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The Self-Accelerating Universe with Vectors in Massive Gravity

Kazuya Koyama, Gustavo Niz, Gianmassimo Tasinato

TL;DR

The paper investigates self-acceleration in massive gravity with vector degrees of freedom by deriving a decoupling-limit action that involves an infinite series of vector–scalar couplings, which can be resummed into non-polynomial interactions. It identifies self-accelerating backgrounds with nontrivial vector profiles, but shows that a ghost is unavoidable whenever a background vector is present, while removing the vector background can avoid ghosts at the cost of strong coupling. Including a bare cosmological constant does not eliminate the ghost in the vector-background case, though it can enlarge ghost-free regions in some branches. The results highlight fundamental limitations for realizing ghost-free, vector-augmented self-acceleration within this massive gravity framework, and point to further work on full non-linear stability and matter couplings.

Abstract

We explore the possibility of realising self-accelerated expansion of the Universe taking into account the vector components of a massive graviton. The effective action in the decoupling limit contains an infinite number of terms, once the vector degrees of freedom are included. These can be re-summed in physically interesting situations, which result in non-polynomial couplings between the scalar and vector modes. We show there are self-accelerating background solutions for this effective action, with the possibility of having a non-trivial profile for the vector fields. We then study fluctuations around these solutions and show that there is always a ghost, if a background vector field is present. When the background vector field is switched off, the ghost can be avoided, at the price of entering into a strong coupling regime, in which the vector fluctuations have vanishing kinetic terms. Finally we show that the inclusion of a bare cosmological constant does not change the previous conclusions and it does not lead to a ghost mode in the absence of a background vector field.

The Self-Accelerating Universe with Vectors in Massive Gravity

TL;DR

The paper investigates self-acceleration in massive gravity with vector degrees of freedom by deriving a decoupling-limit action that involves an infinite series of vector–scalar couplings, which can be resummed into non-polynomial interactions. It identifies self-accelerating backgrounds with nontrivial vector profiles, but shows that a ghost is unavoidable whenever a background vector is present, while removing the vector background can avoid ghosts at the cost of strong coupling. Including a bare cosmological constant does not eliminate the ghost in the vector-background case, though it can enlarge ghost-free regions in some branches. The results highlight fundamental limitations for realizing ghost-free, vector-augmented self-acceleration within this massive gravity framework, and point to further work on full non-linear stability and matter couplings.

Abstract

We explore the possibility of realising self-accelerated expansion of the Universe taking into account the vector components of a massive graviton. The effective action in the decoupling limit contains an infinite number of terms, once the vector degrees of freedom are included. These can be re-summed in physically interesting situations, which result in non-polynomial couplings between the scalar and vector modes. We show there are self-accelerating background solutions for this effective action, with the possibility of having a non-trivial profile for the vector fields. We then study fluctuations around these solutions and show that there is always a ghost, if a background vector field is present. When the background vector field is switched off, the ghost can be avoided, at the price of entering into a strong coupling regime, in which the vector fluctuations have vanishing kinetic terms. Finally we show that the inclusion of a bare cosmological constant does not change the previous conclusions and it does not lead to a ghost mode in the absence of a background vector field.

Paper Structure

This paper contains 22 sections, 124 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Massive Gravity Lagrangian
  3. Self-accelerating solutions with vectors ($\alpha_3=\alpha_4=0$ case)
  4. Self-acceleration from spherically symmetric solutions
  5. Solving the field equations in the decoupling limit
  6. The Lagrangian with vector degrees of freedom
  7. The potential in the decoupling limit
  8. A method for resuming the series
  9. An example
  10. Stability of the self-accelerating configuration ($\alpha_3=\alpha_4=0$ case)
  11. Scalar-Vector Lagrangian
  12. Scalar-tensor Lagrangian
  13. The kinetic terms, and the inevitable ghost degree of freedom
  14. The case of non-vanishing $\alpha_3$ and $\alpha_4$
  15. Lagrangian in the decoupling limit
  16. ...and 7 more sections

Figures (1)

  • Figure 1: The dS and AdS regions of the self-accelerating solution in the decoupling limit (\ref{['decsola3a4']}). Left (right) plot is for $\alpha_5>0$ ($\alpha_5<0$). The white exclusion area is associated to the positiveness of the argument in the square root of $\alpha_5$. In each plot, half of the line $\alpha_3+3 \alpha_4=0$ has to be removed to avoid the curvature of the space-time from diverging, with the middle point being that of the brane action found in Ref. us2.