Anisotropic Inflation from Vector Impurity

TL;DR

This work introduces a cosmological model in which a subdominant, non-minimally coupled vector field acts as an impurity to drive an anisotropic inflationary phase in a Bianchi type-I background. Through slow-roll analysis, the authors derive an explicit relation for the anisotropy $\Sigma$ in terms of the vector amplitude $X$ and the Hubble rate $H$, showing that anisotropy persists along the vector direction while the orthogonal plane isotropizes, thereby evading the cosmic no-hair theorem. The model predicts statistical anisotropy in scalar fluctuations and, crucially, that curvature perturbations can source primordial gravitational waves with a polarized component and potential TB correlations, enabling detectable tensor signals even for low-scale inflation. These signatures offer concrete observational handles to test the vector impurity scenario and its implications for early-universe cosmology. Future work will refine perturbative analyses to quantify these effects and relate them to CMB observations and direct gravitational-wave measurements.

Abstract

We study an inflationary scenario with a vector impurity. We show that the universe undergoes anisotropic inflationary expansion due to a preferred direction determined by the vector. Using the slow-roll approximation, we find a formula to determine anisotropy of the inflationary universe. We discuss possible observable predictions of this scenario. In particular, it is stressed that primordial gravitational waves can be induced from curvature perturbations. Hence, even in low scale inflation, a sizable amount of primordial gravitational waves may be produced during inflation.

Figures (4)

• Figure 1: The phase flow in $X$-$\dot{X}$ plane is depicted. For various initial conditions with small amplitude of $X$, we have plotted the trajectories. Every trajectory converges to the slow roll attractor.
• Figure 2: The phase flow in $\phi$-$\dot{\phi}$ plane is depicted. For the same initial conditions as Fig.1, we have plotted the trajectories. Every trajectory is degenerated irrespective of the initial conditions for X. As we can see, the inflaton rolls down the potential slowly. The inflaton begins to oscillate around the minimum of the potential and the inflation ends with the reheating. Here we have plotted a part of the graph for the sake of visualization , though we started from $\phi_0=10$.
• Figure 3: The Hubble parameter $H$ is plotted as a function of e-folding number $N$. We see a slow-roll phase clearly. We have e-folding number $N\sim$ 40 for this case.
• Figure 4: The ratio $\Sigma/H$ is plotted as a function of e-folding number. In spite of the rapid expansion of universe, the anisotropy remains sizable for some period relevant to observations.