IR/UV mixing from higher-order interactions in a Scalar Field

TL;DR

This work introduces a scalar field model with a marginal quasi-local four-field interaction that generates a per-mode $k^8$-dependent quartic term, turning each mode into a quartic oscillator. The resulting ground-state energy scales as $E_0(k) \,\sim\, k_{Pl}(k^8/k_{box}^5)^{1/3}$, yielding an emergent UV/IR-mixed cutoff $k_{cut} \,\sim\, k_{Pl}^{3/8} k_{box}^{5/8}$ that lowers the effective ultraviolet scale for cosmological boxes while leaving laboratory physics intact. Dimensional regularization of the modified vacuum energy produces a suppressed $ ho_{vac}$ on the order of $10^{-33}$ GeV^4, closer to the observed dark-energy scale, with mild cosmological evolution compatible with hints from DESI. The results illustrate a concrete mechanism for UV/IR mixing in a local-field framework and point to future work on fully covariant nonlocal formulations and cosmological consistency checks.

Abstract

It is well known that the calculated cosmological constant, when regularized with a cutoff, differs hugely from the measured value. These calculations are made on the basis of a wave-vector cut-off that is usually set at the Planck scale. Further, Weinberg's no-go theorem indicates that in the presence of translational invariance, local quantum field theories cannot produce a zero cosmological constant without fine-tuning. Various non-local theories have been constructed, starting from modifications to Einstein's equations, in order to `cancel' away the cosmological constant term. There is also a well-known theory, due to Coleman, that assumes one can compute a probability distribution function for baby universes connected by wormholes that has the most probable value of the constant to be zero under some assumptions. The current paper starts from a QFT in 4-dimensions, breaks translational invariance by confining the fields to a box and adds a marginal (in power-counting terms) non-linear, momentum-dependent term that dominates the dynamics produced by the quadratic terms in the high-energy limit. It immediately produces an equation for the wave-vector cutoff applicable to the theory - the equation is reminiscent of that from UV/IR mixing and it effectively lowers the cutoff massively for a box the size of the Universe. However, as will be shown, the wave-vector cutoff for a box relevant for regular particle physics experiments is much larger, in fact, the Planck scale, so there is no conflict with current experiments, including the Casimir effect. We consider several possibilities for these additional terms and conclude that only one is relevant to a low cut-off. We also make a connection to the recent DESI results.

Figures (2)

• Figure 1: Emergent cutoff $k_{\mathrm{cutoff}}$ as a function of box length $L$.
• Figure 2: Vacuum–energy suppression ratio $\rho_{\mathrm{eff}}/\rho_{\mathrm{naive}}$ vs. $L$.