In this work we consider a cosmological model in which dark energy is portrayed by a canonical scalar field which is allowed to couple to the other species by means of a disformal transformation of the metric. We revisit the current literature by assuming that the disformal function in the metric transformation can depend both on the scalar field itself and on its derivatives, encapsulating a wide variety of scalar-tensor theories. This generalisation also leads to new and richer phenomenology, explaining some of the features found in previously studied models. We present the background equations and perform a detailed dynamical analysis, from where new disformal fixed points emerge, that translate into novel cosmological features. These include early scaling regimes between the coupled species and broader stability parameter regions. However, viable cosmological models seem to have suppressed disformal late-time contributions.
I. IntroductionSince 1998 that we have been witnessing growing observational confirmation of the present accelerated expansion of the Universe [1][2][3][4]. This phenomenon can be attributed to an exotic fluid, the so-called Dark Energy (DE), which must amount to about 70% of the total content of the Universe, and whose effective negative pressure can successfully explain the observations (see [5][6][7] for recent reviews). Presently, the ΛCDM model is the most well-accepted cosmological model, consisting of a cosmological constant dark energy source, Λ, plus a dark matter component, needed in order to make formation of structure possible in the Universe [8]. However, this paradigm faces some theoretical inconsistencies [9], motivating extensions of the concept of dark energy to a scalar field, with General Relativity as the underlying gravitational theory [10][11][12]. These scalar field based models, albeit simple, can give rise to very complex and rich phenomenologies, while making predictions that are testable according to observational constraints [4]. In the plainest scenarios, DE is portrayed as a canonical scalar field, the quintessence field, which does not interact with the other components in the Universe [13,14]. However, there is no fundamental reason to assume such a constraint and, in the simplest extension, the scalar field is allowed to couple non-minimally to the matter sector [15][16][17][18][19][20][21][22][23].One straightforward procedure for introducing a non-trivial coupling between the scalar field and matter is to consider that matter particles propagate in geodesics of a transformed metric,ḡ µν , related to the gravitational metric, g µν , by means of a field-dependent transformation. When this transformation corresponds to a rescaling of the metric we speak of conformal transformations, which affect the length of time-like and space-like intervals and the norm of time-like and space-like vectors while leaving the light cones unchanged:where C is the conformal factor. Conformal transformations are known to preserve the structure of Scalar-Tensor theories of the B...
