Scaling-correspondence mechanism

TL;DR

This paper introduces a novel scaling-correspondence mechanism linking effective field theories and their bare models via a field-map, with applications to inflationary cosmology, demonstrating a power-law inflation model consistent with observations.

Contribution

The paper develops a new scaling-correspondence mechanism extending the scaling transformation of the effective Lagrangian, connecting EFTs with their bare models, and applies it to generate inflation models.

Findings

Found up to N-1 scaling-corresponding models for an EFT with Nth order self-interaction.

Generated a power-law inflation model from a scalar $$ EFT.

Briefly checked the model's consistency with observational constraints.

Abstract

In 1970s, Wilson shown the deep connection of renormalization and scaling of the effective Lagrangian. Polchinski further proved that such connection implied renormalizability of perturbative field theory. We develop the mechanism by an extension of scaling transformation of the effective Lagrangian - introducing a field-map between the quantum fields of the low-energy effective field theory (EFT) and its' scaling-corresponding (bare) model. We study the mechanism through real scalar $\phi^4$ model. We found if there is a self-interaction of order $N$ from the EFT's potential, there are (at most) $N-1$ scaling-corresponding models for the same symmetry group of the EFT. We then study the potential application for cosmology by applying the mechanism to inflation paradigm. We found the generated inflation model (from the real scalar $\phi^4$ EFT) is the power-law inflation model. We briefly check the consistency of the generated inflation model against the inflation's typical observational constraints - spectral index ($n_{s}$), e-folds, and tensor/scalar ratio ($r$).