[Paper Review] Gravitational Field of the Early Universe: I.Non-linear Scalar Field as the Source

S. V. Chervon|ArXiv.org|Jun 10, 1997

Cosmology and Gravitation Theories2 references4 citations

TL;DR

This paper investigates the gravitational field of the early universe using a non-linear scalar field as the primary source, employing the 'fine tuning of the potential' method to derive exact solutions in inflationary cosmology. It presents new exact solutions for standard and conformally-flat spacetimes, synthesizing this approach with Barrow's method to yield a novel exact solution, advancing analytical understanding of early-universe gravity.

ABSTRACT

In this review article we consider three most important sources of the gravitational field of the Early Universe: self-interacting scalar field, chiral field and gauge field. The correspondence between all of them are pointed out. More attention is payed to nonlinear scalar field source of gravity. The progress in finding the exact solutions in inflationary universe is reviewed. The basic idea of `fine turning of the potential' method is discussed and computational background is presented in details. A set of new exact solutions for standard inflationary model and conformally-flat space-times are obtained. Special attention payed to relations between `fine turning of the potential' and Barrow's approaches. As the example of a synthesis of both methods new exact solution is obtained.

Motivation & Objective

• To analyze the gravitational field of the early universe using self-interacting scalar fields as the primary source.
• To explore the correspondence between scalar, chiral, and gauge fields as gravitational sources in early-universe models.
• To develop and apply the 'fine tuning of the potential' method to derive exact solutions in inflationary cosmology.
• To establish a synthesis between the 'fine tuning of the potential' method and Barrow's approach for constructing new exact solutions.
• To present a set of new exact solutions for standard inflationary models and conformally-flat spacetimes.

Proposed method

• The 'fine tuning of the potential' method is systematically applied to derive exact solutions of the Einstein-scalar field equations in the context of early-universe inflation.
• The method involves selecting specific forms of the scalar field potential that allow analytical solutions to the coupled Einstein and scalar field equations.
• Conformally-flat spacetime metrics are used as a framework to simplify the field equations and facilitate exact solution construction.
• The approach is compared and contrasted with Barrow's method, leading to a hybrid technique that combines their strengths.
• A new exact solution is derived by synthesizing the 'fine tuning of the potential' method with Barrow's formalism.
• Computational techniques are detailed to support the derivation and validation of the exact solutions.

Experimental results

Research questions

• RQ1 How can exact solutions be derived for the Einstein-scalar field equations in the early universe using non-linear scalar fields as sources?
• RQ2 What is the role of the 'fine tuning of the potential' method in constructing analytically tractable models of inflationary cosmology?
• RQ3 How do the solutions from the 'fine tuning of the potential' method compare with those obtained via Barrow's approach?
• RQ4 In what ways can the 'fine tuning of the potential' method be unified with Barrow's formalism to yield new exact solutions?
• RQ5 What are the implications of conformally-flat spacetime geometry for the structure of exact solutions in early-universe gravity?

Key findings

• A new exact solution is derived by synthesizing the 'fine tuning of the potential' method with Barrow's approach, representing a novel analytical result in early-universe gravity.
• The paper presents a set of new exact solutions for the standard inflationary model, expanding the known class of analytically solvable early-universe scenarios.
• The correspondence between scalar, chiral, and gauge fields as gravitational sources is clarified, highlighting their interrelations in cosmological models.
• The computational framework for the 'fine tuning of the potential' method is detailed, enabling reproducibility and extension of the results.
• The method successfully produces exact solutions in conformally-flat spacetimes, demonstrating its versatility beyond standard cosmological backgrounds.
• The analysis confirms the viability and utility of the 'fine tuning of the potential' technique in generating physically meaningful solutions for inflationary gravity.