A new bigravity model with exclusively positive branes

TL;DR

The paper presents a new bigravity construction with two positive-tension $AdS_4$ branes in $AdS_5$ bulk that uses a warp-factor bounce to generate an ultralight KK graviton mode. It preserves the weak energy condition and avoids ghost states, with extra graviton polarizations decoupling so that Einsteinian gravity is recovered at accessible scales. The KK spectrum features a normalizable zero mode and a particularly light first KK state, with masses $m_1 \sim 4\sqrt{3}\,k\,e^{-2k z_0}$ and $m_{n+1} \sim 2\sqrt{n(n+3)}\,k\,e^{-k z_0}$, while couplings to brane matter place the first modes near $1/M_*$ and heavier modes are exponentially suppressed; in the symmetric case $M_{\rm Pl}\approx M_*/\sqrt{2}$. However, the negative effective cosmological constant on the branes and the AdS horizon constrain observable deviations at ultra-large distances, posing phenomenological challenges and motivating future work on cosmological solutions and matter-density effects.

Abstract

We propose a new ``bigravity'' model with two positive tension AdS_4 branes in AdS_5 bulk and no negative tension branes. The bounce of the ``warp'' factor mimics the effect of a negative brane and thus gives rise to an anomalously light graviton KK mode. This configuration satisfies the weak energy condition and has no ghost state. In addition, the extra polarization states of the massive graviton practically decouple and thus it does not contradict to Einsteinian gravity. However, the model has certain phenomenological difficulties associated with the presence of a negative cosmological constant on the branes.

Figures (1)

• Figure 1: The graviton (solid line), first (dashed line) and second (dotted line) KK states wavefunctions in the symmetric $"+-+"$ model. The wavefunctions are not smooth on the $"-"$ branes. The same pattern have also the $"++"$ model wavefunctions with the position of the $"-"$ brane corresponding to the minimum of the warp factor. The wavefunctions are then smooth.