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Symmetric Bimetric Cosmology: A Minimal Extension of ΛCDM

Ghani Imadouchene

TL;DR

This work embeds a minimal AdS–dS symmetric cosmology in ghost-free Hassan–Rosen bimetric gravity, where a hidden AdS sector geometrically influences the observable de Sitter universe. The symmetric branch yields an effective cosmological constant $\Lambda_{\rm eff}$ plus a subdominant, ultra-diluted correction $\alpha(1+z)^{-3}$, leading to a slightly phantom-like equation of state $w(z)$ while remaining ghost-free and compatible with current data. The model reproduces the expansion history and structure growth of $\Lambda$CDM to sub-percent accuracy, satisfies the gravitational-wave speed constraint $c_T=1$, and employs Vainshtein screening to align with Solar-System tests. This provides a theoretically controlled, geometric interpretation for the dark sector and opens avenues for exploring perturbations, asymmetric branches, and holographic interpretations within a dual-geometry framework.

Abstract

We construct and analyze a symmetric bimetric cosmological model connecting Anti-de Sitter (AdS) and de Sitter (dS) regimes through a coupled scalar field. Starting from a Lagrangian with Einstein-Hilbert terms for two FLRW metrics and an inter-metric potential, we derive modified Friedmann and Klein-Gordon equations governing their evolution. In the symmetric effective-fluid limit, the model reproduces the main phenomenology of the $Λ$CDM cosmology with a small dynamical correction proportional to $(1+z)^{-3}$, and naturally satisfies local-gravity constraints through Vainshtein screening. This article outlines the theoretical structure and calibration of the model within a dual-geometry cosmological setting.

Symmetric Bimetric Cosmology: A Minimal Extension of ΛCDM

TL;DR

This work embeds a minimal AdS–dS symmetric cosmology in ghost-free Hassan–Rosen bimetric gravity, where a hidden AdS sector geometrically influences the observable de Sitter universe. The symmetric branch yields an effective cosmological constant plus a subdominant, ultra-diluted correction , leading to a slightly phantom-like equation of state while remaining ghost-free and compatible with current data. The model reproduces the expansion history and structure growth of CDM to sub-percent accuracy, satisfies the gravitational-wave speed constraint , and employs Vainshtein screening to align with Solar-System tests. This provides a theoretically controlled, geometric interpretation for the dark sector and opens avenues for exploring perturbations, asymmetric branches, and holographic interpretations within a dual-geometry framework.

Abstract

We construct and analyze a symmetric bimetric cosmological model connecting Anti-de Sitter (AdS) and de Sitter (dS) regimes through a coupled scalar field. Starting from a Lagrangian with Einstein-Hilbert terms for two FLRW metrics and an inter-metric potential, we derive modified Friedmann and Klein-Gordon equations governing their evolution. In the symmetric effective-fluid limit, the model reproduces the main phenomenology of the CDM cosmology with a small dynamical correction proportional to , and naturally satisfies local-gravity constraints through Vainshtein screening. This article outlines the theoretical structure and calibration of the model within a dual-geometry cosmological setting.

Paper Structure

This paper contains 57 sections, 76 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Theoretical Framework: Ghost-Free Hassan--Rosen Bimetric Gravity
  3. Hassan--Rosen Action
  4. FLRW Reduction
  5. Bianchi Constraint and Branch Structure
  6. Symmetric Branch
  7. Construction of the AdS--dS Symmetric Cosmological Model
  8. Dual FLRW Geometry: dS and AdS Branches
  9. Interaction Potential and Curvature Exchange
  10. Emergence of the $(1+z)^{-3}$ Correction
  11. Geometric Interpretation: AdS as an Effective Dark Sector
  12. Cosmological Dynamics and Effective-Fluid Description
  13. Modified Friedmann Equation
  14. Effective Equation of State
  15. Phantom-Like Behaviour Without Fundamental Ghosts
  16. ...and 42 more sections

Figures (3)

  • Figure 1: Comparison between the bimetric AdS--dS model (red dashed line), the $\Lambda$CDM prediction (solid orange line), and BAO measurements of $H(z)$. The bimetric correction proportional to $(1+z)^{-3}$ remains sub-percent for $z\lesssim2$, leading to an observationally indistinguishable expansion history.
  • Figure 2: Growth index $\gamma(z)$ for the AdS--dS symmetric bimetric model. The prediction approaches the General Relativity value $\gamma \simeq 0.55$ at low redshift (dashed line), with deviations of order $10^{-3}$ for the fiducial parameter choice $\alpha=0.01\Omega_\Lambda$. Present $f\sigma_8$ measurements are unable to distinguish the model from $\Lambda$CDM at this level of precision.
  • Figure 3: Effective dark-energy equation of state $w(z)$ in the AdS--dS symmetric bimetric model (red dashed curve), compared with $\Lambda$CDM ($w=-1$, orange line) and the $1\sigma$ confidence regions from Planck+BAO+SN (green) and Pantheon+SH0ES (blue). The predicted deviations from $w=-1$ are at the level of $10^{-2}$ and remain fully compatible with current observational constraints.