Exact cosmological solutions with nonminimal derivative coupling

Journal Article · Sun Nov 15 04:00:00 EST 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.103505· OSTI ID:21308600

Sushkov, Sergey V ^[1]

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1. Department of General Relativity and Gravitation, Kazan State University, Kremlevskaya Str. 18, Kazan 420008 (Russian Federation) and Department of Mathematics, Tatar State University of Humanities and Education, Tatarstan Str. 2, Kazan 420021 (Russian Federation)

We consider a gravitational theory of a scalar field {phi} with nonminimal derivative coupling to curvature. The coupling terms have the form {kappa}{sub 1}R{phi}{sub ,{mu}}{phi}{sup ,{mu}} and {kappa}{sub 2}R{sub {mu}}{sub {nu}}{phi}{sup ,{mu}}{phi}{sup ,{nu}}, where {kappa}{sub 1} and {kappa}{sub 2} are coupling parameters with dimensions of length squared. In general, field equations of the theory contain third derivatives of g{sub {mu}}{sub {nu}} and {phi}. However, in the case -2{kappa}{sub 1}={kappa}{sub 2}{identical_to}{kappa}, the derivative coupling term reads {kappa}G{sub {mu}}{sub {nu}}{phi}{sup ,{mu}}{phi}{sup ,{nu}} and the order of corresponding field equations is reduced up to second one. Assuming -2{kappa}{sub 1}={kappa}{sub 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 depend on the sign of {kappa}. For negative {kappa}, the model has an initial cosmological singularity, i.e., a(t){approx}(t-t{sub i}){sup 2/3} in the limit t{yields}t{sub i}; and for positive {kappa}, the Universe at early stages has the quasi-de Sitter behavior, i.e., a(t){approx}e{sup Ht} in the limit t{yields}-{infinity}, where H=(3{radical}({kappa})){sup -1}. The corresponding scalar field {phi} is exponentially growing at t{yields}-{infinity}, i.e., {phi}(t){approx}e{sup -t/{radical}}{sup ({kappa})}. At late stages, the Universe evolution does not depend on {kappa} at all; namely, for any {kappa} one has a(t){approx}t{sup 1/3} at t{yields}{infinity}. Summarizing, we conclude that a cosmological model with nonminimal derivative coupling of the form {kappa}G{sub {mu}}{sub {nu}}{phi}{sup ,{mu}}{phi}{sup ,{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.

• OSTI ID: 21308600
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 10 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
COSMOLOGICAL MODELS
COUPLING
DE SITTER SPACE
EVOLUTION
FIELD EQUATIONS
GRAVITATION
MATHEMATICAL SOLUTIONS
POTENTIALS
SCALAR FIELDS
SINGULARITY
UNIVERSE