Unification of Inflation with Dark Energy in $f(R)$ Gravity and Axion Dark Matter

Understand

In this work we introduce an effective model of $f(R)$ gravity containing a 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 $m_a\gg H$, the axion field oscillates.