[Paper Review] Quintessential Inflation, Unified Dark Energy and Dark Matter, and Higgs Mechanism

Eduardo Guendelman, Emil Nissimov+1 more|arXiv (Cornell University)|Sep 22, 2016

Cosmology and Gravitation Theories14 citations

TL;DR

This paper proposes a unified gravity-matter model using non-Riemannian spacetime volume forms to describe both early-universe inflation and late-time dark energy/dark matter via a single scalar field ('darkon') and an inflaton field. The formalism generates a dynamically induced cosmological constant and dust-like dark matter, while enabling gravity-assisted electroweak symmetry breaking in the late Universe, with the Higgs field remaining massless during inflation.

ABSTRACT

We describe a new type of gravity-matter models where gravity couples in a non-conventional way to two distinct scalar fields providing a unified Lagrangian action principle description of: (a) the evolution of both "early" and "late" Universe - by the "inflaton" scalar field; (b) dark energy and dark matter as a unified manifestation of a single material entity - the "darkon" scalar field. The essential non-standard feature of our models is employing the formalism of non-Riemannian space-time volume forms - alternative generally covariant integration measure densities (volume elements) defined in terms of auxiliary antisymmetric tensor gauge fields. Although being (almost) pure-gauge degrees of freedom, the non-Riemannian space-time volume forms trigger a series of important features unavailable in ordinary gravity-matter models. When including in addition interactions with the electro-weak model bosonic sector we obtain a gravity-assisted generation of electro-weak spontaneous gauge symmetry breaking in the post-inflationary "late" Universe, while the Higgs-like scalar remains massless in the "early" Universe.

Motivation & Objective

• To unify dark energy and dark matter as manifestations of a single scalar field ('darkon') via a non-Riemannian gravity-matter action.
• To describe both early-universe inflation and late-time dark energy dominance within a single dynamical framework using a unified inflaton field.
• To dynamically generate electroweak symmetry breaking in the post-inflationary era while preserving gauge symmetry during inflation.
• To explore the role of auxiliary antisymmetric tensor fields in modifying spacetime integration measures and inducing new physical effects in gravity and matter couplings.

Proposed method

• Employing a non-Riemannian spacetime volume form Φ(C) defined via an auxiliary rank-3 antisymmetric tensor field Cμνλ to modify the gravitational integration measure.
• Constructing a modified gravity-scalar action where the scalar field Lagrangian couples symmetrically to both Riemannian √−g and non-Riemannian Φ(C) volume forms.
• Deriving a dynamical constraint L(u,Y) = −2M₀ = const from the equations of motion for the measure field Cμνλ, leading to a constant energy density contribution.
• Introducing a second scalar field (inflaton) coupled to the same non-Riemannian structure to generate a two-flat-region effective potential for unified early and late-time cosmology.
• Coupling the system to the SU(2)×U(1) electroweak sector, enabling the emergence of a Higgs-like potential in the late Universe while keeping the Higgs massless during inflation.
• Using hidden Noether symmetries associated with the non-Riemannian volume form to stabilize the dynamics and ensure consistency of the energy-momentum tensor.

Experimental results

Research questions

• RQ1 Can dark energy and dark matter be unified as two manifestations of a single scalar field via a non-Riemannian gravity-matter action?
• RQ2 Can the same scalar field system describe both inflation in the early Universe and dark energy dominance in the late Universe?
• RQ3 How does the inclusion of non-Riemannian volume forms lead to a dynamically generated cosmological constant and dust-like dark matter?
• RQ4 Can gravity-induced symmetry breaking generate the electroweak Higgs potential in the late Universe while preserving massless Higgs fields during inflation?
• RQ5 What role do auxiliary antisymmetric tensor fields play in enabling new physical effects in gravity and matter couplings?

Key findings

• The non-Riemannian volume form Φ(C) leads to a dynamical constraint L(u,Y) = −2M₀ = const, which generates a constant energy density term interpreted as a dynamically generated cosmological constant.
• The energy-momentum tensor of the darkon field splits into two parts: a cosmological constant-like term −2gμνM₀ and a dust-like fluid term proportional to ∂μu∂νu, unifying dark energy and dark matter.
• The model exhibits a hidden nonlinear Noether symmetry due to the non-Riemannian measure, ensuring conservation of the energy-momentum tensor and stabilizing the dynamics.
• The inflaton field acquires an effective potential with two infinitely flat regions—one for early inflation and one for late-time dark energy—enabling quintessential inflation.
• In the late Universe, the Higgs-like scalar field develops an effective potential of the canonical electroweak symmetry-breaking form, while remaining massless during inflation.
• The relative height of the potential barrier between the two flat regions is of the same order as the late-time effective cosmological constant, suggesting a natural connection between inflation and dark energy.