Spontaneous baryogenesis and generation of gravitational waves in a new model of quintessential $\alpha$-attractor

We study the role of $\alpha$-parameter of the newly proposed model of quintessential $\alpha$-attractor inflation (arXiv: 2305.00230 [gr-qc]) to the case of quintessential spontaneous baryogenesis and generation of relic gravitational waves in presence of a rolling scalar field during kination. An \textit{effective 4-Fermi construct} technique has been employed to compute the freeze-out temperature and the baryon-to-entropy ratio, of which the obtained results conform to the experimental requirements for $0.28\leq\alpha\leq 0.30$. This range of $\alpha$ is found to originate from the functional behaviour of the end-value expression of the potential concerned. We also find a blue-tilted gravitational wave spectrum during a transition from inflation to kination. The amplitudes of the gravitational waves during radiation domination satisfy the constraint for nucleosynthesis and the characteristic strain of the ongoing gravitational wave detectors. Thus, the most important observation emerged from the present study is that, increasingly small fractional values of $\alpha$ are favourable for unification of inflation, baryogenesis, quintessence and gravitational waves within a single model. This could have an interesting connection with the fundamental origin of $\alpha$-attractor.