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The study reveals a problem with theories on the Universe's beginning using semiclassical path integrals. A new method shows primordial gravitational waves are unsuppressed, challenging existing models.

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Area of Science:

  • Cosmology
  • Quantum Gravity
  • Theoretical Physics

Background:

  • Theories on the Universe's beginning often use semiclassical path integrals.
  • The Hartle-Hawking no boundary and Vilenkin tunneling proposals are prominent examples.
  • These theories involve integrating over 4-geometries to determine quantum amplitudes for a final 3-geometry.

Purpose of the Study:

  • To identify a fundamental obstruction in semiclassical path integral theories for the Universe's beginning.
  • To introduce a novel mathematical framework for defining the path integral in quantum gravity.
  • To analyze the implications for quantum cosmology, particularly concerning primordial gravitational waves.

Main Methods:

  • Introduction of Picard-Lefschetz theory to define the semiclassical path integral for gravity.
  • Application of this theory to quantum cosmology with a positive cosmological constant.
  • Mathematical analysis of both Lorentzian and Euclidean path integral formulations.

Main Results:

  • Picard-Lefschetz theory renders the Lorentzian path integral mathematically meaningful for quantum cosmology.
  • The Euclidean path integral formulation is found to be mathematically unsound in this context.
  • A general theorem proves that primordial tensor (gravitational wave) fluctuations remain unsuppressed.

Conclusions:

  • The Lorentzian-Picard-Lefschetz approach provides unambiguous predictions for quantum cosmology.
  • The unsuppressed nature of primordial gravitational waves presents a significant challenge to current cosmological models.
  • This work highlights fundamental issues in semiclassical theories of the Universe's origin.