Testing quantum gravity with primordial gravitational waves

Abstract

We propose a testable alternative to inflation directly built in a very general class of ultraviolet complete theories of quantum gravity enjoying Weyl invariance. After the latter is spontaneously broken, logarithmic quantum corrections to the action make both the primordial tensor spectrum (from graviton fluctuations) and the scalar spectrum (from thermal fluctuations) quasi scale invariant. We predict a scalar spectral index $n_{\mathrm{s}}$ which only depends on two parameters and is consistent with observations, a tensor index $n_{\mathrm{t}}=1-n_{\mathrm{s}}>0$, and, if the fundamental energy scale of the theory ${\Lambda }_{\ast }=M_{\text{Pl}}$ is of order of the Planck mass, a tensor-to-scalar ratio $r_{0.05}\approx 0.01$ detectable by BICEP Array and LiteBIRD in the immediate or near future, respectively, and a blue-tilted stochastic gravitational-wave background observable by DECIGO in the further future. From the observational constraint $r_{0.05}<0.036$, we also find the lower bound ${\Lambda }_{\ast }>8.5\times 10^{10}\mathrm{GeV}$, much stronger than any previous one for this class of theories.

1+42 pages, 2 figures. v2: nature of beta coefficients clarified; v3: expanded version, new introduction and summary of setting, derivation of cosmological spectra moved from companion paper arXiv:2206.06384; v4: new lower bound on energy scale, new clarifications on vector perturbations and quantum-to-classical transition, more references added

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