Complex dimensions and their observability

Abstract

We show that the dimension of spacetime becomes complex-valued when its short-scale geometry is invariant under a discrete scaling symmetry. This characteristic can generically arise in quantum gravities, for instance, in those based on combinatorial or multifractal structures or as the partial breaking of continuous dilation symmetry in any conformal-invariant theory. With its infinite scale hierarchy, discrete scale invariance overlaps with the traditional separation between ultraviolet and infrared physics and it can leave an all-range observable imprint, such as a pattern of log oscillations and sharp features in the cosmic microwave background primordial power spectrum.

6 pages, 1 figure. v2: discussion slightly expanded

References in corpus (9)

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• Multifractional theories: an unconventional review
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• Cosmic microwave background and inflation in multi-fractional spacetimes
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• Emergence of Spacetime in a restricted Spin-foam model
• Estimated Age of the Universe in Fractional Cosmology
• Dimensional flow and fuzziness in quantum gravity: emergence of stochastic spacetime
• Emergence of fractal cosmic space from fractional quantum gravity
• Gravitational potential and galaxy rotation curves in multi-fractional spacetimes
• Spectral dimensions and dimension spectra of quantum spacetimes
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Discrete scale invariance in holography revisited
• Covariant Predictions for Planck-Scale Features in Primordial Power Spectra
• Log-periodic gravitational-wave background beyond Einstein gravity
• Fractional entropy of the Brown-Kuchař dust in fractional anti-de Sitter quantum gravity
• Constraining fractionality using some observational tests
• Generalization of electrical resistance scaling to Dirac fields on perforated fractals
• Cosmology of fractional gravity
• A glimpse into the Ultrametric spectrum