Quintessence and phantom cosmology with non-minimal derivative coupling (1002.3478v2)

Abstract: We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological bounce. This variety of behaviors reveals the capabilities of the present scenario.

• The paper analyzes cosmological models driven solely by quintessence or phantom scalar fields with non-minimal derivative coupling to spacetime curvature.
• With zero potential, these models show distinct behaviors and transitions to de Sitter phases, notably allowing phantom fields to avoid the Big Rip singularity.
• Including constant potentials introduces a wider range of dynamics, including cosmological turnaround, bounce, and recollapse scenarios driven purely by the scalar field and its coupling.

Cosmological Dynamics with Non-Minimal Derivative Coupling

The research paper by Saridakis and Sushkov explores the intriguing domain of cosmological models where scalar fields, pivotal in describing phenomena such as dark energy, exhibit non-minimal derivative couplings to the curvature of spacetime. Particularly, the authors examine scenarios involving both quintessence and phantom scalar fields with such couplings, exploring their capacity to account for different cosmological evolutions even in the absence of matter content in the universe.

Central to their analysis is the construction of a gravitational theory incorporating these non-minimal derivatives alongside a scalar field potential $V(\phi)$. The equations governing the cosmic evolution in these frameworks are notably more complex than their conventional counterparts, owing to the interplay between the scalar fields' dynamics and the curvature. Saridakis and Sushkov specifically consider zero and constant potentials, analyzing their effects on the universe's evolution driven purely by the scalar fields.

For zero potentials, they observe distinct behaviors between quintessence and phantom fields, dictated by the coupling parameter $\kappa$. The solutions reveal transitions between de Sitter phases, hinging exclusively on the derivative coupling. Notably, for phantom fields under these conditions, the universe can bypass typical singularities such as the Big Rip, highlighting a significant deviation from standard phantom-driven cosmologies.

When extending the analysis to constant potentials, the range of dynamical behavior expands further, demonstrating scenarios such as the cosmological turnaround and bounce, traditionally reliant on additional matter content or modifications in the gravitational theory. The quintessence models with a negative cosmological constant showcase scenarios culminating in recollapse, while for positive constants, quintessence can lead to an eternal contraction or expansion phase depending on the initial conditions and coupling strengths. The phantom cases distinguishably feature cosmological bounces, where expansion succeeds contraction without encountering singularities.

This extensive exploration of non-minimal derivative couplings presents a framework where diverse cosmic phenomena emerge solely due to interactions between scalar fields and spacetime curvature, bypassing the necessity for exotic matter or alterations in general relativity's foundational principles. These findings substantially contribute to our understanding of possible configurations in scalar-tensor theories and set a precedence for further exploration in quantum field theory contexts and their cosmological implications.

Future work in this domain could extend to scenarios involving both quintessence and phantom fields simultaneously, potentially uncovering rich cosmological dynamics including cyclic models. Such studies could significantly influence our comprehension of the universe's evolution, particularly offering alternatives to conventional inflationary models and late-time acceleration drivers like dark energy.