CC – Cosmological Constant

Introduction

The cosmological constant problem has long been regarded as one of the most serious conceptual challenges at the interface of gravity and quantum field theory. Observationally, cosmic acceleration is well described by a small, positive cosmological constant Λ, corresponding to an energy scale of order H² in units where c = 1. From the perspective of quantum field theory, however, vacuum fluctuations are expected to generate contributions to the energy density many orders of magnitude larger, leading to an apparent fine-tuning problem of order 10¹²⁰. This tension rests on two distinct assumptions. The first is that Λ is a fundamental parameter of the gravitational action, sensitive to ultraviolet physics and subject to radiative corrections. The second is that constant vacuum energy necessarily gravitates and contributes directly to the effective cosmological constant. Together, these assumptions imply an extreme mismatch between ultraviolet and infrared scales. In this work we adopt a different perspective. We argue that the cosmological constant is not a microscopic parameter to be renormalized, but an emergent infrared quantity determined by the entanglement structure of quantum fields on cosmological scales. The central object in our analysis is the causal diamond of a late-time comoving observer, which provides a natural, operationally defined infrared regulator in cosmology. Within this finite region, physically relevant gravitational information is encoded not in the absolute value of the vacuum energy, but in vacuum-subtracted quantities defined relative to a reference state.

Our approach is based on the relative entropy between the physical state of quantum fields and a reference vacuum restricted to the causal diamond. Relative entropy furnishes a well-defined, positive, and ultraviolet-insensitive measure of distinguishability between quantum states. Crucially, the associated modular energy is defined relative to the vacuum, so that constant shifts of the stress tensor cancel identically. In this modular sense, vacuum energy does not gravitate, and radiative instability of Λ is eliminated without modifying Einstein's equations or introducing additional fields. The remaining question is then infrared in nature: how is the value of Λ selected once ultraviolet sensitivity has been removed? We propose that Λ is fixed by an entanglement-based consistency condition on the causal diamond, equating the vacuum-subtracted modular energy of excitations to the generalized entropy associated with the diamond boundary. This condition selects a unique horizon scale R*, which in turn determines an effective cosmological constant Λeff ~ 1/R*². The central claim of this paper is modest but precise. We do not attempt to derive a microscopic value of Λ from Planck-scale physics. Rather, we show that: (i) Λ is determined by infrared, semiclassical observables defined on a finite causal diamond; (ii) constant vacuum-energy contributions decouple identically from this determination; and (iii) in matter+Λ cosmologies the resulting Λeff is naturally of order H², up to a coefficient of order unity, without fine-tuning. In this sense, the traditional cosmological constant problem is resolved. The ultraviolet naturalness crisis arises from an incorrect identification of the source of Λ. Once Λ is recognized as an infrared, entanglement-controlled quantity rather than a renormalized vacuum energy, the apparent 10¹²⁰ discrepancy disappears. What remains is a well-posed infrared selection problem, governed by the geometry and entanglement structure of cosmological causal diamonds. The paper is organized as follows. In Section 2 we introduce causal diamonds in FLRW spacetimes and identify the relevant infrared scale. Section 3 reviews relative entropy and modular energy, emphasizing the exact cancellation of vacuum-energy contributions. In Section 4 we formulate the infrared entanglement equilibrium condition that fixes the horizon scale. Section 5 shows explicitly that the infrared excitation density obtained by causal-diamond averaging in ΛCDM is of order the present critical density. We conclude in Section 6 with a discussion of the scope, limitations, and implications of the framework. Technical details are collected in the appendices..