Ultraheavy particles at the LHC or a next-generation collider?

If the effective cosmological constant $\mathrm{\Lambda }$ of the present universe is due to physical processes in the early universe operating at temperatures just above the electroweak energy scale, it is possible that new particles with multi-$\text{TeV}$ masses exist. These ultraheavy particles may (or may not) show up at the Large Hadron Collider (LHC) or a next-generation proton-proton collider. If they do, they may provide new insights into the early universe and fundamental physics.