Ultraviolet Completion of the Big Bang in Quadratic Gravity

TL;DR

The paper proposes a UV-complete inflation scenario based on quantum quadratic gravity (QQG) with asymptotic freedom in the UV and slow-roll inflation arising from 1-loop running toward the IR, compatible with recent cosmological constraints that disfavour Starobinsky inflation. Inflationary dynamics are driven by RG running of the couplings $\xi$ and $\lambda$ in the presence of a large number $\mathcal{N}$ of matter fields, leading to a kinetic-dominated reheating and an eventual emergence of GR in the IR. In the Einstein frame, the RG-improved $f(R)$ action yields a quasi-de Sitter plateau with predictions $n_s \approx 1 - 4/(3N)$ and $r \approx (8/3) * (2/(\lambda_{tH}^2 N^4))^{1/3}$, with a no-strong-coupling bound $r \gtrsim 0.01$ and $\lambda_{tH} = \lambda_0 \mathcal{N} /(4\pi)^2$. The framework provides a concrete link between UV completion, inflation, reheating, and precision cosmology, identifies viable regions of parameter space (large $\mathcal{N}$ and $\lambda_{tH}\sim O(1)$), and outlines future directions for improving RG analysis and perturbations.

Abstract

We present a quantum quadratic gravity inflationary scenario that can accommodate the new cosmological constraints, which have disfavored Starobinsky inflation. The theory is asymptotically free in the ultraviolet, but 1-loop running is found to dynamically lead to slow-roll inflation toward the infrared. When a large number of matter fields contribute to the beta functions, the spectral index and the tensor-to-scalar ratio can be phenomenologically viable. We find that as inflation ends, the theory approaches its strong coupling regime and general relativity must emerge, as an effective field theory, as the universe must reheat and enter its standard radiation era. In order to avoid strong coupling, a minimum tensor-to-scalar ratio of 0.01 is predicted for this theory. Our framework offers a laboratory for connecting a concrete ultraviolet completion (quantum quadratic gravity) with inflationary dynamics, reheating, and precise cosmological observations.

Figures (5)

• Figure 1: The renormalization group (RG) flow of quadratic gravity with $\mathcal{N}=10$ matter-field content. The two red dashed lines show the separatrices of the RG flow, while the light blue shaded region is tachyon-free Buccio:2024hys. The orange trajectory shows a candidate cosmological evolution: starting from a potential tunneling from a (no-boundary) Euclidean geometry at the top of the trajectory (purple star) $\rightarrow$ slow-roll inflation (potential-dominated) $\rightarrow$ kination (kinetic-dominated) $\rightarrow$ strong-coupling/reheating, where an EH term with effective $M_{\mathrm{Pl}}$ (i.e., GR) emerges eventually.
• Figure 2: Plot of the scalar spectral index $n_\mathrm{s}$ vs the tensor-to-scalar ratio $r$ for Starobinsky inflation (in black), contrasted with our QQG model in color for different values of the coupling $\lambda_{\mathrm{tH}}$. The purple contour corresponds to a combination of CMB (PLANCK18+ACT+SPT+Lensing+BK18) and BAO (DESI) observational constraints.
• Figure 3: Constraints on the QQG parameters $\lambda_{\mathrm{tH}}$ and $\mathcal{N}$ from the observationals bounds on $n_\mathrm{s}$, $r$, and $A_\mathrm{s}$ combined. The dark and pale green regions amount to $1\sigma$ and $2\sigma$ confidence intervals, respectively.
• Figure 4: Phase space trajectories corresponding to the FLRW background evolution of the theory \ref{['eq:SofR']}. The 't Hooft-like coupling is set to $\lambda_{\mathrm{tH}}=1/10$, and curves of constant $|R|$ are shown in red. The inflationary 'attractor' solution is highlighted in green.
• Figure 5: Full Einstein-frame potential, parametrically given by \ref{['eq:varphisol']} and \ref{['eq:Vtilde']} as a function of the dimensionless RG scale $\psi$. The absolute value of the potential is plotted on a logarithmic scale, so we distinguish between positive and negative branches of the potential by using solid and dashed lines, respectively. The right panel corresponds to the branch of the potential when $\psi>\psi_\mathrm{s}$, and vice versa, the the left panel shows the potential when $\psi<\psi_\mathrm{s}$.