Constraining generalized non-local cosmology from Noether symmetries

Area of Science:

• Cosmology
• Theoretical Physics
• Gravitational Theory

Background:

• Non-local theories of gravity offer alternatives to standard models.
• Renormalizability in some non-local theories requires specific exponential coupling functions.
• The origin of these necessary couplings has been an open question.

Purpose of the Study:

• To investigate a generalized non-local theory of gravity.
• To determine the origin and form of coupling functions within this theory.
• To find cosmological solutions derived from the theory's symmetries.

Main Methods:

• Application of the Noether symmetry approach to a generalized non-local gravity Lagrangian.
• Analysis of the resulting constraints on non-local coupling functions.
• Derivation of cosmological solutions in both specific limits and the full theory.

Main Results:

• Noether symmetries constrain non-local coupling functions to be exponential or linear.
• Exponential couplings, crucial for renormalizability, emerge naturally from symmetries.
• De Sitter and power-law cosmological solutions were found for various non-local theories.

Conclusions:

• The study demonstrates that essential non-local couplings are not artificial but arise from fundamental symmetries.
• The generalized non-local theory naturally accommodates necessary couplings and yields viable cosmological solutions.
• This work provides a deeper understanding of non-local gravity and its cosmological implications.