Geometric inflation and dark energy with axion <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity
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Abstract
We present a model of $F(R)$ gravity in the presence of a string theory\nmotivated misalignment axion like particle materialized in terms of a canonical\nscalar field minimally coupled with gravity, and we study the cosmological\nphenomenology of the model, emphasizing mainly on the late-time era. The main\nresult of the paper is that inflation and the dark energy era may be realized\nin a geometric way by an $F(R)$ gravity, while the axion is the dark matter\nconstituent of the Universe. The $F(R)$ gravity model consists of an $R^2$\nterm, which as we show dominates the evolution during the early time, thus\nproducing a viable inflationary phenomenology, and a power law term $\\sim\nR^{\\delta}$ with $\\delta\\ll 1 $ and positive, which eventually controls the\nlate-time era. The axion field remains frozen during the inflationary era,\nwhich is an effect known for misalignment axions, but as the Universe expands,\nthe axion starts to oscillate, and its energy density scales eventually as we\nshow, as $\\rho_a\\sim a^{-3}$. After appropriately rewriting the gravitational\nequations in terms of the redshift $z$, we study in detail the late-time\nphenomenology of the model, and we compare the results with the $\\Lambda$CDM\nmodel and the latest Planck 2018 data. As we show, the model for small\nredshifts $0<z<5$ is phenomenologically similar to the $\\Lambda$CDM model,\nhowever at large redshifts and deeply in the matter domination era, the results\nare different from those of the $\\Lambda$CDM model due to the dark energy\noscillations. For the late-time study we investigate the behavior of several\nwell-known statefinder quantities, like the deceleration parameter, the jerk\nand $Om(z)$, and we demonstrate that the statefinders which contain lower\nderivatives of the Hubble rate have similar behavior for both the $\\Lambda$CDM\nand the axion $F(R)$ gravity model.\n