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 [35] 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