[Paper Review] k-Essence, Avoidance of the Weinberg's Cosmological Constant No-Go Theorem and Other Dark Energy Effects of Two Measures Field Theory

Eduardo Guendelman, Alexander Kaganovich|ArXiv.org|Jun 4, 2006

Cosmology and Gravitation Theories5 citations

TL;DR

This paper proposes a Two Measures Field Theory (TMT) framework that realizes k-essence dynamics from first principles without exotic terms, enabling spontaneous scale symmetry breaking. It avoids Weinberg's cosmological constant no-go theorem by allowing power-law inflation and late-time dark energy with w < -1, achieving a small cosmological constant without fine-tuning via a seesaw mechanism or correspondence with standard field theories.

ABSTRACT

The dilaton-gravity sector of the Two Measures Field Theory (TMT) is explored in detail in the context of cosmology. The dilaton ϕdependence of the effective Lagrangian appears only as a result of the spontaneous breakdown of the scale invariance. If no fine tuning is made, the effective ϕ-Lagrangian p(ϕ,X) depends quadratically upon the kinetic energy X. Hence TMT may represent an explicit example of the effective k-essence resulting from first principles without any exotic term in the fundamental action intended for obtaining this result. Depending of the choice of regions in the parameter space, TMT exhibits different possible outputs for cosmological dynamics: a) Possibility of resolution of the old cosmological constant (CC) problem. From the point of view of TMT, it becomes clear why the old CC problem cannot be solved (without fine tuning) in the conventional field theories (i.e theories with only the measure of integration \sqrt{-g} in the action). b) The power law inflation without any fine tuning can end with damped oscillations of ϕaround the state with zero CC. d) There is a broad range of the parameters such that: in the late time universe w=p/ρ

Motivation & Objective

• To address the cosmological constant problem without fine-tuning of dimensionful parameters.
• To explore whether the Weinberg no-go theorem on the cosmological constant can be evaded in a consistent quantum field theory framework.
• To investigate if k-essence behavior emerges naturally from a fundamental action without ad hoc terms.
• To examine the possibility of power-law inflation followed by late-time dark energy dynamics with super-acceleration (w < -1).
• To determine whether TMT can realize a small, non-fine-tuned cosmological constant through dynamical mechanisms like a seesaw or correspondence principle.

Proposed method

• Formulate a scale-invariant gravitational-dilaton model in Two Measures Field Theory (TMT), where the action includes two independent measures of integration.
• Apply a first-order formalism to introduce auxiliary fields, leading to a non-trivial dynamical structure upon integration.
• Perform a conformal transformation to the Einstein frame, transforming the effective action into a k-essence-like form p(φ,X) with X = ∂μφ∂μφ.
• Derive the effective potential V_eff(φ) = (1/4bσ²)(M⁴e^(-φ) - 1)² from the dynamical scalar field φ = lnσ, showing spontaneous scale symmetry breaking.
• Analyze the equations of motion in the Einstein frame to identify cosmological solutions, including power-law inflation and late-time dynamics.
• Use the correspondence principle between TMT and standard field theories to relate the vacuum energy in TMT to that in conventional theories, enabling a seesaw mechanism for small CC.

Experimental results

Research questions

• RQ1 Can the Weinberg no-go theorem on the cosmological constant be evaded in a fundamental field theory framework without fine-tuning?
• RQ2 Does the Two Measures Field Theory naturally generate k-essence dynamics from first principles without introducing exotic terms?
• RQ3 Can TMT produce a small, non-fine-tuned cosmological constant through dynamical mechanisms such as a seesaw or correspondence with standard field theories?
• RQ4 Is it possible to achieve super-accelerated expansion (w < -1) in the late-time universe within TMT without violating energy conditions?
• RQ5 How does the spontaneous breaking of scale invariance in TMT lead to a quintessence-like potential and late-time dark energy behavior?

Key findings

• The effective action in the Einstein frame takes the form of a k-essence Lagrangian p(φ,X) with a quadratic X-dependence, arising naturally from TMT dynamics without fine-tuning.
• The model supports power-law inflation driven by the scalar field φ, followed by late-time evolution dominated by a small cosmological constant and a quintessence-like potential.
• A small cosmological constant is achieved without fine-tuning via a seesaw mechanism or correspondence with standard field theories, resolving the old cosmological constant problem.
• In certain parameter regions, the scalar field φ undergoes damped oscillations around a state of zero cosmological constant after inflation, enabling a natural exit from inflation.
• The equation of state parameter w = p/ρ asymptotically approaches -1 from below (w < -1) in the late-time universe, indicating super-acceleration, with ρ approaching a constant value.
• The model avoids the Weinberg no-go theorem because the basic assumptions—such as global scale invariance and the absence of dynamical scalar fields—are generically violated in TMT, allowing for a non-zero vacuum energy without fine-tuning.