[Paper Review] Quintessential Cosmological Scenarios in the Relativistic Theory of Gravitation

В. Л. Калашников|ArXiv.org|Aug 23, 2002

Cosmology and Gravitation Theories5 references3 citations

TL;DR

This paper proposes a quintessential cosmological scenario within the Relativistic Theory of Gravitation (RTG) by introducing a scalar field (quintessence) with a state parameter $ w \in [-1, -1/3] $ to drive late-time accelerated expansion. The massive graviton, inherent to RTG, suppresses a second inflation and enforces a closed, causally consistent cosmological evolution, with constraints on the graviton mass $ m_g < 10^{-43}~\text{eV} $ and maximum scaling factor $ a_{\text{max}} \sim 10^{28} $ in the constant-$ w $ case.

ABSTRACT

It is shown that the accelerated expansion of the universe in the framework of the relativistic theory of gravitation can be achieved by the introduction of the quintessential term in the energy-momentum tensor. The value of the minimum scaling factor and the modern observational data for the density and state parameters of the matter give the rough estimations for the maximum graviton mass and the maximum scaling factor. The former can be very low in the case of the primordial inflation and the latter can be extremely large for the scalar field model of the quintessence. In any case, the massive graviton stops the second inflation and provide the closed cosmological scenario in the agreement with the causality principle inherent to the theory.

Motivation & Objective

• To resolve the persistent issue of accelerated cosmic expansion in the Relativistic Theory of Gravitation (RTG), which otherwise only permits short-lived initial acceleration.
• To reconcile RTG’s inherent massive graviton and causality principle with modern observations of late-time acceleration.
• To derive constraints on the graviton mass and maximum scaling factor from the requirement of viable primordial nucleosynthesis and late-time quintessence domination.
• To assess the compatibility of RTG with primordial inflation models and scalar field quintessence scenarios.

Proposed method

• Introduce a quintessence term into the energy-momentum tensor with equation of state $ p = w\rho $, where $ w \in [-1, -1/3] $, to induce late-time repulsion and accelerated expansion.
• Model the cosmological evolution as a four-stage sequence: (1) initial inflation, (2) deceleration due to radiation/matter, (3) second acceleration via quintessence, (4) contraction driven by massive graviton's effective negative cosmological constant.
• Use the field equations of RTG, which separate the effective Riemannian spacetime from a Minkowski background, to derive the dynamics of the scale factor and energy density.
• Apply the vacuum stability principle and causality constraints to restrict the graviton mass and maximum scaling factor.
• Estimate the minimum initial scaling factor required for nucleosynthesis to occur, linking it to the graviton mass via temperature constraints.
• Analyze two quintessence models: (1) constant $ w > -1 $, yielding power-law dependence of $ a_{\text{max}} $ on $ m_g $, and (2) rolling scalar field potential, yielding exponential dependence.

Experimental results

Research questions

• RQ1 Can the RTG framework accommodate late-time accelerated expansion without introducing a cosmological constant?
• RQ2 What constraints does the requirement of successful nucleosynthesis impose on the graviton mass in RTG?
• RQ3 How does the massive graviton's effective negative contribution affect the maximum scale factor in quintessence-driven cosmologies?
• RQ4 Is primordial inflation in RTG compatible with a scalar field or massive graviton origin, given the constraints on initial conditions?
• RQ5 How do different quintessence models (constant $ w $ vs. rolling potential) affect the maximum scale factor and the theory’s consistency with causality?

Key findings

• The graviton mass is constrained to $ m_g < 10^{-43}~\text{eV} $ to ensure the initial temperature exceeds the threshold for nucleosynthesis.
• For a constant quintessence state parameter $ w > -1 $, the maximum scaling factor is estimated at $ a_{\text{max}} \sim 10^{28} $, assuming the present value is normalized to 1.
• The massive graviton terminates the second inflationary phase, enforcing a closed cosmological scenario consistent with the causality principle of RTG.
• In the rolling scalar field model of quintessence, the maximum scaling factor depends exponentially on the graviton mass, indicating a stronger sensitivity than in the constant-$ w $ case.
• The theory remains incompatible with primordial inflation driven by a scalar field due to the extreme difficulty of compressing the universe to Planck-scale size.
• The quintessence hypothesis remains viable in RTG only if it is weakly coupled to matter, extremely light, and does not significantly alter gauge couplings.