[Paper Review] Cosmological consequences of short distance physics

J. C. Niemeyer|arXiv (Cornell University)|Jan 30, 2002

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This paper investigates how quantum gravitational effects at the Planck scale could leave observable imprints on the cosmic microwave background (CMB) through modified dispersion relations and short-distance uncertainty in inflationary cosmology. Using sonic inflation models and a non-local cutoff in field theory, it finds that leading-order corrections to the primordial power spectrum are potentially detectable at O(σ) if adiabaticity breaks, offering a path to probing Planck-scale physics via cosmological data.

ABSTRACT

Inflation can act as a space-time microscope for Planck or string scale effects, leaving potentially observable traces in the primordial perturbation spectrum. I discuss two frameworks that were used recently to study this phenomenon: nonlinear dispersion and short distance uncertainty.

Motivation & Objective

• To assess whether quantum gravitational effects at the Planck scale could leave observable traces in the primordial perturbation spectrum during inflation.
• To examine the robustness of inflationary predictions under modifications to local Lorentz invariance and short-distance physics.
• To evaluate the detectability of trans-Planckian effects through cosmological observables like the CMB power spectrum.
• To compare two frameworks—nonlinear dispersion (sonic inflation) and short-distance uncertainty—with distinct predictions for primordial perturbations.
• To determine the leading-order correction to the power spectrum and its dependence on the dimensionless ratio σ = H/κc, where H is the Hubble scale and κc is the critical wavenumber.

Proposed method

• Uses the sonic inflation framework, modeling trans-Planckian effects via a nonlinear dispersion relation F(k/a) that deviates from linearity at high wavenumbers, mimicking fluid dynamics near a sonic horizon.
• Introduces a modified mode equation for scalar and tensor perturbations, replacing the standard ω² = k² − a′′/a with ω_F² = [aF(k/a)]² − a′′/a, where F captures short-distance physics.
• Defines the dimensionless parameter σ = H/κc to quantify the strength of quantum gravitational corrections, with σ ≲ 10⁻³ expected in realistic models.
• Applies the adiabaticity parameter 𝒞 = |ω′/ω²| to assess the validity of the WKB approximation and estimate non-adiabatic particle production effects.
• Implements a short-distance uncertainty framework via a non-local cutoff in field theory, where modes are generated at a time η_c defined by a(η_c) = ˜k(eβ)¹ᐟ², introducing singular mass and damping terms.
• Analyzes the evolution of ˜k-modes using analytical initial conditions near η_c and performs numerical simulations to extract corrections to the power spectrum.

Experimental results

Research questions

• RQ1 What are the observable cosmological consequences of Planck-scale physics during inflation, particularly in the primordial power spectrum?
• RQ2 How do nonlinear dispersion relations in sonic inflation models affect the generation and evolution of primordial perturbations?
• RQ3 What is the leading-order correction to the primordial power spectrum due to short-distance physics, and is it O(σ) or O(σ²)?
• RQ4 Can deviations from adiabaticity in mode evolution lead to detectable O(σ) effects in the CMB, even if the initial state is adiabatic?
• RQ5 How does the short-distance uncertainty framework compare to sonic inflation in predicting modifications to the primordial spectrum?

Key findings

• Non-adiabatic particle production in sonic inflation models leads to corrections in the power spectrum at most of order 𝒞, which can be as large as σ when adiabaticity breaks.
• Numerical simulations of the ˜k-mode evolution in the short-distance uncertainty framework reveal power spectrum features linear in σ, indicating potentially observable O(σ) effects.
• The adiabaticity parameter 𝒞 is bounded by σ for regular, monotonically increasing F, suggesting that O(σ) corrections are not strictly ruled out even if the mode is initially adiabatic.
• The leading-order correction to the power spectrum is likely O(σ) if adiabaticity breaks, though some models suggest O(σ²) corrections, depending on initial conditions and vacuum choice.
• The short-distance uncertainty model provides a well-defined prescription for mode generation at η_c, offering hope that the model itself may select a preferred vacuum, reducing ambiguity.
• The VSL cosmology framework, when coupled with short-distance uncertainty, shows that a higher effective propagation speed (via group velocity) could solve the horizon problem, but only under specific assumptions about the velocity definition and validity at super-Planckian densities.