Grant N. Remmen

Physical properties of scattering amplitudes are mapped to the Riemann zeta function. Specifically, a closed-form amplitude is constructed, describing the tree-level exchange of a tower with masses $m_n^2 = \mu_n^2$, where $\zeta\left(\frac{1}{2} \pm i\mu_n\right) = 0$. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of $\zeta$. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of $1/\mu_n^2$.

Gergely Kántor, Vasilis Niarchos, Constantinos Papageorgakis

In this paper we deploy for the first time Reinforcement-Learning algorithms in the context of the conformal-bootstrap programme to obtain numerical solutions of conformal field theories (CFTs). As an illustration, we use a soft Actor-Critic algorithm and find approximate solutions to the truncated crossing equations of two-dimensional CFTs, successfully identifying well-known theories like the 2D Ising model and the 2D CFT of a compactified scalar. Our methods can perform efficient high-dimensional searches that can be used to study arbitrary (unitary or non-unitary) CFTs in any spacetime dimension.

Justin Khoury, Thomas Steingasser

We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. This perspective is motivated by the early-time framework for eternal inflation put forth recently, which favors vacua that are relatively short-lived, but applies more generally to any theoretical approach predicting that our vacuum should be metastable. We find that the metastability of the electroweak vacuum, together with the requirement that such a non-trivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around one order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is $\sim 10^{11}$ GeV, simple and well-motivated extensions of the SM - concretely, the $\nu$MSM with an approximate $B-\tilde{L}$ symmetry and the minimal SU(4)/Sp(4) composite Higgs model - can significantly tighten the bound by lowering the instability scale. We find that the bound can be brought down to $\simeq 10$ TeV where our perturbative treatment of the decay rate becomes unreliable. Our results imply that, assuming the SM symmetry breaking pattern, small running Higgs masses are a universal property of theories giving rise to metastability, suggesting a common origin of the two underlying fine-tunings and providing a strong constraint on any attempt to explain metastability.

Ozgur Akarsu, Suresh Kumar, Emre Ozulker, J. Alberto Vazquez

Inspired by the recent conjecture that the universe has transitioned from AdS vacua to dS vacua in the late universe made via graduated dark energy, we extend the $\Lambda$CDM model by a cosmological `constant' ($\Lambda_{\rm s}$) that switches sign at certain redshift, $z_\dagger$, and name it as $\Lambda_{\rm s}$CDM. We discuss the construction and theoretical features of this model, and find out that, when the consistency of $\Lambda_{\rm s}$CDM with the CMB data is ensured, (i) $z_\dagger\gtrsim1.1$ is implied by the condition that the universe monotonically expands, (ii) $H_0$ is inversely correlated with $z_\dagger$ and reaches $\approx74.5~{\rm km\, s^{-1}\, Mpc^{-1}}$ for $z_\dagger=1.5$, (iii) $H(z)$ presents an excellent fit to the Ly-$\alpha$ measurements provided that $z_\dagger\lesssim 2.34$. We further investigate the model constraints by using the full Planck CMB data, with and without BAO data. We find that the CMB data alone does not constrain $z_\dagger$ but CMB+BAO dataset favors the sign switch of $\Lambda_{\rm s}$ providing the constraint: $z_\dagger=2.44\pm0.29$ (68\% CL). Our analysis reveals that the lower and upper limits of $z_\dagger$ are controlled by the Galaxy and Ly-$\alpha$ BAO measurements, respectively, and the larger $z_{\dagger}$ values imposed by the Galaxy BAO data prevent the model from achieving the highest local $H_0$ measurements. In general, $\Lambda_{\rm s}$CDM (i) relaxes the $H_0$ tension while being fully consistent with the TRGB measurement, (ii) removes the discrepancy with the Ly-$\alpha$ measurements, (iii) relaxes the $S_8$ tension, and (iv) finds a better agreement with the BBN constraints of physical baryon density. We find no strong statistical evidence to discriminate between the $\Lambda_{\rm s}$CDM and $\Lambda$CDM models. However, interesting and promising features of $\Lambda_{\rm s}$CDM provide an upper edge over $\Lambda$CDM.

Domènec Espriu, Marc Rodoreda

Some time ago it was pointed out that the presence of cosmological components could affect the propagation of gravitational waves (GW) beyond the usual cosmological redshift and that such effects might be observable in pulsar timing arrays. These analyses were done at leading order in the Hubble constant $H_0$, which is proportional to $\Lambda^{1/2}$ and $\rho_i^{1/2}$ ($\rho_i$ being the various cosmological fluid densities). In this work, we study in detail the propagation of metric perturbations on a Schwarzschild-de Sitter (SdS) background, close to the place where GW are produced, and obtain solutions that incorporate corrections linear in $\rho_i$ and $\Lambda$. At the next-to-leading order the corrections do not appear in the form of $H_0$ thus lifting the degeneracy among the various cosmological components. We also determine the leading corrections proportional to the mass of the final object; they are very small for the distances considered in pulsar timing arrays but may be of relevance in other cases. When transformed into comoving coordinates, the ones used in cosmological measurements, this SdS solution does satisfy the perturbation equations in a Friedmann-Lema\^itre-Robertson-Walker metric up to and including $\Lambda^{3/2}$ terms. This analysis is then extended to the other cosmological fluids, allowing us to consider GW sources in the Gpc range. Finally, we investigate the influence of these corrections in pulsar timing arrays observations.