Pressuron

The action of the scalar–tensor theory that involves the pressuron \Phi can be written as :S= \frac{1}{c}\int d^4x \sqrt{-g} \left[ \sqrt{\Phi} \mathcal{L}_m (g_{\mu \nu}, \Psi) + \frac{1}{2\kappa}\left(\Phi R-\frac{\omega(\Phi)}{\Phi} (\partial_\sigma \Phi)^2-V(\Phi) \right) \right], where R is the Ricci scalar constructed from the metric g_{\mu \nu}, g is the metric determinant, \kappa=\frac{8\pi G}{c^4}, with G the gravitational constant and c the velocity of light in vacuum, V(\Phi) is the pressuron potential and \mathcal{L}_m is the matter Lagrangian and \Psi represents the non-gravitational fields. The gravitational field equations therefore write where \mu_i is the mass of the ith particle, x^\alpha_i its position, and \delta(x^\alpha_i) the Dirac delta function, while at the same time the trace of the stress-energy tensor reduces to T = - c^2 \sum_i \mu_i \delta(x^\alpha_i). Thus, there is an exact cancellation of the pressuron material source term \left( T - \mathcal{L}_m \right) , and hence the pressuron effectively decouples from pressure-free matter fields. In other words, the specific coupling between the scalar field and the material fields in the Lagrangian leads to a decoupling between the scalar field and the matter fields in the limit that the matter field is exerting zero pressure. Link to string theory The pressuron shares some characteristics with the hypothetical string dilaton, and can actually be viewed as a special case of the wider family of possible dilatons. Since perturbative string theory cannot currently give the expected coupling of the string dilaton with material fields in the effective 4-dimension action, it seems conceivable that the pressuron may be the string dilaton in the 4-dimension effective action. == Experimental search ==