James Bonifacio, Kurt Hinterbichler

A compact Riemannian manifold is associated with geometric data given by the eigenvalues of various Laplacian operators on the manifold and the triple overlap integrals of the corresponding eigenmodes. This geometric data must satisfy certain consistency conditions that follow from associativity and the completeness of eigenmodes. We show that it is possible to obtain nontrivial bounds on the geometric data of closed Einstein manifolds by using semidefinite programming to study these consistency conditions, in analogy to the conformal bootstrap bounds on conformal field theories. These bootstrap bounds translate to constraints on the tree-level masses and cubic couplings of Kaluza-Klein modes in theories with compact extra dimensions. We show that in some cases the bounds are saturated by known manifolds.

G. Parimbelli, S. Anselmi, M. Viel, C. Carbone, F. Villaescusa-Navarro, P.S. Corasaniti, Y. Rasera, R. Sheth, G.D. Starkman, I. Zehavi

The linear point (LP), defined as the mid-point between the dip and the peak of the two-point clustering correlation function (TPCF), has been shown to be an excellent standard ruler for cosmology. In fact, it is nearly redshift-independent, being weakly sensitive to non-linearities, scale-dependent halo bias and redshift-space distortions. So far, these findings were tested assuming that neutrinos are massless; in this paper we extend the analysis to massive-neutrino cosmologies. In particular, we examine if the scale-dependent growth induced by neutrinos affects the LP position and if it is possible to detect the neutrino masses using the shift of the LP compared to the massless-neutrino case. For our purposes, we employ two sets of state-of-the-art $N$-body simulations with massive neutrinos. For each of them we measure the TPCF of cold dark matter (CDM) and halos and, to estimate the LP, fit the TPCF with a model-independent parametric fit in the range of scales of the Baryon Acoustic Oscillations (BAO). Overall, we find that the LP retains its features as a standard ruler even when neutrinos are massive. The cosmic distances measured with the LP can therefore be employed to constrain the neutrino mass. In addition, we propose a procedure to constrain the neutrino masses by comparing the measured LP of data to the LP of a mock galaxy catalog with massless neutrinos and fixed cosmological parameters. The small uncertainty of the LP, $\sigma_\mathrm{LP}$, plays a key role in forecasting a possible detection of neutrino masses in future surveys. We find that the sum of the neutrino masses could be detected if several redshift bins are used, provided the survey volume is sufficiently large and the shot-noise of the galaxy sample is sufficiently low.

Karan Jani, Abraham Loeb

Several large-scale experimental facilities and space-missions are being suggested to probe the universe across the gravitational-wave (GW) spectrum. Here we propose Gravitational-wave Lunar Observatory for Cosmology (GLOC) - the first concept design in the NASA Artemis era for a GW observatory on the Moon. We find that a lunar-based observatory is ideal for probing GW frequencies in the range between deci-Hz to 5 Hz, an astrophysically rich regime that is very challenging for both Earth- and space-based detectors. GLOC can survey $\gtrsim 70\%$ of the observable volume of our universe without significant background contamination. Its unprecedented sensitivity would trace the Hubble expansion rate up to redshift $z \sim 3$ and test General Relativity and $\Lambda$CDM cosmology up to $z\sim 100$.