Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2011
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2011ap%26ss.332..491e&link_type=abstract
Astrophysics and Space Science, Volume 332, Issue 2, pp.491-495
Astronomy and Astrophysics
Astrophysics
1
Modified Cosmology, Quadratic Correction, Quartic Potential, Dark And Phantom Energy, Accelerated Expansion, Liouville Cosmology
Scientific paper
We investigate the late-time dynamics of a four-dimensional universe based on modified scalar field gravity in which the standard Einstein-Hilbert action R is replaced by f( φ) R+ f( R) where f( φ)= φ 2 and f( R)= AR 2+ BR μν R μν,( A, B)∈ℝ. We discussed two independent cases: in the first model, the scalar field potential is quartic and for this special form it was shown that the universe is dominated by dark energy with equation of state parameter w≈-0.2 and is accelerated in time with a scale factor evolving like a( t)∝ t 5/3 and B+3 A≈0.036. When, B+3 A→∞ which corresponds for the purely quadratic theory, the scale factor evolves like a( t)∝ t 1/2 whereas when B+3 A→0 which corresponds for the purely scalar tensor theory we found when a( t)∝ t 1.98. In the second model, we choose an exponential potential and we conjecture that the scalar curvature and the Hubble parameter vary respectively like R=η Hdot{φ}/φ,ηin{R} and H=γdot{φ}^{χ},(γ,χ)in{R}. It was shown that for some special values of χ, the universe is free from the initial singularity, accelerated in time, dominated by dark or phantom energy whereas the model is independent of the quadratic gravity corrections. Additional consequences are discussed.
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