[Paper Review] Finite-Temperature Scalar Field Theory in Static de Sitter Space

D. V. Fursaev, Gennaro Miele|High-Energy Physics Literature Database (CERN, DESY, Fermilab, IHEP, and SLAC)|Feb 17, 1993

Cosmology and Gravitation Theories4 citations

TL;DR

This paper computes the finite-temperature one-loop effective potential for a scalar field in static de Sitter space using zeta-function regularization. It reveals that the stress tensor anomaly in the conformally invariant case depends on the thermal state, challenging prior work that neglected horizon effects, and analyzes how curvature influences vacuum minima in ground and de Sitter-invariant states.

ABSTRACT

The finite-temperature one-loop effective potential for a scalar field in the static de Sitter space-time is obtained. Within this framework, by using zeta-function regularization, one can get, in the conformally invariant case, the explicit expression for the stress tensor anomaly. Its value turns out to depend on the thermal state of the system. This conclusion is different from the one derived by other authors, who considered thermal properties of ultraviolet divergences in static spaces ignoring the effects of horizons. The behaviour of the effective potential in the ground state and in de Sitter-invariant state is also studied, showing the role played by the curvature on the minima.

Motivation & Objective

• To compute the finite-temperature one-loop effective potential for a scalar field in static de Sitter spacetime.
• To investigate the role of horizons in thermal quantum field theory by analyzing the stress tensor anomaly in the conformally invariant case.
• To compare the behavior of the effective potential in the ground state versus the de Sitter-invariant state.
• To examine how spacetime curvature influences the location and nature of minima in the effective potential.

Proposed method

• Zeta-function regularization is employed to handle ultraviolet divergences in the one-loop effective potential calculation.
• The analysis is performed in the static coordinate patch of de Sitter space, preserving the global structure for thermal field theory.
• The stress tensor anomaly is computed explicitly in the conformally invariant case using the regularization scheme.
• The effective potential is evaluated for both the ground state and the de Sitter-invariant thermal state to compare curvature effects.
• The paper distinguishes between thermal states and their impact on anomalies, contrasting with prior works that ignored horizon effects.
• Numerical and analytical techniques are used to study the minima of the effective potential under different curvature conditions.

Experimental results

Research questions

• RQ1 How does the stress tensor anomaly in conformally invariant scalar field theory depend on the thermal state in static de Sitter space?
• RQ2 What is the explicit form of the finite-temperature one-loop effective potential in static de Sitter spacetime?
• RQ3 How do the minima of the effective potential differ between the ground state and the de Sitter-invariant thermal state?
• RQ4 In what way does spacetime curvature influence the location and stability of the potential minima?
• RQ5 Why does the inclusion of horizon effects lead to a different conclusion about the anomaly compared to previous studies?

Key findings

• The stress tensor anomaly in the conformally invariant case is shown to depend explicitly on the thermal state of the system, contradicting earlier conclusions that ignored horizon effects.
• The one-loop effective potential is computed explicitly using zeta-function regularization in static de Sitter space.
• The ground state and de Sitter-invariant state yield different behaviors of the effective potential, indicating curvature's role in vacuum structure.
• The minima of the effective potential are shifted by spacetime curvature, demonstrating its influence on symmetry breaking patterns.
• The results suggest that horizon effects are essential in finite-temperature quantum field theory in de Sitter space, particularly for anomaly calculations.
• The paper provides a framework where thermal state dependence of anomalies emerges naturally from the regularization and geometry of the spacetime.