This problem of the past singularity can be cured by adding the term to the Lagrangian in
f (R) dark energy models [37
]. Let us then consider the modified version of the model (4.83
):
Since the presence of the term can drive inflation in the early universe, one may anticipate
that both inflation and the late-time acceleration can be realized for the model of the type (13.37
). This is
like a modified gravity version of quintessential inflation based on a single scalar field [486, 183, 187, 392].
However, we have to caution that the transition between two accelerated epochs needs to occur smoothly
for successful cosmology. In other words, after inflation, we require a mechanism in which the
universe is reheated and then the radiation/matter dominated epochs follow. However, for the
model (13.37
), the Ricci scalar
evolves to the point
and it enters the region
.
Crossing the point
implies the divergence of the scalaron mass. Moreover, in the
region
, the Minkowski space is not a stable vacuum state. This is problematic for the
particle creation from the vacuum during reheating. The similar problem arises for the models
(4.84
) and (4.89
) in addition to the model proposed by Appleby and Battye [35
]. Thus unified
f (R) models of inflation and dark energy cannot be constructed easily in general (unlike a number
of related works [456, 460, 462]). Brookfield et al. [104] studied the viability of the model
(
) by using the constraints coming from Big Bang Nucleosynthesis
and fifth-force experiments and showed that it is difficult to find a unique parameter range for consistency
of this model.
In order to cure the above mentioned problem, Appleby et al. [37] proposed the f (R) model (11.40
).
Note that the case
corresponds to the Starobinsky inflationary model
[564] and the case
corresponds to the model of Appleby and Battye [35
] plus the
term. Although the above mentioned problem can be evaded in this model, the reheating
proceeds in a different way compared to that in the model
[which we
discussed in Section 3.3]. Since the Hubble parameter periodically evolves between
and
, the reheating mechanism does not occur very efficiently [37]. The reheating
temperature can be significantly lower than that in the model
. It will
be of interest to study observational signatures in such unified models of inflation and dark
energy.
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