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We developed a new formula for correlation functions in de Sitter space, crucial for understanding cosmic inflation. This method simplifies calculations and connects to existing flat-space theories.

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Area of Science:

  • Theoretical Physics
  • Cosmology
  • Quantum Field Theory

Background:

  • De Sitter space models are fundamental to inflationary cosmology.
  • Calculating correlation functions in curved spacetime is complex.
  • Existing methods like the CHY formula are established for flat spacetimes.

Purpose of the Study:

  • To propose a novel world sheet formula for tree-level correlation functions.
  • To describe a scalar field with arbitrary mass and quartic self-interaction in de Sitter space.
  • To establish a connection between de Sitter space calculations and flat-space limits.

Main Methods:

  • Developing a world sheet formula based on mass-deformed scattering equations.
  • Utilizing conformal generators in momentum space.
  • Applying the global residue theorem for verification.

Main Results:

  • The proposed formula is valid for correlation functions on the future boundary of de Sitter space.
  • The formula reduces to the CHY formula for scalar field theory amplitudes in the flat space limit.
  • Verification using the global residue theorem confirms reproduction of the Witten diagram expansion at four and six points.

Conclusions:

  • The new formula provides an effective tool for studying quantum field theory in de Sitter space.
  • The work lays the groundwork for extending the formula to n-point functions.
  • This research offers insights into the physics of the early universe and cosmic inflation.