The End (…)
Recently we proposed a mechanism for sequestering the Standard Model vacuum energy that predicts that the universe will collapse. Here we present a simple mechanism for bringing about this collapse, employing a scalar field whose potential is linear and becomes negative, providing the negative energy density required to end the expansion. The slope of the potential is chosen to allow for the expansion to last until the current Hubble time, about 10 years, to accommodate our universe. Crucially, this choice is technically natural due to a shift symmetry. Moreover, vacuum energy sequestering selects radiatively stable initial conditions for the collapse, which guarantee that immediately before the turnaround the universe is dominated by the linear potential which drives an epoch of accelerated expansion for at least an efold. Thus a single, technically natural choice for the slope ensures that the collapse is imminent and is preceded by the current stage of cosmic acceleration, giving a new answer to the ‘Why Now?’ problem. kaloper@physics.ucdavis.edu antonio.padilla@nottingham.ac.uk In [1, 2] we proposed a mechanism for sequestering the matter sector vacuum energy from gravity. The idea is that all the matter sector scales are functions of the 4-volume element of the universe ∫ dx √ g. Picking the specific functional dependence on ∫ dx √ g, reflecting the scaling of dimensional quantities, ensures that the vacuum energy contributions are invisible to gravity at any and all orders of the loop expansion in the matter sector. While this ‘cancellation’ of the vacuum energy does not directly protect from graviton loops, it is radiatively stable to matter corrections, evading the Weinberg no-go theorem [3] (see also [4]). As a bonus, the mechanism renders the contributions from phase transitions automatically small at late times. Since our mechanism is locally Poincaré invariant and diffeomorphism invariant, it does not introduce any new local degrees of freedom, representing a minimal modification of General Relativity by adding two global constraints. For the matter sector scales to be nonzero, the universe should be finite in spacetime, collapsing in the future. This requires dynamics which can turn expansion into contraction in an FRW geometry. A simple possibility is to have a field with a potential that is not bounded from below, or at least is ‘sufficiently negative’ (see, e.g. [5, 6] for earlier considerations). If the negative potentials compensate the positive energy density of the rest, the collapse will occur, and the field theory will not be scale-invariant but will have a nonzero mass gap. Having a negative potential that can destabilize the universe seems to be physically feasible. After all, the Standard Model Higgs appears to be an example of a field with such a potential [7], albeit with a very delayed instability [8]. After vacuum energy cancellation there remains a residual, radiatively stable cosmological constant whose value must be smaller than the value of the turnaround potential if collapse is to occur. By taking the turnaround potential to be a linear function, it too is radiatively stable. This is because a linear potential is exactly shift symmetric in our framework, sufficing not only to protect its form but also the numerical value of its slope. Once set, to the leading order this potential remains the same to all orders in the loop expansion in the matter sector. This is crucial since it allows us to make a technically natural choice of the slope, mslope ≃ MP lH 0 ≃ 10−39 eV, that ensures that collapse will occur after a present Hubble epoch. Further, the vacuum energy sequestering dynamically selects radiatively stable initial conditions that guarantee this turnaround will be preceded by a period of accelerated expansion at the observed scale of dark energy, lasting for at least an efold. This is a new solution to the ‘Why Now?’ problem [9]. It also confirms that wDE ≃ −1 is a transient, as we claimed in [1, 2], and may be observable, along the lines of [6]. As defined in [1, 2], we start with the theory given by