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The Generalized SU(2) Proca (GSU2P) theory has recently garnered attention for its potential to describe key phases of cosmic evolution, including primordial inflation and late-time accelerated expansion. However, its full cosmological implications remain unexplored. In this work, we perform a comprehensive analysis of the dynamical properties of the GSU2P theory in a flat, homogeneous, and isotropic spacetime, through a dynamical-system approach. Our analysis reveals the presence of three pairs of fixed points, one of them corresponding to de-Sitter expansion which may represent either a stable or unstable phase in the evolution of the universe. These points, nonetheless, give rise to an indeterminate or infinite Hubble parameter, which renders them cosmologically unviable. Additionally, we find two key pseudostationary states: the ``attractor lines'', along which the system exhibits constant-roll dynamics, and the ``central zone'', characterized by oscillatory radiation-like behaviour of the field. The dynamics within the central zone could represent a graceful exit from the primordial inflationary phase to a radiation dominated phase, or a state of the dark energy component prior to the late-time cosmic acceleration. However, within the central zone, the dynamics of the vector field leads to recurrent instances of a nonphysical expansion rate. The absence of a limit cycle in the central zone further exacerbates the issue, as the system may follow unbounded phase-space trajectories, and the expansion rate becomes complex once it escapes the region. Collectively, these challenges undermine the viability of the GSU2P theory as a cosmological model for cosmic acceleration., Comment: LaTeX file in RevTeX 4.1 style, 22 pages, 11 figures

We introduce a multifield dark energy model with a nonflat field-space metric, in which one field is dynamical while the others have constant spatial gradients. The model is predictive at the background level, leading to an early dark energy component at high redshifts and a suppressed fraction of late-time anisotropy. Both features have simple expressions in terms of the curvature scale of the field-space, and correspond to stable points in the phase space of possible solutions. Because of the coupling between time and space-dependent scalar fields, vector field perturbations develop tachyonic instabilities at scales below the Hubble radius, thus being potentially observable in the number count of galaxies. Overall, the presence of a nontrivial field-space curvature also leads to the appearance of instabilities on scalar perturbations, which can impact the matter density distribution at large scales., Comment: 10 pages, 3 figures. Minor typo corrected. Matches published version

We explore the cosmological dynamics of a minimalistic yet generic string-inspired model for multifield dark energy. Adopting a supergravity four-dimensional viewpoint, we motivate the model's structure arising from superstring compactifications involving a chiral superfield and a pure $U(1)$ gauge sector. The chiral sector gives rise to a pair of scalar fields, such as the axio-dilaton, which are kinetically coupled. However, the scalar potential depends on only one of them, further entwined with the vector field through the gauge kinetic function. The model has two anisotropic attractor solutions that, despite a steep potential and thanks to multifield dynamics, could explain the current accelerated expansion of the Universe while satisfying observational constraints on the late-times cosmological anisotropy. Nevertheless, justifying the parameter space allowing for slow roll dynamics together with the correct cosmological parameters, would be challenging within the landscape of string theory. Intriguingly, we find that the vector field, particularly at one of the studied fixed points, plays a crucial role in enabling geodesic trajectories in the scalar field space while realizing slow-roll dynamics with a steep potential. This observation opens a new avenue for exploring multifield dark energy models within the superstring landscape., Comment: Submitted to JHEP. Comments are welcome!

Since current challenges faced by $\Lambda$CDM might be hinting at new unravelled physics, here we investigate a plausible cosmological model where a vector field acts as source of dark energy. In particular, we examine whether an energy-momentum exchange between dark energy and dark matter could provide an explanation for current discrepancies in cosmological parameters. We carefully work out equations governing background and linear order perturbations and implement them in a Boltzmann code. We found that a negative coupling makes the dark energy equation of state less negative and closer to a cosmological constant during the matter dominated epoch than an uncoupled vector dark energy model. While the effect of the coupling is hardly noticeable through its effect on matter density perturbations, matter velocity perturbations and gravitational potentials are enhanced at late-times when dark energy dominates. Therefore, data of redshift space distortions help to narrow down these kinds of couplings in the dark sector. We computed cosmological constraints and found common parameters also present in $\Lambda$CDM are in good agreement with the Planck Collaboration baseline result. Our best fit for a negatively coupled vector field predicts a higher growth rate of matter perturbations at low redshift, thus exacerbating the disagreement with redshift space distortions data. While a positively coupled vector field can lead to power suppression of $P_{\rm{m}}(k,z=0)$ on small scales as well as a lower growth rate of matter perturbations than the standard model, it might compromise the goodness of fit to the CMB angular power spectrum on small scales. We conclude that our negatively coupled vector dark energy model does not solve current tensions (i.e., $H_0$ and $\sigma_8$). (abridged), Comment: Accepted version to appear in JCAP. A discussion on positively coupled vector dark energy was added. A few figures were added for sake of clarity. Conclusions unchanged

Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a set of autonomous first-order differential equations. The fixed points of this autonomous set encode the asymptotic evolution of the model. Usually, these points can be written as analytical expressions for the variables in terms of the parameters of the model, which allows a complete characterization of the corresponding parameter space. However, a thoroughly analytical treatment is impossible in some cases. In this work, we give an example of a dark energy model, a scalar field coupled to a vector field in an anisotropic background, where not all the fixed points can be analytically found. Then, we put forward a general scheme that provides a numerical description of the parameter space. This allows us to find interesting accelerated attractors of the system with no analytical representation. This work may serve as a template for the numerical analysis of highly complicated dynamical systems., Comment: 13 pages, 13 figures, 1 table. Changes match the published version

We consider scalar-vector-tensor (SVT) theories with second-order equations of motion and tensor propagation speed equivalent to the speed of light. Under the sub-horizon and the quasi-static approximations we find analytical formulae for an effective dark energy fluid, i.e., sound speed, anisotropic stress as well as energy density and pressure. We took advantage of our general, analytical fluid description and showed that it is possible to design SVT cosmological models which are degenerate with $\Lambda$CDM at the background level while having gravity strength $G_{\rm eff}

This paper investigates the cosmological dynamics arising from the interaction between a 2-form field and cold dark matter within a Bianchi I background. Employing a dynamical system analysis, we identify two attractors yielding to exponential expansion of the Universe, i.e., de-Sitter solutions. Notably, these solutions exhibit a pivotal distinction: one is indistinguishable from the cosmological constant scenario, while the other corresponds to an \emph{anisotropic de-Sitter} expansion sourced by the 2-form field. To validate the asymptotic behavior of our model, we conduct a numerical exploration of its expansion history. Our analysis reveals that the coupling between the dark sectors amplifies the shear during the matter-dominated epoch, offering a potential avenue to address certain observational discrepancies related to the structure formation process. Then, we constrain the parameter space of the model using recent observational datasets. Remarkably, we find that the current shear is precisely constrained to be approximately $\Sigma_0 \approx - 10^{-4}$. We also discuss some key differences in the expansionary dynamics sourced by the 2-form field compared to a 1-form field, i.e., a vector field, offering insights into their respective impacts on the support they provide to late-time anisotropy., Comment: Accepted in Physics of the Dark Universe. List of authors updated and several modifications in V2. 18 pages + references, 7 figures

We present an effective Eulerian description, in the non-relativistic regime, of the growth of cosmological perturbations around a homogeneous but anisotropic Bianchi I spacetime background. We assume a small deviation from isotropy, sourced at late times for example by dark energy anisotropic stress. We thus derive an analytic solution for the linear dark matter density contrast, and use it in a formal perturbative approach which allows us to derive a second order (non-linear) solution. As an application of the procedure followed here we derive analytic expressions for the power spectrum and the bispectrum of the dark matter density contrast. The power spectrum receives a quadrupolar correction as expected, and the bispectrum receives several angle-dependent corrections. Quite generally, we find that the contribution of a late-time phase of anisotropic expansion to the growth of structure peaks at a finite redshift between CMB decoupling and today, tough the exact redshift value is model-dependent., Comment: 20 pages + 4 appendixes, 2 figures. This version matches the published one, with minor changes in appendix D

In this paper, we study the late time cosmology of a non-canonical scalar field ($k$-essence) coupled to a vector field in a Bianchi-I background. Specifically, we study three cases: canonical scalar field (quintessence) with exponential potential as a warm up, the dilatonic ghost condensate, and the Dirac Born Infeld field with exponentials throat and potential. By using a dynamical system approach, we show that anisotropic dark energy fixed points can be attractors for a suitable set of parameters of each model. We also numerically integrate the associated autonomous systems for particular initial conditions chosen in the deep radiation epoch. We find that the three models can give an account of an equation of state of dark energy close to $-1$ nowadays. However, a non-negligible spatial shear within the observational bounds nowadays is possible only for thequintessence and the Dirac Born Infeld field. We also find that the equation of state of dark energy and the shear oscillate around nowadays, whenever the coupling of the k-essence field to the vector field is strong enough. The reason of these oscillations is explained in the appendix., Comment: V2: Typos corrected and comments added, 18 pages, 8 figures. arXiv admin note: text overlap with arXiv:2012.09946

In this paper, we study a triad of inhomogeneous scalar fields, known as "solid", as a source of homogeneous but anisotropic dark energy. By using a dynamical system approach, we find that anisotropic accelerated solutions can be realized as attractor points for suitable choices of the parameters of the model. We complement the dynamical analysis with a numerical solution whose initial conditions are set in the deep radiation epoch. The model can give an account of a non-negligible spatial shear within the observational bounds nowadays, even when the later is set to zero at early times. However, we find that there is a particular region in the parameter space of the model in which the Universe isotropizes. The anisotropic attractors, the particular isotropic region, and a nearly constant equation of state of dark energy very close to $- 1$ are key features of this scenario. Following a similar approach, we also analyzed the full isotropic version of the model. We find that the solid can be characterized by a constant equation of state and thus being able to simulate the behavior of a cosmological constant., Comment: LaTeX file in RevTeX 4.1 style, 14 pages, 6 figures. V2: typos corrected, a few clarifying comments added and references added. Matches the published version

In this paper we study some models where non-Abelian gauge vector fields endowed with a SU(2) group representation are the unique source of inflation and dark energy. These models were first introduced under the name of gaugeflation and gaugessence, respectively. Although several realizations of these models have been discussed, not all available parameters and initial conditions are known. In this work, we use a dynamical system approach to find the full parameter space of the massive version of each model. In particular, we found that the inclusion of the mass term increases the length of the inflationary period. Additionally, the mass term implies new behaviors for the equation of state of dark energy allowing to distinguish this from other prototypical models of accelerated expansion. We show that an axially symmetric gauge field can support an anisotropic accelerated expansion within the observational bounds., Comment: 20 pages, 22 figures. V2: typos corrected and references added. Published version

In the context of the dark energy scenario, the Einstein Yang-Mills Higgs model in the SO(3) representation was studied for the first time by M. Rinaldi (see JCAP 1510, 023 (2015)) in a homogeneous and isotropic spacetime. We revisit this model, finding in particular that the interaction between the Higgs field and the gauge fields generates contributions to the momentum density, anisotropic stress and pressures, thus making the model inconsistent with the assumed background. We instead consider a homogeneous but anisotropic Bianchi-I space-time background in this paper and analyze the corresponding dynamical behaviour of the system. We find that the only attractor point corresponds to an isotropic accelerated expansion dominated by the Higgs potential. However, the model predicts non-negligible anisotropic shear contributions nowadays, i.e. the current Universe can have hair although it will loose it in the future. We investigate the evolution of the equation of state for dark energy and highlight some possible consequences of its behaviour related to the process of large-scale structure formation. As a supplement, we propose the "Higgs triad" as a possibility to make the Einstein Yang-Mills Higgs model be consistent with a homogeneous and isotropic spacetime., Comment: LaTeX file in RevTeX 4.1 style, 13 pages, 19 figures. v2: cosmetic changes and references added. Version to appear in Journal of Cosmology and Astroparticle Physics

In this work we revisit the topological mass generation of 2-forms and establish a connection to the unique derivative coupling arising in the quartic Lagrangian of the systematic construction of massive $2-$form interactions, relating in this way BF theories to Galileon-like theories of 2-forms. In terms of a massless $1-$form $A$ and a massless $2-$form $B$, the topological term manifests itself as the interaction $B\wedge F$, where $F = {\rm d} A$ is the field strength of the $1-$form. Such an interaction leads to a mechanism of generation of mass, usually referred to as "topological generation of mass" in which the single degree of freedom propagated by the $2-$form is absorbed by the $1-$form, generating a massive mode for the $1-$form. Using the systematical construction in terms of the Levi-Civita tensor, it was shown that, apart from the quadratic and quartic Lagrangians, Galileon-like derivative self-interactions for the massive 2-form do not exist. A unique quartic Lagrangian $\epsilon^{\mu\nu\rho\sigma}\epsilon^{\alpha\beta\gamma}_{\;\;\;\;\;\;\sigma}\partial_{\mu}B_{\alpha\rho}\partial_{\nu}B_{\beta\gamma}$ arises in this construction in a way that it corresponds to a total derivative on its own but ceases to be so once an overall general function is introduced. We show that it exactly corresponds to the same interaction of topological mass generation. Based on the decoupling limit analysis of the interactions, we bring out supporting arguments for the uniqueness of such a topological mass term and absence of the Galileon-like interactions. Finally, we discuss some preliminary applications in cosmology., Comment: 14 pages, 3 figures, journal version

In this paper, we study the correspondence between a field theory in de Sitter space in $D$-dimensions and a dual conformal field theory in a euclidean space in $(D-1)$-dimensions. In particular, we investigate the form in which this correspondence is established for a system of interacting scalar and a vector fields propagating in de Sitter space. We analyze some necessary (but not sufficient) conditions for which conformal symmetry is preserved in the dual theory in $(D-1)$-dimensions, making possible the establishment of the correspondence. The discussion that we address on this paper is framed on the context of inflationary cosmology, so, the results obtained here pose some relevant possibilities of application to the calculation of the fields's correlation functions and of the primordial curvature perturbation $\zeta$, in inflationary models including coupled scalar and vector fields., Comment: 11 pages, paper published in 2016 as preliminary work to arXiv:1706.05099 and arXiv:1905.00900. Possible overlap with these papers

We consider a model based on $p-$form kinetic Lagrangians in the context of dark energy. The Lagrangian of the model is built with kinetic terms of the field strength for each $p$-form coupled to a scalar field $\phi$ through a kinetic function. We assume that this scalar field is responsible for the present accelerated expansion of the Universe. Since we are interested in cosmological applications, we specialize the analysis to a 4-dimensional case, using an anisotropic space-time. By studying the dynamical equations, we investigate the evolution of the dark energy density parameter, the effective equation of state and the shear induced by the anisotropic configuration., Comment: 6 pages, 2 figures; to appear in the Proceedings of the Fifteenth Marcel Grossmann Meeting (MG15) held at "La Sapienza" University in Rome, Italy, July 1-7, 2018; based on the talk given at the parallel session DE1 "Dark Energy and the Accelerating Universe". Complementary to arXiv:1810.05301 and arXiv:1902.05846

We use conformal symmetry to constrain the shape of inflationary correlators in the presence of long-lived vector field perturbations. Applying conformal Ward identities, we derive general expressions, up to amplitudes and normalization factors, for the two and three point correlators in the presence of vector fields mediated by the interaction $f(\phi)\left(F_{\mu \nu}F^{\mu \nu}+\alpha\tilde{F}_{\mu \nu}F^{\mu \nu}\right)$, where $f(\phi)$ is a suitable coupling function between the scalar and the vector field. The previous interaction allows for isotropy and parity symmetry breaking and is consistent with super horizon conformal symmetry. As an application of the conformal field theory techniques followed here, we evaluate the mixed tensor-scalar $\langle \gamma \zeta \rangle$ and tensor-scalar-scalar $\langle \gamma \zeta \zeta \rangle$ correlators which are interesting to look for parity violating effects related with chiral gravitational waves. Finally, we derive consistency relations for the three point correlators obtained., Comment: Typos corrected, some clarifying comments added and references added. Matches the published version

We study the dynamics of dark energy in the presence of a 2-form field coupled to a canonical scalar field $\phi$. We consider the coupling proportional to $e^{-\mu \phi/M_{\rm pl}} H_{\alpha \beta \gamma}H^{\alpha \beta \gamma}$ and the scalar potential $V(\phi) \propto e^{-\lambda \phi/M_{\rm pl}}$, where $H_{\alpha \beta \gamma}$ is the 2-form field strength, $\mu, \lambda$ are constants, and $M_{\rm pl}$ is the reduced Planck mass. We show the existence of an anisotropic matter-dominated scaling solution followed by a stable accelerated fixed point with a non-vanishing shear. Even if $\lambda \geq {\cal O}(1)$, it is possible to realize the dark energy equation of state $w_{\rm DE}$ close to $-1$ at low redshifts for $\mu \gg \lambda$. The existence of anisotropic hair and the oscillating behavior of $w_{\rm DE}$ are key features for distinguishing our scenario from other dark energy models like quintessence., Comment: 11 pages, 5 figures

We study the cosmology in the presence of arbitrary couplings between $p$-forms in 4-dimensional space-time for a general action respecting gauge symmetry and parity invariance. The interaction between 0-form (scalar field $\phi$) and 3-form fields gives rise to an effective potential $V_{\rm eff}(\phi)$ for the former after integrating out the contribution of the latter. We explore the dynamics of inflation on an anisotropic cosmological background for a coupled system of 0-, 1-, and 2-forms. In the absence of interactions between 1- and 2-forms, we derive conditions under which the anisotropic shear endowed with nearly constant energy densities of 1- and 2-forms survives during slow-roll inflation for an arbitrary scalar potential $V_{\rm eff}(\phi)$. If 1- and 2-forms are coupled to each other, we show the existence of a new class of anisotropic inflationary solutions in which the energy density of 2-form is sustained by that of 1-form through their interactions. Our general analytic formulas for the anisotropic shear are also confirmed by the numerical analysis for a concrete inflaton potential., Comment: 23 pages, 4 figures, version to be published in JCAP

Inspired in the Standard Model of Elementary Particles, the Einstein Yang-Mills Higgs action with the Higgs field in the SU(2) representation was proposed in Class. Quantum Grav. 32 (2015) 045002 as the element responsible for the dark energy phenomenon. We revisit this action emphasizing in a very important aspect not sufficiently explored in the original work and that substantially changes its conclusions. This aspect is the role that the Yang-Mills Higgs interaction plays at fixing the gauge for the Higgs field, in order to sustain a homogeneous and isotropic background, and at driving the late accelerated expansion of the Universe by moving the Higgs field away of the minimum of its potential and holding it towards an asymptotic finite value. We analyse the dynamical behaviour of this system and supplement this analysis with a numerical solution whose initial conditions are in agreement with the current observed values for the density parameters. This scenario represents a step towards a successful merging of cosmology and well-tested particle physics phenomenology., Comment: LaTeX file in RevTeX 4.1 style, 15 pages, 22 figures. v2: Some clarifications made about the difference between the results of this paper and those of M. Rinaldi's and also about the influence of the initial conditions on the dynamics of the system. References added. v3: A new section about observational signatures. v4: Version published in Classical and Quantum Gravity

In this paper we consider a model based on interacting $p-$forms and explore some cosmological applications. Restricting to gauge invariant actions, we build a general Lagrangian allowing for arbitrary interactions between the $p-$forms (including interactions with a $0-$form, scalar field) in a given background in $D$ dimensions. For simplicity, we restrict the construction to up to first order derivatives of the fields in the Lagrangian. We discuss with detail the four dimensional case and devote some attention to the mechanism of topological mass generation originated by couplings of the form $B\wedge F$ between a $p-$form and a $(3-p)-$form. As a result, we show the system of the interacting $p-$forms $(p=1,2,3)$ is equivalent to a parity violating, massive, Proca vector field model. Finally, we discuss some cosmological applications. In a first case we study a very minimalistic system composed by a $3-$form coupled to a $0-$form. The $3-$form induces an effective potential which acts as a cosmological constant term suitable to drive the late time accelerated expansion of the universe dominated by dark energy. We study the dynamics of the system and determine its critical points and stability. Additionally, we study a system composed by a scalar field and a $1$-form. This case is interesting because the presence of a coupled $1-$form can generate non vanishing anisotropic signatures during the late time accelerated expansion. We discuss the evolution of cosmological parameters such as the equation of state in this model., Comment: Several modifications and updates. The discussion about the $3-$forms is reviewed and corrected. A new application included. Several references added. Main conclusions unchanged

In this paper we use conformal field theory techniques to constrain the form of the correlations functions of an inflationary scalar-vector model described by the interaction term $f_1(\phi)F_{\mu \nu}F^{\mu \nu} + f_2(\phi)\tilde{F}_{\mu \nu}F^{\mu \nu}$. We use the fact that the conformal group is the relevant symmetry group acting on super horizon scales in an inflationary de Sitter background. As a result, we find that super horizon conformal symmetry, constraints the form of the coupling functions $f_1, f_2$ to be homogeneous functions of the same degree. We derive the general form of the correlators involving scalar and vector perturbations in this model and determine its squeezed limit scaling behaviour for super horizon scales. The approach followed here is useful to constraint the shape of scalar-vector correlators, and our results agree with recent literature on the subject, but don't allow us to determine amplitude factors of the correlators., Comment: References added. Discussion about invariance under special conformal transformations improved. Matches published version

Inflationary models including vector fields have attracted a great deal of attention over the past decade. Such an interest owes to the fact that they might contribute to, or even be fully responsible for, the curvature perturbation imprinted in the cosmic microwave background. However, the necessary breaking of the vector field's conformal invariance during inflation is not without problems. In recent years, it has been realized that a number of instabilities endangering the consistency of the theory arise when the conformal invariance is broken by means of a non-minimal coupling to gravity. In this paper, we consider a massive vector field non-minimally coupled to gravity through the Gauss-Bonnet invariant, and investigate whether the vector can play the role of a curvaton while evading the emergence of instabilities and preserves the large-scale isotropy., Comment: Typos corrected, some clarifying comments added. Matches the published version

We consider cosmological inflationary models in which vector fields play some role in the generation of the primordial curvature perturbation $\zeta$. 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: $P_\zeta(\vec{k})\equiv P_\zeta(k)[1+g_\zeta(k)(\hat{n} \cdot \hat{k})^2 ]$, where $g_{\zeta}(k)$ 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 $g_{\zeta}(k)$ on the NG parameters by means of the $\delta N$ formalism. We focus specifically on the details for the $f_{\rm NL}$ NG parameter, associated with the bispectrum $B_\zeta$, 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., Comment: LaTex file, 19 pages, 14 figures. v2: the title has been changed a bit to reflect, in a better way, the purpose and contents of the paper. Just a few changes to satisfy the referee requirements. Conclusions unchanged. Version to be published in Physical Review D

A full-relativistic approach is used to compute the radius of the innermost stable circular orbit (ISCO), the Keplerian, frame-dragging, precession and oscillation frequencies of the radial and vertical motions of neutral test particles orbiting the equatorial plane of a magnetized neutron star. The space-time around the star is modelled by the six parametric solution derived by Pachon et al. It is shown that the inclusion of an intense magnetic field, such as the one of a neutron star, have non-negligible effects on the above physical quantities, and therefore, its inclusion is necessary in order to obtain a more accurate and realistic description of the physical processes occurring in the neighbourhood of this kind of objects such as the dynamics of accretion disk. The results discussed here also suggest that the consideration of strong magnetic fields may introduce non-negligible corrections in, e.g., the relativistic precession model and therefore on the predictions made on the mass of neutron stars., Comment: LaTeX file, 13 pages, 4 figures

We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation \tau_{NL} \geqslant ((6/5) f_{NL})^2. It has been claimed that the following variation: \tau_{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 \tau_{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 \zeta. 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 \tau_{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), Comment: LaTex file, 12 pages, 4 figures. v2: minor cosmetic changes, references added and updated, version to be published in Journal of Cosmology and Astroparticle Physics

We consider inflationary models in which vector fields are responsible for part or eventually all of the primordial curvature perturbation \zeta. 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 \delta N formalism to do a complete tree level calculation of the non-Gaussianity parameters f_{NL} and \tau_{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 \tau^{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., Comment: LaTeX file, 11 pages. v2: a few minor changes, references added and updated. v3: version to be published in Modern Physics Letters A

Whether analytic exact vacuum(electrovacuum) solutions of the Einstein(Einstein-Maxwell) field equations can accurately describe or not the exterior spacetime of compact stars remains still an interesting open question in Relativistic Astrophysics. As an attempt to establish their level of accuracy, the radii of the Innermost Stable Circular Orbits (ISCOs) of test particles given by analytic exterior spacetime geometries have been compared with the ones given by numerical solutions for neutron stars (NSs) obeying a realistic equation of state (EoS). It has been so shown that the six-parametric solution of Pach\'on, Rueda, and Sanabria (2006) (hereafter PRS) is more accurate to describe the NS ISCO radii than other analytic models. We propose here an additional test of accuracy for analytic exterior geometries based on the comparison of orbital frequencies of neutral test particles. We compute the Keplerian, frame-dragging, as well as the precession and oscillation frequencies of the radial and vertical motions of neutral test particles for the Kerr and PRS geometries; then we compare them with the numerical values obtained by Morsink and Stella (1999) for realistic NSs. We identify the role of high-order multipole moments such as the mass quadrupole and current octupole in the determination of the orbital frequencies especially in the rapid rotation regime. The results of this work are relevant to cast a separatrix between black hole (BH) and NS signatures as well as probe the nuclear matter EoS and NS parameters from the Quasi-Periodic Oscillations (QPOs) observed in Low Mass X-Ray Binaries., Comment: 14 pages, 10 figures

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation \zeta was 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 \zeta, 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 \zeta for 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., Comment: LaTeX file, 26 pages. v2: A short discussion added regarding the role of the diagrams in high precision cosmology as well as in those cases where the loop contributions are larger than the tree level terms, generating large and observable levels of (anisotropic) non-gaussianity; references added, conclusions unchanged. v3: version to appear in Journal of Cosmology and Astroparticle Physics

We study the statistical descriptors for some cosmological inflationary models that allow us to get large levels of non-gaussianity and violations of statistical isotropy. Basically, we study two different class of models: a model that include only scalar field perturbations, specifically a subclass of small-field slow-roll models of inflation with canonical kinetic terms, and models that admit both vector and scalar field perturbations. We study the former to show that it is possible to attain very high, including observable, values for the levels of non-gaussianity f_{NL} and \tao_{NL} in the bispectrum B_\zeta and trispectrum T_\zeta of the primordial curvature perturbation \zeta respectively. Such a result is obtained by taking care of loop corrections in the spectrum P_\zeta, the bispectrum B_\zeta and the trispectrum T_\zeta . Sizeable values for f_{NL} and \tao_{NL} arise even if \zeta is generated during inflation. For the latter we study the spectrum P_\zeta, bispectrum B_\zeta and trispectrum $T_\zeta of the primordial curvature perturbation when \zeta 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. The levels of non-gaussianity f_{NL} and \tao_{NL}, are calculated and related to the level of statistical anisotropy in the power spectrum, g_\zeta . For very small amounts of statistical anisotropy in the power spectrum, the levels of non-gaussianity may be very high, in some cases exceeding the current observational limit., Comment: Latex file, 113 pages. PhD Thesis. Supervisor: Yeinzon Rodriguez.

We use the \delta N formalism to study the trispectrum T_\zeta of the primordial curvature perturbation \zeta when 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, \tau_{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_\zeta. Such consistency relations will put under test this scenario against future observations. Comparison with the expected observational bound on \tau_{NL} from WMAP, for generic inflationary models, is done., Comment: LaTeX file, 12 pages, no figures. v2: Minor changes, conclusions unchanged. v3: Version accepted for publication in Physics Letters B

We study the spectrum P_\zeta and bispectrum B_\zeta of the primordial curvature perturbation \zeta when 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_\zeta and (or) in B_\zeta) 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_\zeta. 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., Comment: LaTeX file, 11 pages, Main body: 8 pages, References: 3 pages. v2: Minor corrections. References added. Conclusions unchanged. v3: Minor corrections. Some references added and others updated. Version accepted for publication in Physical Review D

The perturbation of a light field might affect preheating and hence generate a contribution to the spectrum and non-gaussianity of the curvature perturbation \zeta. The field might appear directly in the preheating model (curvaton-type preheating) or indirectly through its effect on a mass or coupling (modulated preheating). We give general expressions for \zeta based on the \delta N formula, and apply them to the cases of quadratic and quartic chaotic inflation. For the quadratic case, curvaton-type preheating is ineffective in contributing to \zeta, but modulated preheating can be effective. For quartic inflation, curvaton-type preheating may be effective but the usual \delta N formalism has to be modified. We see under what circumstances the recent numerical simulation of Bond et al. [0903.3407] may be enough to provide a rough estimate for this case. This paper is dedicated to the memory of Lev Kofman who died on 12th November 2009, Comment: The discussion around Eqs. (100) and (101) corrected and clarified (v4), Added new insights into (i) the status of the box size upon which loop contributions depend and (ii) the relevance for massless preheating of the numerical simulation of Bond et al. (v3) This paper is dedicated to the memory of Lev Kofman who died on 12th November 2009

We calculate the trispectrum T_\zeta of the primordial curvature perturbation \zeta, 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 \tau_{NL} if T_\zeta is 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 \tau_{NL} in the bispectrum B_\zeta and trispectrum T_\zeta of \zeta, respectively, are also studied for the case in which \zeta is not generated during inflation., Comment: LaTex File, 27 pages, 8 figures. v2: Previous Section 2 has been removed. Two new sections (3 and 4) discussing the classicality condition given by Byrnes, Choi, and Hall, in JCAP 0902, 017 (2009), and the probability that an observer sees a non-gaussian distribution have been added. v3: Version accepted for publication in Physical Review D

We show in this paper that it is possible to attain very high, {\it including observable}, values for the level of non-gaussianity f_{NL} associated with the bispectrum B_\zeta of the primordial curvature perturbation \zeta, in a subclass of small-field {\it slow-roll} models of inflation with canonical kinetic terms. Such a result is obtained by taking care of loop corrections both in the spectrum P_\zeta and the bispectrum B_\zeta. Sizeable values for f_{NL} arise even if \zeta is generated during inflation. Five issues are considered when constraining the available parameter space: 1. we must ensure that we are in a perturbative regime so that the \zeta series expansion, and its truncation, are valid. 2. we must apply the correct condition for the (possible) loop dominance in B_\zeta and/or P_\zeta. 3. we must satisfy the spectrum normalisation condition. 4. we must satisfy the spectral tilt constraint. 5. we must have enough inflation to solve the horizon problem., Comment: LaTeX file, 40 pages, 6 figures, Main body: 26 pages, Appendix: 8 pages, References: 6 pages. v2: minor grammatical changes, references added and updated, a few changes reflecting the fact that <\zeta> = 0, conclusions unchanged. Version accepted for publication in Journal of Cosmology and Astroparticle Physics