Cosmological constraints from UV/IR mixing
Niccolò Cribiori, Flavio Tonioni
TL;DR
The paper formulates a holography-inspired UV/IR mixing bound for $d$-dimensional EFTs with a cosmic horizon, constraining the inflaton to a finite interval and bounding the excursion $\Delta \varphi$ via $\kappa_d \Delta \varphi \le \dfrac{p}{2\lambda} \ln \dfrac{(l_{\mathrm{P}, d}^d V_1)^{1/(1-(d-2)q)}}{(l_{\mathrm{P}, d}^d V_2)^{d-1}}$. By combining the entropy bound rationale with a species-scale and horizon-based UV cutoff, the authors derive a central UV/IR mixing relation and obtain explicit expressions for the interval endpoints $\varphi_1$ and $\varphi_2$, as well as a bound on the number of extra dimensions in terms of inflationary observables $N_{\mathrm{e}}$ and $r$. Applying these bounds to chaotic inflation, $\alpha$-attractors, and modular-invariant cosmologies shows that the entire inflationary epoch can typically extend beyond the EFT-valid interval, signaling a tension between standard slow-roll models and quantum-gravity consistency. The work suggests that precise measurements of $r$ could constrain or reveal the number of extra dimensions, and highlights the need for refined parameter control ($p$, $q$, $\lambda$) and potential multi-field extensions to assess the robustness of these holographic bounds.
Abstract
Holography and entropy bounds suggest that the ultraviolet (UV) and infrared (IR) cutoffs of gravitational effective theories are related to one another as a form of UV/IR mixing. Motivated by this, we derive a bound on the allowed scalar field range in theories with cosmic horizons. We show how this bound challenges several inflationary scenarios, such as $α$-attractors and modular-invariant inflation. Besides, we find a relation between the number of extra spatial dimensions and the tensor-to-scalar ratio.