Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2009-10-06
Phys.Rev.D80:103505,2009
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, 2 figures. Accepted to PRD
Scientific paper
10.1103/PhysRevD.80.103505
We consider a gravitational theory of a scalar field $\phi$ with nonminimal derivative coupling to curvature. The coupling terms have the form $\kappa_1 R\phi_{,\mu}\phi^{,\mu}$ and $\kappa_2 R_{\mu\nu}\phi^{,\mu}\phi^{,\nu}$ where $\kappa_1$ and $\kappa_2$ are coupling parameters with dimensions of length-squared. In general, field equations of the theory contain third derivatives of $g_{\mu\nu}$ and $\phi$. However, in the case $-2\kappa_1=\kappa_2\equiv\kappa$ the derivative coupling term reads $\kappa G_{\mu\nu}\phi^{,mu}\phi^{,\nu}$ and the order of corresponding field equations is reduced up to second one. Assuming $-2\kappa_1=\kappa_2$, we study the spatially-flat Friedman-Robertson-Walker model with a scale factor $a(t)$ and find new exact cosmological solutions. It is shown that properties of the model at early stages crucially depends on the sign of $\kappa$. For negative $\kappa$ the model has an initial cosmological singularity, i.e. $a(t)\sim (t-t_i)^{2/3}$ in the limit $t\to t_i$; and for positive $\kappa$ the universe at early stages has the quasi-de Sitter behavior, i.e. $a(t)\sim e^{Ht}$ in the limit $t\to-\infty$, where $H=(3\sqrt{\kappa})^{-1}$. The corresponding scalar field $\phi$ is exponentially growing at $t\to-\infty$, i.e. $\phi(t)\sim e^{-t/\sqrt{\kappa}}$. At late stages the universe evolution does not depend on $\kappa$ at all; namely, for any $\kappa$ one has $a(t)\sim t^{1/3}$ at $t\to\infty$. Summarizing, we conclude that a cosmological model with nonminimal derivative coupling of the form $\kappa G_{\mu\nu}\phi^{,mu}\phi^{,\nu}$ is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential.
No associations
LandOfFree
Exact cosmological solutions with nonminimal derivative coupling does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Exact cosmological solutions with nonminimal derivative coupling, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact cosmological solutions with nonminimal derivative coupling will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-357597