Non-minimal derivative coupling gravity in cosmology

TL;DR

This paper reviews non-minimal derivative coupling scalar field theory in cosmology, analyzing its implications for universe expansion and cosmological constant values using observational data.

Contribution

It provides a comprehensive review of NMDC scalar field theory and applies observational datasets to constrain the cosmological constant within this framework.

Findings

Power-law expansion yields negative cosmological constant.

Super-acceleration expansion yields positive cosmological constant.

NMDC effect is negligible at late times, similar to ΛCDM.

Abstract

We give a brief review of the non-minimal derivative coupling (NMDC) scalar field theory in which there is non-minimal coupling between the scalar field derivative term and the Einstein tensor. We assume that the expansion is of power-law type or super-acceleration type for small redshift. The Lagrangian includes the NMDC term, a free kinetic term, a cosmological constant term and a barotropic matter term. For a value of the coupling constant that is compatible with inflation, we use the combined WMAP9 (WMAP9+eCMB+BAO+ $H_0$) dataset, the PLANCK+WP dataset, and the PLANCK $TT,TE,EE$+lowP+Lensing+ext datasets to find the value of the cosmological constant in the model. Modeling the expansion with power-law gives a negative cosmological constants while the phantom power-law (super-acceleration) expansion gives positive cosmological constant with large error bar. The value obtained is of the same order as in the $\Lambda$CDM model, since at late times the NMDC effect is tiny due to small curvature.