Quasi-pole quintessential inflation in metric-affine gravity

Abstract

We study quintessential inflation in the framework of metric-affine gravity. It is well known that non-minimal couplings with the Holst invariant can generate a quasi-pole inflationary behaviour resulting in a Starobinsky-like phenomenology. The same quasi-pole behaviour can also be used in order to "flatten" the scalar potential in the Dark Energy era providing a successful framework for quintessential inflation. Agreement with all the observational constraints, reduces the predicted scalar spectral index to a narrow window: $0.966 \lesssim n_s \lesssim 0.967$, making the model highly testable and falsifiable.

Figures (7)

• Figure 1: Left: The scalar field potential \ref{['eq:potin']} as a function of the canonical field $\chi$. The two plateau regions lie in the vicinity of the quasi-pole positions, indicated by the vertical dashed lines. Right: The kinetic function $k(\phi)$ given in eq. \ref{['eq:kinetic']} as a function of the scalar field. In both panels, the parameters are $\delta_\beta = 10$, $\tilde{\xi} = -10$, and $\kappa = 1/2$.
• Figure 2: $r$ vs. $n_s$ (top-left), $\delta_\beta$ vs. $n_s$ (top-right), $|\tilde{\xi}|$ vs. $\delta_\beta$ (bottom-left), $|\tilde{\xi}|$ vs. $\delta_\beta$ (bottom-right) for $\phi_p = 2$ at $N_* = 58.9$ (blue, dashed) and $\phi_p = 10.4$ at $N_* = 60.5$ (black, continuous). Since these two models represent two extreme cases for our viable parameter space, the predictions for all other viable sets of $\phi_p$ and $N_*$ will fall between the two lines. See section \ref{['sec:parameters']} for the details on the parameter space, and section \ref{['sec:conclusions']} for the discussion of the results.
• Figure 3: Left: Benchmark potential for the first scenario with $|\phi_p| = 12$, $\delta_\beta=100$, $\tilde{\xi} =-69.5$, $\kappa=10.633$. The markers indicate critical field values: horizon exit of the pivot scale ($\chi_*$, black star), end of inflation ($\chi_{\rm end}$, black dot), freezing during radiation domination ($\chi_F$, black square), and present day ($\chi_0$, red square). Right: The mapping between the canonical field $\chi$ and the original field $\phi$. Note that the field freezes while the $\chi$-$\phi$ relation is still linear.
• Figure 4: Top left: Evolution of the effective equation of state $w_{\text{eff}} \equiv P_{\rm tot}/\rho_{\rm tot}$ for the benchmark potential of Fig. \ref{['fig:benchmark_potential']}. Bottom left: Evolution of the fractional energy densities for the scalar field (blue), radiation (orange), and cold matter (green). Top right: Barotropic parameter of the canonical scalar field. Bottom right: Ratio of total to kinetic scalar energy density. The integration starts $N=40$$e$-folds after horizon exit. Today corresponds to $N_0 \sim 123.1$.
• Figure 5: Left: Evolution of the density parameters for the scalar field $\Omega_\chi$ (blue), radiation $\Omega_r$ (orange), and cold matter $\Omega_m$ (green). Right: Magnified view around matter-radiation equality. The transient scaling behavior successfully generates an Early Dark Energy peak comprising $\sim 8\%$ of the total energy budget.