[Paper Review] Cosmological Perturbations in the 5D Holographic Big Bang Model

Natacha Altamirano, Elizabeth Gould+2 more|arXiv (Cornell University)|Mar 2, 2017

Cosmology and Gravitation Theories23 references3 citations

TL;DR

This paper proposes a 5D holographic Big Bang model where our 3-brane universe emerges from the collapse of a 5D star, avoiding a big bang singularity. It computes cosmological curvature perturbations induced by a thin, relativistic atmosphere in the 5D bulk, finding a power spectrum that is scale-invariant on small scales, red on intermediate scales, and blue on large scales—broadly consistent with observations but disfavored by 2.7σ compared to a simple power law.

ABSTRACT

The 5D Holographic Big Bang is a novel model for the emergence of the early universe out of a 5D collapsing star (an apparent white hole), in the context of Dvali-Gabadadze-Porrati (DGP) cosmology. The model does not have a big bang singularity, and yet can address cosmological puzzles that are traditionally solved within inflationary cosmology. In this paper, we compute the exact power spectrum of cosmological curvature perturbations due to the effect of a thin atmosphere accreting into our 3-brane. The spectrum is scale-invariant on small scales and red on intermediate scales, but becomes blue on scales larger than the height of the atmosphere. While this behaviour is broadly consistent with the non-parametric measurements of the primordial scalar power spectrum, it is marginally disfavoured relative to a simple power law (at 2.7$σ$ level). Furthermore, we find that the best fit nucleation temperature of our 3-brane is at least 3 orders of magnitude larger than the 5D Planck mass, suggesting an origin in a 5D quantum gravity phase.

Motivation & Objective

• To provide a concrete, predictive framework for the 5D holographic Big Bang model as an alternative to inflationary cosmology.
• To investigate how a thin, relativistic atmosphere in the 5D bulk affects cosmological perturbations on the 3-brane.
• To test the model’s predictions against non-parametric measurements of the primordial scalar power spectrum.
• To constrain the nucleation temperature and 5D Planck mass using observational and theoretical bounds.
• To assess the model’s consistency with the holographic entropy bound and other theoretical constraints.

Proposed method

• Model the 5D bulk spacetime as a Schwarzschild geometry with a 3-brane embedded at a time-dependent radial position.
• Introduce a thin, spherically symmetric atmosphere of relativistic particles in the 5D bulk, described by a matter Lagrangian in the DGP action.
• Solve the modified Einstein equations in the 5D bulk with the atmosphere's energy-momentum tensor to compute perturbations.
• Compute the scalar curvature power spectrum on the brane using the induced metric and perturbation theory in the braneworld framework.
• Use the Hubble parameter evolution due to the atmosphere to derive the time-dependent perturbation growth.
• Compare the predicted power spectrum to non-parametric CMB reconstructions and evaluate goodness-of-fit at the 2.7σ level.

Experimental results

Research questions

• RQ1 How do cosmological curvature perturbations arise in the 5D holographic Big Bang model due to a thin, infalling atmosphere?
• RQ2 What is the scale dependence of the primordial power spectrum generated by the atmosphere, and how does it compare to observations?
• RQ3 What constraints does the model place on the nucleation temperature of the 3-brane and the 5D Planck mass?
• RQ4 To what extent does the model satisfy the holographic entropy bound, and what does this imply for its viability?
• RQ5 How do relativistic corrections and atmospheric stability affect the predicted power spectrum shape?

Key findings

• The power spectrum of cosmological curvature perturbations is scale-invariant on small scales and red on intermediate scales, but exhibits a blue tilt on large scales beyond the atmosphere's height.
• The model’s predicted power spectrum is broadly consistent with non-parametric CMB reconstructions but is disfavored by 2.7σ compared to a simple power-law model.
• The best-fit nucleation temperature of the 3-brane is at least three orders of magnitude larger than the 5D Planck mass, suggesting a quantum gravity origin.
• The model violates the holographic entropy bound by at least 2.5 orders of magnitude, with the least severe violation occurring at the parameter boundary of BBN and thin atmosphere constraints.
• The atmosphere’s relativistic sound speed (c/2) and hydrostatic equilibrium profile may introduce O(0.2) corrections that could affect the spectrum shape, though these are currently neglected.
• The model remains a viable candidate for early universe cosmology, though it faces theoretical and empirical challenges, including stability of the atmosphere and consistency with entropy bounds.