Model for Emergence of Spacetime from Fluctuations.

Area of Science:

• Theoretical Physics
• Quantum Gravity
• Cosmology

Background:

• The standard formulation of gravity and matter path integrals relies on a chosen basis in the field space.
• Physical regimes exist that do not admit such position bases, termed pregeometric.
• Understanding the emergence and properties of spacetime in these regimes is crucial.

Purpose of the Study:

• To define a Euclidean path integral for gravity and matter that is independent of the choice of basis in the space of fields.
• To describe physical regimes that do not admit position bases (pregeometric regimes).
• To elucidate the mechanism by which emergent spacetime properties, like dimension, depend on fundamental physical parameters.

Main Methods:

• Utilizing a result from Hawking and Gilkey to construct the path integral.
• Developing a framework to describe pregeometric physical regimes.
• Analyzing the dependence of emergent spacetime geometry on the balance of matter and gravitational forces.

Main Results:

• A novel Euclidean path integral for gravity and matter is defined, invariant under basis transformations.
• This path integral successfully describes pregeometric regimes where spacetime is not fundamental.
• The dimension and volume of emergent spacetimes are shown to depend on the balance of fermionic pressure and bosonic/gravitational pull.
• This balance is determined by the number and masses of contributing bosonic and fermionic species at a given energy scale.

Conclusions:

• The developed path integral offers a more general description of gravity and matter, applicable beyond standard spacetime formulations.
• An explicit mechanism is provided for the energy-dependent effective dimension of spacetime.
• This work offers insights into the fundamental nature of spacetime and its emergence from more basic constituents.