[Paper Review] Effective quantum gravity, cosmological constant and the Standard Model of particle physics

Breno L. Giacchini, Tibério de Paula Netto+1 more|arXiv (Cornell University)|Dec 12, 2021

Cosmology and Gravitation Theories50 references6 citations

TL;DR

This paper proposes that effective quantum gravity, using the Vilkovisky–DeWitt geometric formulation of the effective action, enables a gauge- and parametrization-invariant renormalization group running of the cosmological constant and Newton's constant. It shows that the observed vacuum energy density in late-time cosmology imposes severe constraints on physics beyond the Standard Model, implying that any new physics must be consistent with the running of the vacuum energy density derived from quantum gravity effects.

ABSTRACT

The renormalization group in effective quantum gravity can be consistently formulated using the Vilkovisky and DeWitt version of effective action and assuming a non-zero cosmological constant. Taking into account that the vacuum counterpart of the cosmological constant is dramatically different from the observed energy density of vacuum, the running of the last quantity in the late cosmology indicates strong constraints on the physics beyond the minimal Standard Model of particle physics.

Motivation & Objective

• To address the gauge and parametrization dependence in standard effective field theory approaches to quantum gravity and cosmological constant running.
• To apply the Vilkovisky–DeWitt geometric effective action to derive a consistent, universal running of the vacuum energy density and Newton's constant in effective quantum gravity.
• To investigate the cosmological implications of this running, particularly its constraints on physics beyond the Standard Model.
• To demonstrate that the observed small value of the cosmological constant imposes strong bounds on new physics via the running of vacuum energy.

Proposed method

• Utilizes the Vilkovisky–DeWitt effective action, which provides a geometric, covariant formulation in field space, eliminating gauge and parametrization ambiguities.
• Applies the one-loop renormalization group equations derived from this effective action to the running of the vacuum energy density ρΛ and Newton's constant G.
• Assumes a non-zero cosmological constant in the action and uses the Landau–DeWitt gauge condition to fix the field-space metric uniquely.
• Derives the universal form of the running: ρΛ = ρ₀Λ + (3ν/8πG)(H² − H₀²), with G(µ) = G₀ / (1 + ν log(H²/H₀²)).
• Fixes the parameter a = −1/2 in the field-space metric Gij = 1/2(δμν,αβ + a gμν gαβ) via Vilkovisky's prescription, ensuring consistency and uniqueness.
• Performs numerical estimates of the running effects in late-time cosmology and compares them with observational constraints on vacuum energy.

Experimental results

Research questions

• RQ1 Can the Vilkovisky–DeWitt effective action resolve the gauge and parametrization dependence in the running of ρΛ and G in quantum gravity?
• RQ2 Does the running of the vacuum energy density derived from effective quantum gravity lead to observable cosmological constraints on new physics?
• RQ3 How does the running of the cosmological constant in effective quantum gravity affect the fine-tuning problem of the vacuum energy?
• RQ4 What are the implications of the observed small vacuum energy density for models of physics beyond the Standard Model?

Key findings

• The Vilkovisky–DeWitt effective action provides a gauge- and parametrization-invariant formulation of the running of ρΛ and G in effective quantum gravity, resolving a long-standing ambiguity in standard approaches.
• The running of the vacuum energy density is given by ρΛ = ρ₀Λ + (3ν/8πG)(H² − H₀²), with G(µ) = G₀ / (1 + ν log(H²/H₀²)), and this form is exact beyond one-loop order.
• The parameter ν, which governs the running, is constrained by the observed small value of the cosmological constant, leading to strong bounds on new physics.
• Numerical estimates show that the running of vacuum energy in late-time cosmology imposes severe constraints on models of physics beyond the Standard Model, particularly those involving new scalar or massive fields.
• The requirement that the running vacuum energy density remains consistent with observations implies that any new physics must either be very weakly coupled or have a very high mass scale.
• The Vilkovisky–DeWitt formalism is not just a mathematical tool but leads to physically testable predictions, as the running effects can be falsified by cosmological observations.