Int J Theor Phys (2012) 51:2406–2418
DOI 10.1007/s10773-012-1120-z
Curvature Induced Acceleration and Reheating
of the Universe
B. Modak · R.N. Bose · M.K. Dutta
Received: 22 November 2011 / Accepted: 27 February 2012 / Published online: 21 March 2012
© Springer Science+Business Media, LLC 2012
Abstract We present some solutions in a modified theory of gravity with R
2
and
1
R
terms in
the Einstein-Hilbert action with an ideal fluid in FLRW spacetime. Graceful exit from early
inflation to radiation dominated era is obtained in the strong curvature regime preceding
a fluctuation of effective equation of state parameter at the end of inflation. In the weak
curvature regime the universe evolves through a radiation era that subsequently turns to a
matter era and finally transits to late time accelerating era.
Keywords Cosmology · Graceful exit · Re-heating · Late time acceleration
1 Introduction
Observation of high redshift of type Ia supernova [1, 2] and CMBR anisotropic spectrum
of WMAP [3–5] confirm that the present expansion of the universe is accelerated, while
at early era it was vacuum dominated. The most accepted explanation of present cosmic
acceleration is to invoke the dark energy dominated universe and the fractional densities
DE
∼ 0.7,
DM
∼ 0.26 and
B
∼ 0.04 are consistent for a spatial flat universe. The exact
nature of dark energy is not known, however it acts like a non-local fluid of large negative
pressure (p
e
< −ρ
e
/3), or a vacuum dominated (p
e
≈−ρ
e
) universe, while the dark matter
is a pressureless localised matter consisting of non-interacting particles.
The dark energy dominantly controls the early evolution as well as late time expansion
of the universe. The early universe evolves through an inflationary era, when the vacuum
B. Modak () · R.N. Bose
Department of Physics, University of Kalyani, Kalyani 741235, India
e-mail: bijanmodak@yahoo.co.in
R.N. Bose
e-mail: boserabin@gmail.com
M.K. Dutta
Department of Physics, B R SN College, Barrackpore 740120, India
e-mail: malaydutta1984@yahoo.com