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Large Scale Structure Formation of Normal Branch in DGP Brane World Model

Yong-Seon Song

TL;DR

The paper investigates large-scale structure formation in the normal branch of the DGP brane-world model using the Sawicki-Song-Hu scaling method to solve coupled on-brane and off-brane perturbations through the master variable Omega. It derives the full perturbation framework, shows that quasi-static growth yields a deeper Newtonian potential and suppressed ISW effect relative to LCDM, and demonstrates the scaling method's validity up to the present epoch while revealing its breakdown in the de Sitter asymptotic limit. A key finding is that even small deviations of the effective equation of state $w_{ m eff}$ below $-1$ produce detectable departures from LCDM in the perturbed potential, with potential observational signatures in ISW-galaxy and ISW-lensing cross-correlations. The work provides a concrete, testable prediction for the normal DGP branch and outlines observational strategies, particularly at high redshift, to distinguish it from LCDM and the self-accelerating branch.

Abstract

In this paper, we study the large scale structure formation of the normal branch in DGP model (Dvail, Gabadadze and Porrati brane world model) by applying the scaling method developed by Sawicki, Song and Hu for solving the coupled perturbed equations of motion of on-brane and off-brane. There is detectable departure of perturbed gravitational potential from LCDM even at the minimal deviation of the effective equation of state w_eff below -1. The modified perturbed gravitational potential weakens the integrated Sachs-Wolfe effect which is strengthened in the self-accelerating branch DGP model. Additionally, we discuss the validity of the scaling solution in the de Sitter limit at late times.

Large Scale Structure Formation of Normal Branch in DGP Brane World Model

TL;DR

The paper investigates large-scale structure formation in the normal branch of the DGP brane-world model using the Sawicki-Song-Hu scaling method to solve coupled on-brane and off-brane perturbations through the master variable Omega. It derives the full perturbation framework, shows that quasi-static growth yields a deeper Newtonian potential and suppressed ISW effect relative to LCDM, and demonstrates the scaling method's validity up to the present epoch while revealing its breakdown in the de Sitter asymptotic limit. A key finding is that even small deviations of the effective equation of state below produce detectable departures from LCDM in the perturbed potential, with potential observational signatures in ISW-galaxy and ISW-lensing cross-correlations. The work provides a concrete, testable prediction for the normal DGP branch and outlines observational strategies, particularly at high redshift, to distinguish it from LCDM and the self-accelerating branch.

Abstract

In this paper, we study the large scale structure formation of the normal branch in DGP model (Dvail, Gabadadze and Porrati brane world model) by applying the scaling method developed by Sawicki, Song and Hu for solving the coupled perturbed equations of motion of on-brane and off-brane. There is detectable departure of perturbed gravitational potential from LCDM even at the minimal deviation of the effective equation of state w_eff below -1. The modified perturbed gravitational potential weakens the integrated Sachs-Wolfe effect which is strengthened in the self-accelerating branch DGP model. Additionally, we discuss the validity of the scaling solution in the de Sitter limit at late times.

Paper Structure

This paper contains 7 sections, 37 equations, 2 figures.

Table of Contents

  1. introduction
  2. linear perturbation equations of normal branch DGP
  3. On-brane perturbed equations of motion
  4. Off-brane perturbed equation of motion
  5. Scaling solution
  6. The validity of scaling method in asymptotic limit
  7. conclusion

Figures (2)

  • Figure 1: The perturbed potentials $(\Phi-\Psi)/2$ in quasi-static limit. The effective equation of state $w_{\rm eff}$ varies with $\Omega_{\sigma}$ with fixing all other cosmological parameters. The dotted curve represents $(\Phi-\Psi)/2$ of LCDM, and the solid curves represent $(\Phi-\Psi)/2$ with varying $w_{\rm eff}$ from $-1.03$ to $-1.12$.
  • Figure 2: The perturbed potentials $(\Phi-\Psi)/2$ at scales of nearly horizon size are plotted. The solid curves represent the quasi static solutions, and the dash curves represent the dynamic scaling solutions scales at $k= 10^{-3} {\rm Mpc^{-1}}$ and $k=5\times 10^{-4} {\rm Mpc^{-1}}$.