Researchers propose a simple model inside Einstein’s gravity where the energy that drives cosmic acceleration changes sign late in the Universe’s history. The idea is to start with dark energy that behaves like a negative vacuum (called anti–de Sitter, or AdS) at intermediate times and then switch smoothly to a positive vacuum (de Sitter, or dS) at late times. The switch is driven by a “phantom” scalar field — a field whose kinetic term has the opposite sign from ordinary fields — rolling up a bounded hill-shaped potential rather than down.

What the authors built is a concrete Lagrangian for that phantom field and a simple potential shaped like a hyperbolic tangent. Because the potential approaches fixed plateaus at early and late times, the field can move from a negative-energy plateau to a positive one without blowing up. The wrong sign in the kinetic term reverses the usual force on the field and makes it climb the potential. The evolution is smooth: energy density crosses zero, the total energy of the Universe remains positive, and the late-time fate is a stable de Sitter state rather than a doomsday “Big Rip.” The model also has a microphysical sound speed equal to the speed of light, which avoids some obvious dynamical instabilities.

The construction was tuned to keep the early Universe essentially the same as in the standard Lambda cold dark matter (ΛCDM) model so that the cosmic microwave background (CMB) distance scale is preserved. That allows a suppressed expansion rate at intermediate redshifts to be compensated by a faster expansion today, which can raise the inferred Hubble constant H0. In a representative case studied here (the “mirror” transition), the potential crosses zero near redshift zt ≈ 2.12 and the field’s energy density crosses zero later at z† ≈ 1.79. The authors and other analyses suggest this kind of late-time sign switch can help with the H0 tension and may also affect other mild tensions in the data, such as those involving the amplitude of matter clustering (S8) and the growth rate of structure.