Vector Field Models of Inflation and Dark Energy

TL;DR

This work investigates vector-field cosmologies as alternatives to scalar inflaton/quintessence, analyzing space-like and time-like vectors in cosmological backgrounds with and without nonminimal couplings. They derive scaling solutions for space-like vectors in a Bianchi I setting, showing that anisotropic dark-energy behavior can be compatible with observational bounds under late onset or cancellation of anisotropy, and demonstrate stability of spin-1 perturbations. Time-like vectors with curvature and Gauss-Bonnet couplings are shown to realize both inflation and $\Lambda$CDM-like late-time acceleration, including a vector-Gauss-Bonnet construction that can reproduce the concordance expansion with polynomial couplings. The results highlight a rich phenomenology where vector fields drive cosmic acceleration, predict potential direction-dependent signatures in the CMB, and provide a framework for comparing anisotropic and isotropic cosmologies within vector-tensor theories.

Abstract

We consider several new classes of viable vector field alternatives to the inflaton and quintessence scalar fields. Spatial vector fields are shown to be compatible with the cosmological anisotropy bounds if only slightly displaced from the potential minimum while dominant, or if driving an anisotropic expansion with nearly vanishing quadropole today. The Bianchi I model with a spatial field and an isotropic fluid is studied as a dynamical system, and several types of scaling solutions are found. On the other hand, time-like fields are automatically compatible with large-scale isotropy. We show that they can be dynamically important if non-minimal gravity couplings are taken into account. As an example, we reconstruct a vector-Gauss-Bonnet model which generates the concordance model acceleration at late times and supports an inflationary epoch at high curvatures. The evolution of vortical perturbations is considered.

Figures (1)

• Figure 2: Two types of scenarios with a minimally coupled vector field that satisfy the CMBR quadrupole constraint. The solid (black) lines are the vector field density fraction $U = \rho_A/(\rho_m+\rho_A)$, the dashed (red) lines are the effective total equations of state of the universe $w_{eff}$, and the dash-dotted (blue) lines describe the evolution of eccentricity, $E=500e_*^2$. In the LHS figure, the displacement of the field from the minimum of its potential is important only at late times and only then significant anisotropies begin to form. The potential here is an exponential, $V(x) \sim e^{-x}$. In the RHS figure, the potential is a double-power law $V(x) \sim x^{-4}+V_+ x$. The dynamics of the field is such that though there are significant anisotropies, the eccentricity at the present is nearly zero. Note that we have chosen both the models in such a way that they feature a recently begun acceleration. Thus these models are viable though finely tuned.