[Paper Review] Cosmological perturbations from five-dimensional inflation

Ignatios Antoniadis, Jules Cunat+1 more|arXiv (Cornell University)|Nov 29, 2023

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes that five-dimensional (5D) inflation can generate a large extra dimension (~micron scale), reconciling the hierarchy between gravitational weakness and the observable universe's size. It computes cosmological perturbations in 5D slow-roll inflation, showing enhanced power at large angular scales (>10°) due to Kaluza-Klein mode summation, with a nearly scale-invariant spectrum consistent with CMB observations.

ABSTRACT

It was recently proposed that five-dimensional inflation can relate the causal size of the observable universe to the present weakness of gravitational interactions by blowing up an extra compact dimension from the microscopic fundamental length of gravity to a large size in the micron range, as required in the Dark Dimension proposal. Here, we compute the power spectrum of all primordial fluctuations emerging from a 5-dimensional inflaton in a slow-roll region of its potential, showing an interesting change of behaviour at large scales corresponding to angles larger than about 10 degrees in the sky.

Motivation & Objective

• To explore whether five-dimensional inflation can simultaneously resolve the hierarchy between gravitational and gauge interaction strengths and the cosmological horizon problem.
• To compute the primordial power spectrum of cosmological fluctuations in a 5D inflationary model with a compact extra dimension.
• To determine how Kaluza-Klein (KK) mode summation modifies scalar, tensor, and vector perturbations compared to 4D inflation.
• To assess the consistency of the resulting power spectrum with CMB observations, particularly at low multipoles (l ≲ 30).
• To evaluate the role of the radion and KK excitations in generating primordial density perturbations and their impact on non-Gaussianity.

Proposed method

• Adapted 4D single-field inflation formalism to five dimensions, extending the computation of scalar, tensor, and vector perturbations to 5D spacetime with a compact fifth dimension.
• Treated the 5D inflaton and 5D graviton as primary fields, decomposing them into 4D zero-modes (inflaton, radion, spin-2 graviton, vector) and massive KK modes.
• Performed mode decomposition in Fourier space over the compact dimension, summing over all Kaluza-Klein modes to compute the effective 4D power spectra.
• Applied the slow-roll approximation to the 5D inflaton potential, deriving expressions for power spectra in terms of 5D slow-roll parameters ε and η.
• Incorporated the Z₂ orbifold projection (S¹/ℤ₂) to project out the vector zero-mode and half the massive KK modes, modifying low-momentum behavior.
• Derived power spectra for scalar, tensor, and vector perturbations in both limits: R₀k ≪ 1 (large scales) and R₀k ≫ 1 (small scales), with explicit expressions for spectral tilts and amplitudes.

Experimental results

Research questions

• RQ1 How does the inclusion of a compact fifth dimension in inflation modify the power spectrum of primordial fluctuations compared to standard 4D inflation?
• RQ2 What is the behavior of the scalar power spectrum at large angular scales (θ > 10°) in a 5D inflationary model with a micron-sized extra dimension?
• RQ3 How do Kaluza-Klein mode summations affect the spectral tilt and amplitude of cosmological perturbations in 5D inflation?
• RQ4 To what extent are vector and isocurvature perturbations suppressed in 5D inflation, and how do they compare to 4D models?
• RQ5 Can 5D inflation produce a nearly scale-invariant power spectrum consistent with CMB observations, particularly at low multipoles?

Key findings

• The scalar power spectrum exhibits enhanced power at large scales (R₀k ≪ 1) due to the 1/k-like behavior of KK mode contributions, leading to a nearly vanishing spectral index.
• The tensor power spectrum scales as 𝒫_T ≃ (8R₀H³/π²)(k/aH)^(-3ε) for R₀k ≫ 1, with a tensor-to-scalar ratio r = 24ε, consistent with 4D inflation but modified by the 5D geometry.
• Vector perturbations are suppressed at large scales (R₀k ≪ 1) due to Z₂ projection, with 𝒫_V ≃ (4πR₀H³/45)(R₀k)^3(k/aH)^(-3ε), contrasting with the enhanced power in scalar and tensor modes.
• The radion contribution to the scalar power spectrum is suppressed by the first slow-roll parameter ε, similar to isocurvature and entropy perturbations generated at second order.
• The model predicts a nearly scale-invariant power spectrum at small scales (R₀k ≫ 1), matching CMB observations, while deviations appear at large scales (θ > 10°), potentially testable in future low-multipole CMB data.
• The 5D inflaton potential's slow-roll parameters ε and η determine the spectral tilt and tensor-to-scalar ratio, with constraints ε_V < 0.003 and η_V ∈ [-0.02, -0.01] from current CMB data.