Abstract
The latest cosmological observations by the Planck collaboration (and combined with others) are compatible with a phantom-like behaviour ( w < − 1 ) for the dark energy equation of state that drives the current acceleration of the Universe. With this mindset, we look into models where dark energy is described by a 3-form field minimally coupled to gravity. When compared to a scalar field, these models have the advantage of more naturally accommodating a cosmological-constant and phantom-like behaviours. We show how the latter happens for a fairly general class of positive-valued potentials, and through a dynamical system approach, we find that in such cases the 3-form field leads the Universe into a Little Sibling of the Big Rip singular event into the future. In this work, we explore the possibility of avoiding such singularity via an interaction in the dark sector between cold dark matter and the 3-form field. For the kind of interactions considered, we deduce a condition for replacing the LSBR by a late time de Sitter phase. For specific examples of interactions that meet this condition, we look for distinctive imprints in the statefinder hierarchy { S 3 ( 1 ) ; S 4 ( 1 ) } , { S 3 ( 1 ) ; S 5 ( 1 ) } , and in the growth rate of matter, ϵ ( z ) , through the composite null diagnostic (CND).
Highlights
It has been almost two decades since the supernova measurements [1,2] that led to the discovery of the current acceleration of the expansion of the universe, few advances have been made on the nature of the so-called dark energy (DE)—the fluid that drives this acceleration and comprises about 70% of the energy density of the Universe
The ΛCDM model—which is favoured by most observations—does little to alleviate this issue, offering no answers as to why the value of the cosmological constant Λ is so small when compared to the expected value from quantum field theory or why the energy densities of DE and of dark matter (DM) are on the same order of magnitude today
In order to overcome these theoretical shortcomings of ΛCDM, various alternative descriptions of DE were presented along the years, from models with dynamical fields to modified theories of gravity [3,4,5]
Summary
It has been almost two decades since the supernova measurements [1,2] that led to the discovery of the current acceleration of the expansion of the universe, few advances have been made on the nature of the so-called dark energy (DE)—the fluid that drives this acceleration and comprises about 70% of the energy density of the Universe. As noted in [18], in many cases where the 3-form presents a phantom-like behaviour, the late-time de Sitter stage can be replaced by a Little Sibling of the Big Rip (LSBR) event in the future [21,22] This leads to a divergence of the scale factor and the Hubble rate at an infinite cosmic time and to the dissociation of local bounded structures in our Universe at finite cosmic time, though the cosmic time derivatives of the Hubble rate remain finite. In the case where these critical points represent stable equilibrium points, we find that as χ → ±χc , the field χ saturates the Friedmann Equation (1), driving the Hubble rate to infinity, while the time derivative of the Hubble rate remains finite-valued [18]: Ḣ(χ→±χc ) = − V,χ2 (±χc ) Since this divergence of the Hubble rate happens in the asymptotic future, we come to the conclusion that the Universe can evolve towards a Little Sibling of the Big Rip (LSBR) event.
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