Baryogenesis in the paradigm of quintessential inflation

We explore the possibility of baryogenesis in the framework of quintessential inflation. We focus on the model independent features of the underlying paradigm and demonstrate that the required baryon asymmetry can successfully be generated in this scenario. To this effect, we use the effective field theory framework with desired terms in the Lagrangian necessary to mimic baryon number violation à la spontaneous baryogenesis which can successfully evade Sakharov’s requirement allowing us to generate the observed baryon asymmetry in the equilibrium process. Our estimates are independent of the underlying physical process responsible for baryon number violation. The underlying framework of quintessential inflation essentially includes the presence of kinetic regime after inflation which gives rise to blue spectrum of gravitational wave background at high frequencies. In addition to baryogenesis, we discuss the prospects of detection of relic gravitational wave background, in the future proposed missions, sticking to model independent treatment.

Figure 1

Figure shows the evolution of field energy density versus redshift on log scale. It is clear from the plot that kinetic regime establishes fast after the end of inflation such that $H_{\mathrm{end}}\simeq H_{\mathrm{kin}}$; $T_{\mathrm{end}}\simeq T_{\mathrm{kin}}(a_{\mathrm{end}}\simeq a_{\mathrm{kin}})$, which we have used for the model independent estimates obtained in this paper. Obviously, the related numeric requires the knowledge of the underlying inflationary model; we have assumed the field potential to be a generalized exponential potential $V\sim \exp (-\lambda {\varphi }^n/M_{\mathrm{Pl}}^n)$ to obtain this plot. We also checked it in other models of quintessential inflation, for instance, the model discussed in Ref. [33].

Figure 2

Feynman diagrams for left panel $CPT$ violating interaction given in (27), the nonconserved baryon current is $\overline{q}{\gamma }^{\mu }q$, in the right panel a four Fermi type interaction with Yukawa coupling mediated by the scalar field.

Figure 3

Figure (a) shows the allowed region of fermion masses and the instant preheating coupling g. Lower mass fermion couplings give rise to $\gamma \approx {10}^6$ with lowest possible value of $g\gtrsim {10}^{-4}$ for $r=0.05$. Higher mass fermion couplings are constrained by the lower bound on $\gamma$ necessary to keep cutoff scale $M$ below $M_{\mathrm{Pl}}$, see Eq. (38). Figure (b) is a schematic diagram which shows the postinflationary evolution of ${\rho }_{\varphi }$, it depicts energy density versus the scale factor on logarithmic scale; solid red line is back ground energy density(radiation/matter) and blue dashed line depicts field energy density.

Figure 4

Figure displays the relic gravitational wave spectrum; left panel corresponds to three different values of tensor-to-scalar ratio $r$ with the coupling constant $g$ being taken to the lowest value allowed by the BBN bound. The right panel displays the spectrum for three different values of the coupling $g$ with $r=0.05$. Dashed lines are the sensitivity curves of future GW experiments: SKA, LISA, Advanced-LIGO and DECIGO (2 lines show the original and upgraded sensitivity curves [82]).