Abstract
Theories with compact extra dimensions are sometimes unstable to decay into a bubble of nothing -- an instability resulting in the destruction of spacetime. We investigate the existence of these bubbles in theories where the moduli fields that set the size of the extra dimensions are stabilized at a positive vacuum energy -- a necessary ingredient of any theory that aspires to describe the real world. Using bottom-up methods, and focusing on a five-dimensional toy model, we show that four-dimensional de Sitter vacua admit bubbles of nothing for a wide class of stabilizing potentials. We show that, unlike ordinary Coleman-De Luccia tunneling, the corresponding decay rate remains non-zero in the limit of vanishing vacuum energy. Potential implications include a lower bound on the size of compactified dimensions.
Highlights
A wide range of experimental evidence strongly indicates that our Universe is entering a phase of accelerated expansion [1,2,3]
The exponential factor governing the decay rate is obtained by evaluating the action of the bounce relative to that of the false vacuum, that is ΔS ≡ SEjCDL − SEjdS, and the action evaluated on any nSoEn1⁄4sin−g2uπla2rRs0ξomlaux tdioξnρ3tUo t.hWe fhieenldtheequdaetiSointtsecr avnacbueuwmriettneenrgays is much smaller than the potential barrier separating false and true vacua, ΔS is given by Eq (1)
This can affect the viability of proposed de Sitter constructions, with potential implications for our understanding of the string landscape and the cosmological constant problem
Summary
A wide range of experimental evidence strongly indicates that our Universe is entering a phase of accelerated expansion [1,2,3]. We discuss an additional instability of de Sitter and Minkowski vacua that may be present in theories with stabilized extra dimensions This decay is a generalization of Witten’s “bubble of nothing” [30]—a catastrophic instability that destroys the spacetime. Interpreting φ as the radial modulus of an extra dimension compactified on an S1, we show that a wide range of scalar potentials with a local de Sitter vacuum are compatible with the existence of a bubble of nothing. The instanton describing this instability corresponds to a solution to the CDL equations with unusual boundary conditions. The exponential factor governing the decay rate is obtained by evaluating the action of the bounce relative to that of the false vacuum, that is ΔS ≡ SEjCDL − SEjdS, and the action evaluated on any nSoEn1⁄4sin−g2uπla2rRs0ξomlaux tdioξnρ3tUo t.hWe fhieenldtheequdaetiSointtsecr avnacbueuwmriettneenrgays is much smaller than the potential barrier separating false and true vacua, ΔS is given by Eq (1)
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