Modular fluctuations in cosmology

Verlinde and Zurek (VZ) have proposed that quantum gravity fluctuations in causal diamonds lead to observable effects. In particular, they argued that in quantum gravity causal diamonds have an uncertainty in their size that scales as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>δ</a:mi><a:mi>L</a:mi><a:mo>∼</a:mo><a:msqrt><a:mrow><a:msub><a:mo>ℓ</a:mo><a:mi>p</a:mi></a:msub><a:mi>L</a:mi></a:mrow></a:msqrt></a:math>, i.e. fluctuations are enhanced from the Planck scale. In this work, we explore the origin of the VZ scaling by studying scalar perturbations in inflationary cosmology. We reinterpret these cosmological perturbations as fluctuations of the modular Hamiltonian associated with a causal diamond, establishing a connection between modular fluctuations and observable primordial perturbations. Independent of assumptions about the modular Hamiltonian or the background spacetime, our results show that—whenever an (effective) spherically symmetric perturbation is quantized—it can lead to the VZ scaling. However, whether such a mode exists in the vacuum of any theory of quantum gravity remains an open question.