Non-minimal derivative coupling gravity in cosmology

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.

11 pages, 2 figures with additional references and corrections

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• Reheating predictions in Gravity Theories with Derivative Coupling
• Non-minimal Derivative Coupling Scalar Field and Bulk Viscous Dark Energy
• Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation
• Successful Higgs inflation from combined nonminimal and derivative couplings
• Dynamical Stability in presence of non-minimal derivative dependent coupling of $k$-essence field with a relativistic fluid
• Inflation and reheating in quadratic metric-affine gravity with derivative couplings
• Chiral gravitational waves and primordial black holes in UV-protected Natural Inflation
• Thick brane in reduced Horndeski theory
• Warm inflation with an oscillatory inflaton in the non-minimal kinetic coupling model
• General Einstein-Cartan quadratic gravity with derivative couplings
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• Non-minimal derivative coupling in Palatini cosmology: acceleration in chaotic inflation potential
• Constant-roll inflation driven by a scalar field with non-minimal derivative coupling
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• Testing kinetically coupled inflation models with CMB distortions
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• Non-Minimal Inflation with a scalar-curvature mixing term $\frac{1}{2}\xi R{\varphi }^2$
• Dynamics of holographic dark energy with apparent-horizon cutoff and non-minimal derivative coupling gravity in non-flat FLRW universe
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• Nonminimal Derivative Coupling Cosmology and the Speed of Gravitational Waves
• Ultra-compact Objects of Non-minimally Coupled Dark Matter
• Noether symmetry approach in non-minimal derivative coupling gravity