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We apply a new version of quintessential $\alpha$-attractor inflatonpotential (arXiv: 2305.00230 [gr-qc]) to make a detailed analysis of thephenomenon of \emph{spontaneous baryogenesis} in the post-inflationary kinationperiod. In this context, we compute various temperatures, their respectivenumber of e-folds, densities and the freeze-out values of baryon-to-entropyratio ($\eta_F$) at different mass scales, as functions of $\alpha$. Thenumerical calculations show that the baryon-to-entropy ratio is obtained as:for $\alpha = 0.29 - 0.30$, $\eta_F = 8.7\times 10^{-11} - 8.5\times 10^{-11}$and for $\alpha = 4.2 - 4.3$, $\eta_F = 8.5\times 10^{-11} - 8.6\times10^{-11}$. The results are found to satisfy experimental bounds quitesatisfactorily. We also find a blue-tilted spectrum of relic gravitationalwaves (GW) of frequencies lying in two narrow bands corresponding to the tworegions of $\alpha$, indicated above, \emph{viz.,} $f_{\mathrm{end}} =2.00\times 10^{10} - 2.10\times 10^{10}$ Hz for lower region of $\alpha$ and$f_{\mathrm{end}} = 2.12\times 10^{10} - 2.11\times 10^{10}$ Hz for higherregion of $\alpha$, during transition from inflation to kination, which issupported by current literature. The present-day peak values of the amplitudesof GWs emitted during radiation domination,($(\Omega_{\mathrm{GW},0}^{(\mathrm{RD})})_{\mathrm{peak}}$), are found to be$\sim 10^{-7}$, which is consistent with the requirement for nucleosynthesisand the associated root-mean-square values,($\Omega_{\mathrm{GW},0}^{(\mathrm{RD})}\sim 10^{-18}$), conform to thecharacteristic strain of the ongoing GW-detectors. In this way, a unifiedpicture of the roles of quintessential $\alpha$-attractor model, consideredhere, in inflation, quintessence, spontaneous baryogenesis and thegravitational waves production, emerges from the present study.

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