de Sitter nonlinear sigma model and accelerating universe

Abstract

We consider a cosmology with a noncompact nonlinear sigma model. The target space is of de Sitter type and four scalar fields are introduced. The potential is absent but cosmological constant term Λ is added. One of the scalar fields is time dependent and the remaining three fields have no time dependence but only spatial dependence. We show that a very simple ansatz for the scalar fields results in the accelerating universe with an exponential expansion at late times. It is pointed out that the presence of the energy density and pressure coming from the spatial variation of the three scalar fields plays an essential role in our analysis which includes Λ = 0 as a special case and it discriminate from the standard Λ-dominated acceleration. We perform a stability analysis of the solutions and find that some solutions are classically stable and attractor. We also present a nonperturbative solution which asymptotically approaches an exponential acceleration and discuss possible cosmological implications in relation to dark energy. It turns out that the equation of state approaches asymptotically ω = −1 both from above and below, but the crossing does not occur. It predicts present value of ω ∼ −1 ∓ 0.07, which is within the region allowed by the observational data. This solution also exhibits a power law expansion at early times, and the energy density of the scalar fields mimics that of the stiff matter.

Primordial gravitational waves from the space-condensate inflation model

“…where V φ ≡ dV /dφ. To preserve the cosmological principles of homogeneity and isotropy for this model in the flat FLRW background with metric, ds 2 = −dt 2 + a(t) 2 (dx 2 + dy 2 + dz 2 ), we choose a spatially linear background solution for σ a [21,22,[25][26][27][28]35] ,…”

Large scale suppression of scalar power on a spatial condensation

“…To see this fact explicitly, one can read the (0, i)-component of the perturbed Einstein equation δG 0 i = modes δσ a 's is also well-defined and does not violate the energy condition. Here we express the longitudinal mode δσ a in terms of a scalar mode u with a normalization [16,19], 17) where k is the comoving wave number. We introduce the 1/k factor to define the canonical kinetic term for the scalar mode u in the form of the perturbed Lagrangian.…”

“…We also consider a background solution with spatially linear configurations, σ a ∼ x a , (a = 1, 2, 3), and σ i = 0, (i = 4, · · · ,N ). Then the usual cosmological evolution for the single field under the FRW metric with the background solution for σ a guarantees the homogeneity and isotropy of the cosmological principle [16][17][18][19] . In the perturbation level, fluctuations for σ i , (i = 4, · · · ,N ), are decoupled and have no influence to cosmological observables [19].…”

Cosmological perturbations of a quartet of scalar fields with a spatially constant gradient

“…Therefore, the coordinate dependent ansatz in the nonlinear sigma model in gravity theories can be considered as a method of constructing the massive gravity theories [16]. Recently, the four scalar fields were combined into de Sitter target space and used in describing the late-time accelerating universe [17]. See also [18,19] for related topics.…”