𝒩-field cosmology in hyperbolic field space: stability and general solutions

Abstract

We study the dynamics of a cosmological model with a perfect fluid and 𝒩 fields on a hyperbolic field space interacting via a symmetric potential. We list all late-time solutions, investigate their stability and briefly discuss predictions of the theory. Moreover, for the case of two scalar fields and an exponential potential we prove that the field equations are Liouville integrable and we provide for the first time the general solution for a region of the parameter space.

Hyperbolic inflationary model with nonzero curvature

“…We follow the procedure presented earlier in [27] and we consider the new variables a = 8 3 xz − y 2 and the conservation laws…”

“…Furthermore, because the scalar fields do not need to have the same values at the beginning and the end of inflation, that means that there are no observable non-Gaussianities in the power spectrum [25,26]. The analytic solution for the cosmological field equations of the hyperbolic inflation in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) background space was determined in [27]. Other extensions were proposed recently in [28,29].…”

New Anisotropic Exact Solution in Multifield Cosmology

“…( 9) Equation ( 5) can be seen as a second conservation law for the dynamical system. In the case of a spatially flat FLRW universe, i.e.,β = 0 and K = 0, the analytic solution of the field equation was presented recently in [28] using the Lie symmetry approach.…”

“…Multiscalar field models have been proposed as alternative models for the description of the whole cosmological history [22,23]. In the multiscalar field model the additional degrees of freedom provide new dynamical behaviours in the cosmological dynamics [24][25][26][27][28][29][30]. Some anisotropic exact solutions in multifield cosmology can be found in [20,31,32].…”

Hyperbolic inflation in the Jordan frame

“…Specifically, the dynamics of the two scalar fields are defined on a two-dimensional hyperbolic space. This model is also known as Chiral theory and it has been widely studied in the literature before [21][22][23][24][25][26][27][28][29][30]. This two-scalar field model for the exponential scalar field potential it admits an attractor which can provide the asymptotic behaviour of the hyperbolic inflation.…”