Cosmology with Nonminimal Derivative Couplings

TL;DR

This paper investigates cosmology with nonminimal derivative couplings (NMDC) between a scalar field and gravity, extending ordinary nonminimal coupling by including derivative terms. Using a simplified NMDC Lagrangian with $L = -R + f_1(\phi,\phi_{;\alpha}) R + \phi_{;\alpha}\phi^{;\alpha} - 2 V(\phi)$ and $f_1(\phi,\phi_{;\alpha}) = \xi f(\phi) + \mu \phi_{;\alpha}\phi^{;\alpha}$, the author derives the coupled field equations and analyzes them in a second-order approximation for $V(\phi) = \lambda f(\phi)^M$ with $f(\phi) = \phi^{2m}$. The results show that NMDCs substantially widen the inflationary attractor sector (allowing $M \ge 2$ without an upper bound) and can produce multiple inflationary epochs (quasi-de Sitter, power-law, quasi-de Sitter) without introducing additional fields. The work also discusses how the NMDC/NMC sequence can influence bubble nucleation during first-order phase transitions, offering a mechanism for graceful exit and potential observational signatures such as gravitational waves, thereby enriching early-universe model-building and phenomenology.

Abstract

We study a theory which generalizes the nonminimal coupling of matter to gravity by including derivative couplings. This leads to several interesting new dynamical phenomena in cosmology. In particular, the range of parameters in which inflationary attractors exist is greatly expanded. We also numerically integrate the field equations and draw the phase space of the model in second order approximation. The model introduced here may display different inflationary epochs, generating a non-scale-invariant fluctuation spectrum without the need of two or more fields. Finally, we comment on the bubble spectrum arising during a first-order phase transition occurring in our model.