[Paper Review] About the cosmological constant in geometric scalar theory of gravity

I. C. Jardim, R. R. Landim|arXiv (Cornell University)|Aug 11, 2015

Cosmology and Gravitation Theories7 references3 citations

TL;DR

This paper investigates the inclusion of the cosmological constant in geometric scalar gravity (GSG), showing it cannot be modeled as a matter field due to inconsistencies with de Sitter geometry. To resolve this, the authors introduce a modified theory (GSGII) with an interaction term between the scalar field and vacuum curvature, restoring the Kottler solution and enabling black hole formation, while numerical analysis confirms GSGII better supports accelerated cosmic expansion than GSGI.

ABSTRACT

In this paper we study how to include the cosmological constant in geometric scalar theory of gravity (GSG). Firstly we show that the cosmological constant could not be modeled by a matter field, unlike in General Relativity. We also show that a spherically symmetric matter distribution, over the de Sitter vacuum, does not produce the Kottler solution and no black hole. To circumvent this problem we introduce an coupling term between the scalar field and the vacuum curvature in way to provide the Kottler solution. We also apply the original (GSGI) and the modified (GSGII) geometric scalar theory of gravity to the Friedmann-Robertson-Walker cosmology. A numerical analysis indicates that GSGII is most sensible to the cosmological constant them GSGI.

Motivation & Objective

• To determine whether the cosmological constant can be consistently incorporated into geometric scalar theory of gravity (GSG).
• To assess if the cosmological constant can be modeled as a matter field in GSG, as in General Relativity.
• To investigate whether a spherically symmetric matter distribution over a de Sitter vacuum yields the Kottler solution and black hole formation.
• To develop a modified field equation in GSG that supports the Kottler solution while preserving solar system tests.
• To compare the cosmological behavior of GSGI and GSGII using Friedmann-Robertson-Walker metrics.

Proposed method

• Model the cosmological constant as a matter field in a Minkowski background to test its compatibility with de Sitter geometry.
• Introduce a vacuum state with non-zero curvature (de Sitter/anti-de Sitter) instead of Minkowski, altering the background geometry.
• Derive the field equations for a spherically symmetric matter distribution in the de Sitter vacuum background to assess black hole formation.
• Modify the field equation by adding an interaction term between the scalar field and vacuum curvature to restore the Kottler solution.
• Apply both GSGI and GSGII to Friedmann-Robertson-Walker cosmology, deriving coupled equations for the scale factor and scalar field.
• Perform numerical analysis on the scale factor evolution to compare the influence of the cosmological constant in GSGI versus GSGII.

Experimental results

Research questions

• RQ1 Can the cosmological constant be modeled as a matter field in geometric scalar gravity, as in General Relativity?
• RQ2 Does a spherically symmetric matter distribution over a de Sitter vacuum in GSG produce the Kottler solution and black holes?
• RQ3 Why does the standard GSG fail to support black hole solutions in a de Sitter vacuum, and how can this be corrected?
• RQ4 How does the modified field equation in GSGII restore the Kottler solution while preserving solar system consistency?
• RQ5 How do GSGI and GSGII differ in their ability to drive accelerated cosmic expansion in Friedmann-Robertson-Walker cosmology?

Key findings

• The cosmological constant cannot be modeled as a matter field in GSG due to geometric incompatibility with de Sitter space-time.
• A spherically symmetric matter distribution over a de Sitter vacuum in GSG does not produce the Kottler solution, implying no black hole formation.
• The original GSGI theory fails to support black holes, contradicting standard stellar evolution models.
• The modified GSGII theory, with an interaction term between the scalar field and vacuum curvature, successfully restores the Kottler solution.
• Numerical analysis shows that GSGII produces a faster-growing scale factor and stronger cosmic acceleration than GSGI under identical initial conditions.
• GSGII is more sensitive to the cosmological constant than GSGI, indicating a stronger response to dark energy-like effects in cosmological evolution.