Resolution of the cosmological constant problem by unimodular gravity and signature reversal symmetry

The (old) cosmological constant problem consists of two different problems. The first is the huge discrepancy between the value of the cosmological constant deduced from observations and its value expected from cosmological constant-like theoretical contributions (such as vacuum expectation value of Higgs potential). The second problem is why the value of the cosmological constant has its particular (very small) value. It is well-known that unimodular gravity solves the first problem while it leaves the second problem unsolved. In this paper I show that the second problem may also be resolved in the context of unimodular gravity by letting our 4-dimensional spacetime be a brane in a D = 2(2n + 1) dimensional bulk and imposing the signature reversal symmetry