NANOGrav data favors a blue-tilted tensor spectrum with nt ≈ 2.2, radiation-dominated reheating, and alpha-vacuum states over standard Bunch-Davies, with a frequency-dependent alpha suggested to resolve the blue-tilt tension.
Choice of Quantum Vacuum for Inflation Observables
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abstract
We investigate the modifications to inflationary observables that arise when adopting an $\alpha$-vacuum instead of the standard Bunch--Davies vacuum for quantum fluctuations during inflation. Within the Starobinsky inflationary model, we compute and compare the scalar spectral index, its running, and the running of the running arising from different choices of the initial vacuum state. We further examine the energy scales associated with $\alpha$-vacua and argue that, for any number of extra spatial dimensions, the relevant scale can be truncated at the Hubble scale, $\sim$$\mathcal{O}(10^{13})\,\mathrm{GeV}$, without conflict with current Cavendish-type experimental bounds on sub-millimeter gravity ($\sim$$250\,\mu\mathrm{m}$). Our analysis demonstrates that the $\alpha$-vacuum is subject to stringent constraints as a viable de~Sitter-invariant alternative to the Euclidean (Bunch--Davies) vacuum, with the corrections that it induces in the inflationary observables being strongly limited by the latest Planck data.
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No violation of the bipartite temporal Bell inequality occurs for coherent states of primordial perturbations, with only slight differences from the squeezed vacuum case at large squeezing and a unique dependence on the imaginary phase of the wave function.
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Constraints on the inflationary vacuum and reheating era from NANOGrav
NANOGrav data favors a blue-tilted tensor spectrum with nt ≈ 2.2, radiation-dominated reheating, and alpha-vacuum states over standard Bunch-Davies, with a frequency-dependent alpha suggested to resolve the blue-tilt tension.
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Bipartite temporal Bell inequality for squeezed coherent state of inflationary perturbations
No violation of the bipartite temporal Bell inequality occurs for coherent states of primordial perturbations, with only slight differences from the squeezed vacuum case at large squeezing and a unique dependence on the imaginary phase of the wave function.