Analytic Singular Slow-roll Inflation

Abstract

We study a class of minimally coupled scalar field theories which leads to analytic solutions for the Hubble rate and the scalar field. The inflationary phenomenology for this class of models can be studied fully analytically. The resulting phenomenology is compatible with the ACT data and for limiting cases, the spectral index is bluer than the ACT constraints and tends to the value $n_{\mathcal{S}}=0.98$, while in the limiting case, the tensor-to-scalar ratio takes very small values, nearly zero. More importantly, the resulting cosmology describes a Universe that has a finite scale factor at $t=0$, thus non-singular, evolves and expands realizing a slow-roll inflationary era and after that it reaches classically a pressure singularity. Classically, the Universe can pass through this singularity, and a turnaround cosmology is realized with the Universe contracting after the turnaround point. However, before the singularity is realized classically, the quantum phenomena dominate the evolution, avoiding the singularity. Specifically we consider the Nojiri-Odintsov conformal anomaly mechanism and we prove that the conformal anomaly erases the classical singular evolution and at the same time it generates extreme particle creation, which eventually reheats the Universe. Thus in this model the scalar field oscillations and the numerous couplings of the inflaton to the Standard Model particles are not required for reheating. In this context, scalar perturbations are enhanced and thus the formation of primordial black holes and the generation of secondary gravitational waves is enhanced. We also discuss several other mechanisms that may lead to the avoidance of the pressure singularity.

Figures (3)

• Figure 1: Marginalized curves of the Planck 2018 data and the analytic slow-roll model (\ref{['mainequation']}), confronted with the ACT data, the Planck 2018 data, and the updated Planck constraints on the tensor-to-scalar ratio for $N\sim 50-60$ and $m$ in the range $\alpha=[6,14]$.
• Figure 2: Graphical presentation of the scale factor $a(\eta)$ (upper left), the Hubble rate (upper right) as a function of the rescaled dimensionless time variable $\eta$, before the turnaround point. Also in the bottom left plot we present the Hubble radius $R_H(\eta)$ and in the bottom right the acceleration $a"(\eta)$ for the time interval for which inflation occurs $(\eta_i,\eta_f)$. We used the values of the free parameters that yield a viable inflationary evolution $(m,N)=(6,55.5)$ and $(\beta,\eta,\lambda)=(10^{-20},10^{-3},10^{-23})$.
• Figure 3: The trajectories in the $\dot{\varphi}-\varphi$ space, for $\varphi=2$ (red curve) and $\varphi=4$ (blue curve), in the range $(\varphi_i,\varphi_f)$. We used the values of the free parameters that yield a viable inflationary evolution $(m,N)=(6,55.5)$ and $(\beta,\eta,\lambda)=(10^{-20},10^{-3},10^{-23})$.