Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter. (arXiv:1905.03496v1 [gr-qc])
<a href="http://arxiv.org/find/gr-qc/1/au:+Odintsov_S/0/1/0/all/0/1">S.D. Odintsov</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Oikonomou_V/0/1/0/all/0/1">V.K. Oikonomou</a>
In this work we introduce an effective model of $f(R)$ gravity containing a In this work we introduce an effective model of $f(R)$ gravity containing a http://arxiv.org/icons/sfx.gif
non-minimal coupling to the axion scalar field. The axion field is described by
the misalignment model, in which the primordial $U(1)$ Peccei-Quinn symmetry is
broken during inflation and the $f(R)$ gravity is described by the $R^2$ model,
and in addition, the non-minimal coupling has the form $sim
h(phi)R^{gamma}$, with $0
non-minimal coupling to the axion scalar field. The axion field is described by
the misalignment model, in which the primordial $U(1)$ Peccei-Quinn symmetry is
broken during inflation and the $f(R)$ gravity is described by the $R^2$ model,
and in addition, the non-minimal coupling has the form $sim
h(phi)R^{gamma}$, with $0<gamma<0.75$. By appropriately constraining the
non-minimal coupling at early times, the axion field remains frozen in its
primordial vacuum expectation value, and the $R^2$ gravity dominates the
inflationary era. As the Universe expands, when $H$ equals the axion mass $m_a$
and for cosmic times for which $m_agg H$, the axion field oscillates. By
assuming a slowly varying evolution of the axion field, the axion energy
density scales as $rho_asim a^{-3}$, where $a$ is the scale factor,
regardless of the background Hubble rate, thus behaving as cold dark matter. At
late times, the axion still evolves as $rho_asim a^{-3}$, however the Hubble
rate of the expansion and thus the dynamical evolution of the Universe is
controlled by terms containing the higher derivatives of $sim R^{gamma}$,
which are related to the non-minimal coupling, and as we demonstrate, the
resulting solution of the Friedman equation at late times is an approximate de
Sitter evolution. The late-time de Sitter Hubble rate scales as $Hsim
Lambda^{1/2}$, where $Lambda$ is an integration constant of the theory, which
has its allowed values very close to the current value of the cosmological
constant. Finally, the theory has a prediction for the existence of a
pre-inflationary primordial stiff era, in which the energy density of the axion
scales as $rho_asim a^{-6}$.
