Scalar and vector modes in inflation with antisymmetric tensor field

TL;DR

This paper analyzes scalar and vector cosmological perturbations in inflation driven by a rank-2 antisymmetric tensor field $B_{\mu\nu}$ minimally coupled to gravity. Using an SVT decomposition and Newtonian gauge, the authors derive the second-order action and examine stability, finding a ghost in at least one scalar mode and gradient instabilities in the minimally coupled setup, while vector modes can be ghost-free with real subhorizon sound speeds but exhibit problematic superhorizon growth. The work highlights that non-minimal curvature couplings do not remove the scalar instabilities, and it emphasizes the need for further extensions (kinetic terms, parity-odd contributions, and full metric-tensor perturbations) to achieve a fully viable perturbation theory for antisymmetric-tensor inflation. Overall, the study maps the challenges and points toward directions for stabilizing perturbations in this inflationary framework.

Abstract

We investigate the scalar and vector modes arising from cosmological perturbations within the framework of an inflationary scenario driven by an antisymmetric tensor field, minimally coupled to gravity. After eliminating gauge artifacts, there remain four scalar and six vector modes of interest which can be studied separately. We analyze the stability of these modes, while looking for generic instabilities like ghost and gradient instabilities that could potentially plague the theory. Further, we investigate the evolution of these modes across different regimes, particularly subhorizon and superhorizon scales.

Figures (5)

• Figure 1: The numerical evolution of the real and imaginary parts of the $V_x$ and $V_y$ modes in the subhorizon limit is shown in the left panel for a $k$ value equal to 10. The right panel gives the modulus value of the corresponding vector modes. We have used a $\tau$ value of the order 1.
• Figure 2: The numerical evolution of the real parts of $U_i$ modes are shown in the left panel, while the right panel showcases the behavior of the corresponding part of the $C_i$ modes. The value of $k$ is taken to be 10, while $\tau$ is of the order 1.
• Figure 3: The plot shows the evolution of the real parts of the $C_x$ and $C_y$ modes. The $X$ axis is on logarithmic scale. The dashed vertical line represents the horizon crossing for the modes. $k$, $\tau$ values are 10 and $10^{-7}$ respectively.
• Figure 4: The numerical evolution of the real part of the $U_x$ and $U_y$ modes are shown respectively in the left and right panels. The $X$ axis is on logarithmic scale. The dashed vertical line represents the horizon crossing for the modes. $k$, $\tau$ values are 10 and $10^{-7}$ respectively.
• Figure 5: The numerical evolution of the real part of the $V_x$ and $V_y$ modes are shown respectively in the left and right panels. The $X$ axis is on logarithmic scale. The dashed vertical line represents the horizon crossing for the modes. $k$, $\tau$ values are 10 and $10^{-7}$ respectively.