A special relativity based on the de Sitter group is introduced, which is the theory that might hold up in the presence of a non-vanishing cosmological constant. Like ordinary special relativity, it retains the quotient character of spacetime, and a notion of homogeneity. As a consequence, the underlying spacetime will be a de Sitter spacetime, whose associated kinematics will differ from that of ordinary special relativity. The corresponding modified notions of energy and momentum are obtained, and the exact relationship between them, which is invariant under a re-scaling of the involved quantities, explicitly exhibited. Since the de Sitter group can be considered a particular deformation of the Poincaré group, this theory turns out to be a specific kind of deformed (or doubly) special relativity. Some experimental consequences, as well as the causal structure of spacetime-modified by the presence of the de Sitter horizon-are briefly discussed.

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 dualF µν .Along the line of modifying gravity in a scalar-tensor way, many proposals have been made to write down theories whose dynamics stem from second order equations of motion for both the tensor and the scalar degrees of freedom [1-5], thus generalizing an old proposal [6]; such theories have been dubbed Galileons. The obvious next move consists in obtaining a similar general action for a vector field [7] (see also in Refs. [8][9][10][11]), thereby forming the vector Galileon case [12,13], which was investigated thoroughly [14][15][16][17][18][19][20][21]. Demanding U(1) invariance led to a no-go theorem [22] which can be by-passed essentially by dropping the U(1) invariance hypothesis. Cosmological implications of such a model can be found e.g. in Refs. [23][24][25][26][27][28][29][30][31][32][33][34][35].Recent papers [12,36,37] have derived the most general action containing a vector field, with different conclusions as to the number of possible terms given the underlying hypothesis. In Refs. [12,37], the Lagrangian was built from contractions of derivative terms with Levi-Civita tensors, whereas Ref.[36] used a more systematic approach based on the Hessian condition. It appears that a consensus has finally been reached, suggesting only a finite number of terms in the theory, all of them being given in an explicit form. To describe this consensus and complete the discussion, we examine in the present paper an alternative explanation for the presence of, allegedly, only a finite number of terms in the generalized Proca theory, using the tools developed in Ref. [36] where the infinite series of terms was conjectured. This discussion also allows us to compare the systematic procedure used in Ref. [36] with the construction based on Levi-Civita tensors of Refs. [12,37]. We then summarize these previously obtained results and settle the whole point in as definite a manner as possible.Focusing on the parity violating sector of the model, not thoroughly investigated in Refs. [12,37], certain terms obtained in Ref. [36] should not appear according to the abovementioned discussion. Indeed, we show that, because of an identity not taken...

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 λhs s2ℋ†ℋ and non-minimally to gravity via ξs s2 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, 102 GeV≲ ms≲ 106 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.

The infinite cosmological "constant" limit of the de Sitter solutions to Einstein's equation is studied. The corresponding spacetime is a singular, four-dimensional cone-space, transitive under proper conformal transformations, which constitutes a new example of maximally-symmetric spacetime. Grounded on its geometric and thermodynamic properties, some speculations are made in connection with the primordial universe.

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation ζ 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 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 ζ 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