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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 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 the context of scalar-tensor theories, the inclusion of new degrees of freedom coupled non-minimally to the gravitational sector might produce some appealing effects on the cosmic expansion history. We investigate this premise by including a canonical SU(2) Yang- Mills field to the total energy budget of the universe coupled to the standard quintessential field by a disformal transformation. From the dynamical system analysis, we study three cases of cosmological interest that span most of the physical phase space of the model: the uncoupled limit, the isotropic, and the Abelian cases. New scaling solutions with a non-vanishing gauge field are found in all cases which can be interesting for early cosmological scenarios. Some of these scaling solutions even exhibit anisotropic features. Also, the background evolution of the universe is studied by means of numerical analysis. As an interesting result, the disformal coupling changes the equation of state of the gauge field from radiation to matter at some stages of the evolution of the universe, thereby the gauge field can contribute to some fraction of the total dark matter. We have also quantified the redshift-dependent contribution of the gauge field in the form of dark radiation during the radiation era to the effective number of relativistic species. This depends essentially on the initial conditions and, more importantly, on the disformal coupling function., Comment: LaTeX file in jcappub style, 40 pages, 11 figures. v2: some cosmetic changes and new references added. v3 and v4: more changes to add clarity to the paper and new material added. Conclusions unchanged. v5: version to appear in International Journal of Modern Physics D

We consider an UV-protected Natural Inflation scenario involving Chern-Simons-like interactions between the inflaton and some beyond the Standard Model gauge fields. The accelerated expansion of the Universe is supported by a combination of a gravitationally-enhanced friction sensitive to the scale of inflation and quantum friction effects associated with the explosive production of gauge fluctuations. The synergy of these two velocity-restraining mechanisms allows for: $i)$ Natural Inflation potentials involving only sub-Planckian coupling constants, $ii)$ the generation of a dark matter component in the form of primordial black holes, and $iii)$ a potentially observable background of chiral gravitational waves at small scales., Comment: Some clarifying comments added, 1 figure added and 1 figure modified. Several references added. Matches published version

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

If cosmic inflation was driven by an electrically neutral scalar field stable on cosmological time scales, the field necessarily constitutes all or part of dark matter (DM). We study this possibility in a scenario where the inflaton field $s$ resides in a hidden sector, which is coupled to the Standard Model sector through the Higgs portal $\lambda_{hs} s^2\mathcal{H}^\dagger\mathcal{H}$ and non-minimally to gravity via $\xi_s s^2 R$. We study scenarios where the field $s$ first drives inflation, then reheats the Universe, and later constitutes all DM. We consider two benchmark scenarios where the DM abundance is generated either by production during reheating or via non-thermal freeze-in. In both cases, we take into account all production channels relevant for DM in the mass range from keV to PeV scale. On the inflationary side, we compare the dynamics and the relevant observables in two different but well-motivated theories of gravity (metric and Palatini), discuss multifield effects in case both fields ($s$ and $h$) were dynamical during inflation, and take into account the non-perturbative nature of particle production during reheating. We find that, depending on the initial conditions for inflation, couplings and the DM mass, the scenario works well especially for large DM masses, $10^2$ GeV$\lesssim m_{s}\lesssim 10^6$ GeV, although there are also small observationally allowed windows at the keV and MeV scales. We discuss how the model can be tested through astrophysical observations., Comment: 36 pages, 11 figures. v2: Two appendices, discussion, and references added. Matches the version accepted for publication in JCAP

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

We consider a scenario in which the inflaton $\phi$ is a pseudoscalar field non-minimally coupled to gravity through a term of the form ${\cal X} R \phi^2$. The pseudoscalar is also coupled to a $U(1)$ gauge field (or an ensemble of ${\cal N}$ gauge fields) through an axial coupling of the form $\phi F \tilde{F}$. After M. M. Anber and L. Sorbo, Phys. Rev. D 81, 043534 (2010), Ref. [1], it is well known that this axial coupling leads to a production of gauge particles which acts as a friction term in the dynamics of the inflaton, producing a slow-roll regime even in presence of a steep potential. A remarkable result in this scenario, is that the spectrum of the chiral gravitational waves sourced by the scalar-gauge field interplay can be enhanced due to the non-minimal coupling with gravity, leading to measurable signatures, while maintaining agreement with current observational constraints on $n_s$ and $r$. The inclusion of non-minimal coupling could be helpful to alleviate tensions with non-Gaussianity bounds in models including axial couplings., Comment: Two figures and one appendix added. Several references added. Matches the version accepted for publication in PRD

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

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 St\"uckelberg 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 St\"uckelberg 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 $A_\mu$, the Faraday tensor $F_{\mu \nu}$ and its Hodge dual $\tilde{F}_{\mu \nu}$., Comment: LaTeX file in jcappub style, 11 pages, no figures. v2: Minor changes according to the referee requirements. A new parity-violating term in the Lagrangian has been uncovered and the text has been changed accordingly. The conclusions are, essentially, unchanged. v3: Miscellaneous changes. Version to be published in Journal of Cosmology and Astroparticle Physics

Various extensions of standard inflationary models have been proposed recently by adding vector fields. Because they are generally motivated by large-scale anomalies, and the possibility of statistical anisotropy of primordial fluctuations, such models require to introduce non-standard couplings between vector fields on the one hand, and either gravity or scalar fields on the other hand. In this article, we study models involving a vector field coupled to a scalar field. We derive restrictive necessary conditions for these models to be both stable (Hamiltonian bounded by below) and causal (hyperbolic equations of motion)., Comment: 20 pages, references added, v2 matches published version in JCAP

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

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

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