Fractional gravity yields stable de Sitter expansion and exact bouncing solutions driven by phantom (w < -1) or ghost (negative energy) fluids, with results independent of the form-factor representation.
Superrenormalizable gauge and gravitational theories
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abstract
We investigate 4-dim gauge theories and gravitational theories with nonpolynomial actions containing an infinite series in covariant derivatives of the fields representing the expansion of a transcendental entire function. A class of entire functions is explicitly constructed such that: (i) the theory is perturbatively superrenormalizable; (ii) no (gauge-invariant) unphysical poles are introduced in the propagators. The nonpolynomial nature is essential; it is not possible to simultaneously satisfy (i) and (ii) with any polynomial series in derivatives. Cutting equations are derived verifying the absence of unphysical cuts and the Bogoliubov causality condition within the loop expansion. A generalized KL representation for the 2-point function is obtained exhibiting the consistency of physical positivity with the improved convergence of the propagators. Some physical effects, such as extended bound excitations in the spectrum, are briefly discussed.
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A minimal proper time τ_min is introduced into QFT to suppress high-energy modes, achieve asymptotic safety via dimensional reduction, and allow a deterministic regime near the Planck scale.
Specific choices of form factors in ghost-free infinite derivative gravity cancel all one-loop logarithmic UV divergences except the Gauss-Bonnet term and a surface term.
Higher-order curvature operators like R□R add new poles and shift existing ones in the graviton propagator, with a method to correctly derive the Einstein frame action illustrated for f(R) gravity.
Nonlocal Källén-Lehmann spectral densities in the Higgs sector yield exponentially suppressed scattering amplitudes above Λ_NL and suppress the real part of the Higgs self-energy at p² ~ -Λ²_NL, solving the hierarchy problem and testable via LHC global fits.
Gauge-invariant entire-function regulators of the covariant Laplace-Beltrami operator yield UV-finite nonlocal QFTs with exponential damping and no additional singularities.
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Emerging Nonlocal K\"{a}ll\`{e}n-Lehmann Higgs Spectra at the LHC
Nonlocal Källén-Lehmann spectral densities in the Higgs sector yield exponentially suppressed scattering amplitudes above Λ_NL and suppress the real part of the Higgs self-energy at p² ~ -Λ²_NL, solving the hierarchy problem and testable via LHC global fits.