Pure Natural Quintessential Inflation and Dark Energy

We propose the pure natural quintessential inflation model which is motivated by Witten's conjecture, where the axion couples to pure Yang-Mills $SU(N)$ gauge field at large N limit. This modifies the standard cosine potential which is presented in the natural inflation, making it compatible with current CMB data. Our model gives a successful inflation as well as acceleration at the late times by quintessence inflaton field($\phi$). Here the inflaton field is responsible for inflation, after that the field enters into peculiar type of reheating and then they act as dynamical dark energy field which follows the same inflation potential and same model parameters. The dynamical field slowly rolls until the Hubble drops to mass of the quintessence field and it reaches the current dark energy field value. Here the dark energy scale is field dependent. Our quintessence model follows thawing frozen approach therefore the frozen quintessence field evolves with respect to cosmic time from initial field value($\phi_{i}$) to present non-zero minimum field value($\phi_{0}$). The obtained field value turned into ultra-light and it satisfies the present dark energy density which is $V(\phi_{0}) \approx \Lambda_{\text{DE}}^{4} = (2.3 \times 10^{-3}\text{eV})^{4}$.