is to review the moment transport equations methodology and the subsequent calculation of the $f_{NL}$ parameter.

astro-ph.CO↗

arXiv2015

Analysis of Vector-Inflation Models Using Dynamical Systems

We analyze two possible vector-field models using the techniques of dynamical systems. The first model involves a U(1)-vector field and the second a triad of SU(2)-vector fields. Both models include a gauge-fixing term and a power-law potential. A dynamical system is formulated and it is found that one of the critical points, for each model, corresponds to inflation, the origin of these critical points being the respective gauge-fixing terms. The conditions for the existence of an inflationary era which lasts for at least 60 efolds are studied.

gr-qc↗

arXiv2014

Scale and shape dependent non-Gaussianity in the presence of inflationary vector fields

We consider cosmological inflationary models in which vector fields play some role in the generation of the primordial curvature perturbation $ζ$. Such models are interesting because the involved vector fields naturally seed statistical anisotropy in the primordial fluctuations which could eventually leave a measurable imprint on the cosmic microwave background fluctuations. In this article, we estimate the scale and shape dependent effects on the non-Gaussianity (NG) parameters due to the scale dependent statistical anisotropy in the distribution of the fluctuations. For concreteness, we use a power spectrum (PS) of the fluctuations of the quadrupolar form: $P_ζ(\vec{k})\equiv P_ζ(k)[1+g_ζ(k)(\hat{n} \cdot \hat{k})^2 ]$, where $g_ζ(k)$ is the only quantity which parametrizes the level of statistical anisotropy and $\hat{n}$ is a unitary vector which points towards the preferred direction. Then, we evaluate the contribution of the running of $g_ζ(k)$ on the NG parameters by means of the $δN$ formalism. We focus specifically on the details for the $f_{\rm NL}$ NG parameter, associated with the bispectrum $B_ζ$, but the structure of higher order NG parameters is straightforward to generalize. Although the level of statistical anisotropy in the PS is severely constrained by recent observations, the importance of statistical anisotropy signals in higher order correlators remains to be determined, this being the main task that we address here. The precise measurement of the shape and scale dependence (or running) of statistical parameters such as the NG parameters and the statistical anisotropy level could provide relevant elements for model building and for the determination of the presence (or nonpresence) of inflationary vector fields and their role in the inflationary mechanism.

astro-ph.CO↗

arXiv2013

Statistical Anisotropy in Inflationary Models with Many Vector Fields and/or Prolonged Anisotropic Expansion

We study the most general contributions due to scalar field perturbations, vector field perturbations, and anisotropic expansion to the generation of statistical anisotropy in the primordial curvature perturbation ζ. Such a study is done using the δN formalism where only linear terms are considered. Here, we consider two specific cases that lead to determine the power spectrum P_ζ(k) of the primordial curvature perturbation. In the first one, we consider the possibility that the n-point correlators of the field perturbations in real space are invariant under rotations in space (statistical isotropy); as a result, we obtain as many levels of statistical anisotropy as vector fields present and, therefore, several preferred directions. The second possibility arises when we consider anisotropic expansion, which leads us to obtain I+a additional contributions to the generation of statistical anisotropy of ζcompared with the former case, being I and a the number of scalar and vector fields involved respectively.

astro-ph.CO↗

arXiv2013

The Different Varieties of the Suyama-Yamaguchi Consistency Relation

We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation τ_{NL} \geqslant (\frac{6}{5} f_{NL})^2, the latter involving the levels of non-gaussianity f_{NL} and τ_{NL} in the primordial curvature perturbation ζ, they being scale-invariant. We explicitly state under which conditions the SY consistency relation has been claimed to hold in its different varieties (implicitly) presented in the literature since its inception back in 2008; as a result, we show for the first time that the variety τ_{NL} ({\bf k}_1, {\bf k}_1) \geqslant (\frac{6}{5} f_{NL} ({\bf k}_1))^2, which we call "the fifth variety", is always satisfied even when there is strong scale-dependence and high levels of statistical anisotropy as long as statistical homogeneity holds: thus, an observed violation of this specific variety would prevent the comparison between theory and observation, shaking this way the foundations of cosmology as a science.

astro-ph.CO↗

arXiv2013

The Vector Curvaton

We analyze a massive vector field with a non-canonical kinetic term in the action, minimally coupled to gravity, where the mass and kinetic function of the vector field vary as functions of time during inflation. The vector field is introduced following the same idea of a scalar curvaton, which must not affect the inflationary dynamics since its energy density during inflation is negligible compared to the total energy density in the Universe. Using this hypothesis, the vector curvaton will be solely responsible for generating the primordial curvature perturbation ζ. We have found that the spectra of the vector field perturbations are scale-invariant in superhorizon scales due to the suitable choice of the time dependence of the kinetic function and the effective mass during inflation. The preferred direction, generated by the vector field, makes the spectrum of ζdepend on the wavevector, i.e. there exists statistical anisotropy in ζ. This is discussed principally in the case where the mass of the vector field increases with time during inflation, where it is possible to find a heavy field (M >> H) at the end of inflation, making the particle production be practically isotropic; thus, the longitudinal and transverse spectra are nearly the same order which in turn causes that the statistical anisotropy generated by the vector field is within the observational bounds.

astro-ph.CO↗

arXiv2013

The different varieties of the Suyama-Yamaguchi consistency relation and its violation as a signal of statistical inhomogeneity

We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation τ_{NL} \geqslant ((6/5) f_{NL})^2. It has been claimed that the following variation: τ_{NL} ({\bf k}_1, {\bf k_3}) \geqslant (6/5)^2 f_{NL} ({\bf k}_1) f_{NL} ({\bf k}_3), which we call "the fourth variety", in the collapsed (for τ_{NL}) and squeezed (for f_{NL}) limits is always satisfied independently of any physics; however, the proof depends sensitively on the assumption of scale-invariance which only applies for cosmological models involving Lorentz-invariant scalar fields (at least at tree level), leaving room for a strong violation of this variety of the consistency relation when non-trivial degrees of freedom, for instance vector fields, are in charge of the generation of ζ. With this in mind as a motivation, we explicitly state under which conditions the SY consistency relation has been claimed to hold in its different varieties (implicitly) presented in the literature; as a result, we show for the first time that the variety τ_{NL} ({\bf k}_1, {\bf k}_1) \geqslant ((6/5) f_{NL} ({\bf k}_1))^2, which we call "the fifth variety", is always satisfied even when there is strong scale-dependence as long as statistical homogeneity holds: thus, an observed violation of this specific variety would prevent the comparison between theory and observation, shaking this way the foundations of cosmology as a science. Later, we concern about the existence of non-trivial degrees of freedom, concretely vector fields for which the levels of non-gaussianity have been calculated for very few models, finding that the fourth variety of the SY consistency relation is indeed strongly violated for some specific wavevector configurations while the fifth variety continues to be well satisfied. (Abridged)

astro-ph.CO↗

arXiv2013

The Suyama-Yamaguchi consistency relation in the presence of vector fields

We consider inflationary models in which vector fields are responsible for part or eventually all of the primordial curvature perturbation ζ. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity is generated due to the superhorizon evolution, we use the δN formalism to do a complete tree level calculation of the non-Gaussianity parameters f_{NL} and τ_{NL} in the presence of vector fields. We isolate the isotropic pieces of the non-Gaussianity parameters, which anyway have contributions from the vector fields, and show that they obey the Suyama-Yamaguchi consistency relation τ^{iso}_{NL}>=(6/5f^{iso}_{NL})^2. Other ways of defining the non-Gaussianity parameters, which could be observationally relevant, are stated and the respective Suyama-Yamaguchi-like consistency relations are obtained.

astro-ph.CO↗

arXiv2012

On the true nature of renormalizability in Horava-Lifshitz gravity

We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.

hep-th↗

arXiv2011

Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation ζwas developed a few years ago following the spirit of the Feynman rules in Quantum Field Theory. The methodology is very useful and time-saving, as it is for the case of the Feynman rules in the particle physics context, but, unfortunately, is not very well known by the cosmology community. In the present work, we extend such an approach in order to include not only scalar field perturbations as the generators of ζ, but also vector field perturbations. The purpose is twofold: first, we would like the diagrammatic approach (which we would call the Feynman-like rules) to become widespread among the cosmology community; second, we intend to give an easy tool to formulate any correlator of ζfor those cases that involve vector field perturbations and that, therefore, may generate prolonged stages of anisotropic expansion and/or important levels of statistical anisotropy. Indeed, the usual way of formulating such correlators, using the Wick's theorem, may become very clutter and time-consuming.

astro-ph.CO↗

arXiv2010

Non-gaussianity from the trispectrum and vector field perturbations

We use the δN formalism to study the trispectrum T_ζof the primordial curvature perturbation ζwhen the latter is generated by vector field perturbations, considering the tree-level and one-loop contributions. The order of magnitude of the level of non-gaussianity in the trispectrum, τ_{NL}, is calculated in this scenario and related to the order of magnitude of the level of non-gaussianity in the bispectrum, f_{NL}, and the level of statistical anisotropy in the power spectrum, g_ζ. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on τ_{NL} from WMAP, for generic inflationary models, is done.

astro-ph.CO↗

arXiv2010

On the Issue of the ζSeries Convergence and Loop Corrections in the Generation of Observable Primordial Non-Gaussianity in Slow-Roll Inflation. Part II: the Trispectrum

We calculate the trispectrum T_ζof the primordial curvature perturbation ζ, generated during a {\it slow-roll} inflationary epoch by considering a two-field quadratic model of inflation with {\it canonical} kinetic terms. We consider loop contributions as well as tree level terms, and show that it is possible to attain very high, {\it including observable}, values for the level of non-gaussianity τ_{NL} if T_ζis dominated by the one-loop contribution. Special attention is paid to the claim in JCAP {\bf 0902}, 017 (2009) [arXiv:0812.0807 [astro-ph]] that, in the model studied in this paper and for the specific inflationary trajectory we choose, the quantum fluctuations of the fields overwhelm the classical evolution. We argue that such a claim actually does not apply to our model, although more research is needed in order to understand the role of quantum diffusion. We also consider the probability that an observer in an ensemble of realizations of the density field sees a non-gaussian distribution. In that respect, we show that the probability associated to the chosen inflationary trajectory is non-negligible. Finally, the levels of non-gaussianity f_{NL} and τ_{NL} in the bispectrum B_ζand trispectrum T_ζof ζ, respectively, are also studied for the case in which ζis not generated during inflation.

astro-ph↗

arXiv2009

Non-gaussianity at tree and one-loop levels from vector field perturbations

We study the spectrum P_ζand bispectrum B_ζof the primordial curvature perturbation ζwhen the latter is generated by scalar and vector field perturbations. The tree-level and one-loop contributions from vector field perturbations are worked out considering the possibility that the one-loop contributions may be dominant over the tree level terms (both (either) in P_ζand (or) in B_ζ) and viceversa. The level of non-gaussianity in the bispectrum, f_{NL}, is calculated and related to the level of statistical anisotropy in the power spectrum, g_ζ. For very small amounts of statistical anisotropy in the power spectrum, the level of non-gaussianity may be very high, in some cases exceeding the current observational limit.

astro-ph.CO↗