Frame (in)equivalence in quantum field theory and cosmology

Area of Science:

• Theoretical Physics
• Cosmology
• Quantum Field Theory

Background:

• Frame equivalence is crucial for theories of early Universe dynamics and inflation.
• Understanding the path integral measure in quantum field theory with gravity is essential.

Purpose of the Study:

• To investigate frame equivalence in quantum field theory in the presence of gravity.
• To determine the implications of diffeomorphism invariance on the path integral measure.
• To introduce and analyze the concept of a 'frame discriminant'.

Main Methods:

• Revisiting the definition of the path integral measure in curved spacetime.
• Analyzing the consequences of diffeomorphism invariance on the measure.
• Deriving the quantum effective action and identifying the frame discriminant.
• Applying the findings to scalar-tensor theories in Einstein and Jordan frames.

Main Results:

• The path integral measure must depend non-trivially on fields in quantum field theory with gravity.
• Diffeomorphism invariance necessitates a field-dependent measure, leading to non-trivial transformations between frames.
• A new finite contribution, the 'frame discriminant', arises in the quantum effective action.
• In scalar-tensor theories, the frame discriminant acts as a scale-invariant regularization in the Jordan frame.

Conclusions:

• The frame discriminant is a critical, previously overlooked, contribution to quantum effective actions.
• Accurate assessment of early Universe dynamics and inflation requires accounting for the frame discriminant.
• The frame discriminant offers a novel perspective on regularization schemes in specific theoretical frameworks.