Three-form cosmology

Abstract

Cosmology of self-interacting three-forms is investigated. The minimally coupled canonical theory can naturally generate a variety of isotropic background dynamics, including scaling, possibly transient acceleration and phantom crossing. An intuitive picture of the cosmological dynamics is presented employing an effective potential. Numerical solutions and analytical approximations are provided for scenarios which are potentially important for inflation or dark energy.

The anisotropy of a three- and a one-form

“…Three-fields are among the competitors for "the" model of inflation [3,4]; they support a perfectly isotropic background [5,6]; they inflate easily and exhibit some very peculiar dynamics [7]; they can drive a late-time "dark energy" era with peculiar matter interactions [8,9]; and, last but not least, they support couplings with a variety of other forms, including the obvious one-form case.…”

3-Form Cosmology: Phantom Behaviour, Singularities and Interactions

“…Following [6][7][8][9], we use the parametrization A ijk = a 3 (t) χ(t) ijk , where t is the cosmic time, a(t) is the scale factor, χ(t) is a comoving scalar quantity associated with the amplitude of the 3-form field, and ijk = +1 (−1) if ijk is an even (odd) permutation of 123. If we consider the Universe to be filled only by a 3-form, the Friedmann and Raychaudhuri equations read, respectively [6,8,9]:…”

“…The points χ = ±χ c play a critical role in 3-form cosmology, as the Friedmann Equation (1) imposes that-for expanding cosmologies (H > 0) and positive potentials-the field χ must decay monotonically until it enters the interval [−χ c , χ c ], from which it does not escape [8,9,18]. These points are static solutions of Equation (2), and represent stable (unstable) states of equilibrium of the system whenever ∂V/∂χ 2 = (2χ) −1 ∂V/∂χ is negative (positive) at χ = ±χ c [18].…”

“…to modified theories of gravity [3][4][5]. Among these proposals, we encounter the 3-form field [6][7][8][9], which has been the focus of attention in recent years, both in the context of late-time DE and in early inflation [6][7][8][9][10][11][12][13][14][15][16][17][18]. This identification of DE with a 3-form comes somewhat naturally given the well established equivalence between a massless 3-form field and a cosmological constant [19].…”

“…While a dynamical systems approach has been employed in systems with 3-form since the early papers of Koivisto and Nunes [6,8,9], the existence of fixed points corresponding to infinite amplitudes of the 3-form field were overlooked in the literature. By using a set of compact variables, we were able to identify and characterise such points for the first time.…”