The pressuron is a hypothetical scalar particle which couples to both gravity and matter theorised in 2013.^[1] Although originally postulated without self-interaction potential, the pressuron is also a dark energy candidate when it has such a potential.^[2] The pressuron takes its name from the fact that it decouples from matter in pressure-less regimes,^[2] allowing the scalar–tensor theory of gravity involving it to pass solar system tests, as well as tests on the equivalence principle, even though it is fundamentally coupled to matter. Such a decoupling mechanism could explain why gravitation seems to be well described by general relativity at present epoch, while it could actually be more complex than that. Because of the way it couples to matter, the pressuron is a special case of the hypothetical string dilaton.^[3] Therefore, it is one of the possible solutions to the present non-observation of various signals coming from massless or light scalar fields that are generically predicted in string theory.

Mathematical formulation

The action of the scalar–tensor theory that involves the pressuron ${\displaystyle \Phi }$ can be written as

${\displaystyle S={\frac {1}{c}}\int d^{4}x{\sqrt {-g}}\left[{\sqrt {\Phi }}{\mathcal {L}}_{m}(g_{\mu \nu },\Psi )+{\frac {1}{2\kappa }}\left(\Phi R-{\frac {\omega (\Phi )}{\Phi }}(\partial _{\sigma }\Phi )^{2}-V(\Phi )\right)\right],}$

where ${\displaystyle R}$ is the Ricci scalar constructed from the metric ${\displaystyle g_{\mu \nu }}$, ${\displaystyle g}$ is the metric determinant, ${\displaystyle \kappa ={\frac {8\pi G}{c^{4}}}}$, with ${\displaystyle G}$ the gravitational constant^[4] and ${\displaystyle c}$ the velocity of light in vacuum, ${\displaystyle V(\Phi )}$ is the pressuron potential and ${\displaystyle {\mathcal {L}}_{m}}$ is the matter Lagrangian^[5] and ${\displaystyle \Psi }$ represents the non-gravitational fields. The gravitational field equations therefore write^[2]

${\displaystyle R_{\mu \nu }-{\frac {1}{2}}g_{\mu \nu }R=\kappa ~{\frac {1}{\sqrt {\Phi }}}T_{\mu \nu }+{\frac {1}{\Phi }}[\nabla _{\mu }\nabla _{\nu }-g_{\mu \nu }\Box ]\Phi +{\frac {\omega (\Phi )}{\Phi ^{2}}}\left[\partial _{\mu }\Phi \partial _{\nu }\Phi -{\frac {1}{2}}g_{\mu \nu }(\partial _{\alpha }\Phi )^{2}\right]-g_{\mu \nu }{\frac {V(\Phi )}{2\Phi }},}$

and

${\displaystyle {\frac {2\omega (\Phi )+3}{\Phi }}\Box \Phi =\kappa {\frac {1}{\sqrt {\Phi }}}\left(T-{\mathcal {L}}_{m}\right)-{\frac {\omega '(\Phi )}{\Phi }}(\partial _{\sigma }\Phi )^{2}+V'(\Phi )-2{\frac {V(\Phi )}{\Phi }}}$.

where ${\displaystyle T_{\mu \nu }}$ is the stress–energy tensor of the matter field, and ${\displaystyle T=g^{\mu \nu }T_{\mu \nu }}$ is its trace.

Experimental search

References