Quintessence, the gravitational constant, and gravity

Abstract

Dynamical vacuum energy or quintessence, a slowly varying and spatially inhomogeneous component of the energy density with negative pressure, is currently consistent with the observational data. One potential difficulty with the idea of quintessence is that couplings to ordinary matter should be strongly suppressed so as not to lead to observable time variations of the constants of nature. We further explore the possibility of an explicit coupling between the quintessence field and the curvature. Since such a scalar field gives rise to another gravity force of long range ( > ∼ H −1 0 ), the solar system experiments put a constraint on the non-minimal coupling: |ξ| < ∼ 10 −2 .

f(R) Theories

“…For example, the action of a nonminimally coupled scalar field with a coupling ξ corresponds to F ( φ ) = 1 − ξφ 2 and ω ( φ ) = 1, which gives the field-dependent coupling Q ( φ ) = ξφ /[1 − ξφ 2 (1 − 6 ξ )] 1/2 . In fact the dynamics of dark energy in such a theory has been studied by a number of authors [22, 601, 151, 68, 491, 44, 505]. In the following we shall focus on the constant coupling models with the action (10.10).…”

Holographic-dark-energy model with non-minimal coupling

“…(2) allows existence of the solution to the conditions of acceleration. Also, the addition of a non-minimal coupling between the scalar and the curvature had been justified in quintessence model [16,17,18]. In order to obtain solutions to field equations in Eqs.…”

“…According to ref. [17], the Brans-Dicke parameter is expressed as ω BD ∼ (ξκ 2 φ 2 0 ) −1 ≫ 1 under the assumption. Thus, in the present model, the non-minimal coupling parameter of limited range (0.146 < ∼ ξ < ∼ 0.167) provides an accelerating universe to be consistent with observations.…”

k-essence cosmologies in Kantowski–Sachs and Bianchi space–times

“…There are several other dark energy candidates suggested in the literature, such as vacuum polarisation [15,16], vector field models [17], tachyons [18][19][20], Chaplygin gas [21], k-essence [22,23], Cardassian expansion [24], quasi-steady state cosmology [25], and scalartensor models [26].…”