String-inspired cosmology: a late time transition from a scaling matter era to a dark energy universe caused by a Gauss–Bonnet coupling

Abstract

The Gauss-Bonnet (GB) curvature invariant coupled to a scalar field φ can lead to an exit from a scaling matter-dominated epoch to a late-time accelerated expansion, which is attractive to alleviate the coincident problem of dark energy. We derive the condition for the existence of cosmological scaling solutions in the presence of the GB coupling for a general scalar-field Lagrangian density p(φ, X), where X = −(1/2)(∇φ) 2 is a kinematic term of the scalar field. The GB coupling and the Lagrangian density are restricted to be in the form f (φ) ∝ e λφ and p = Xg(Xe λφ ), respectively, where λ is a constant and g is an arbitrary function. We also derive fixed points for such a scaling Lagrangian with a GB coupling f (φ) ∝ e µφ and clarify the conditions under which the scaling matter era is followed by a de-Sitter solution which can appear in the presence of the GB coupling. Among scaling models proposed in the current literature, we find that the models which allow such a cosmological evolution are an ordinary scalar field with an exponential potential and a tachyon field with an inverse square potential, although the latter requires a coupling between dark energy and dark matter.

Models off(R)cosmic acceleration that evade solar system tests

“…The addition of a non-linear function of the Ricci scalar R to the Einstein-Hilbert action has been demonstrated to cause acceleration for a wide variety of f (R) functions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,…”

Quintessential and Phantom Power-Law Solutions in Scalar Tensor Model of Dark Energy

“…In [23] the GB correction was proposed to study the dynamics of dark energy, where it was found that quintessence or phantom phase may occur in the late time universe. Different aspects of accelerating cosmologies with GB correction have been also discussed in [24], [25], [26], [27], [28], [29]. The modified GB theory applied to dark energy has been suggested in [30], and further studies of the modified GB model applied to late time acceleration, have been considered among others, in [31], [32], [33], [34], [35].…”

Delicatef(R)gravity models with a disappearing cosmological constant and observational constraints on the model parameters

“…It is tempting to study the string curvature corrections to Einstein gravity amongst which the Gauss-Bonnet correction enjoys special status. A large number of papers are devoted to the cosmological implications of string curvature corrected gravity [2,3,4,5,6,7,8,9,10,11]. These models suffer from several problems.…”

“…For instance, the Gauss-Bonnet theory with dynamical dilaton might cause transition from matter scaling regime to late time acceleration allowing to alleviate the fine tuning and coincidence problems. However, it is difficult to reconcile this model with nucleosynthesis [4,5]. Another possibility of large scale modification is provided by non-locally corrected gravity which typically involves inverse of d'Alembertian of Ricci scalar.…”