pressuron

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

:$S=\; \backslash frac\{1\}\{c\}\backslash int\; d^4x\; \backslash sqrt\{-g\}\; \backslash left[\; \backslash sqrt\{\backslash Phi\}\; \backslash mathcal\{L\}\_m\; (g\_\{\backslash mu\; \backslash nu\},\; \backslash Psi)\; +$

\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 $g\_\{\backslash mu\; \backslash nu\}$, $g$ is the metric determinant, $\backslash kappa=\backslash frac\{8\backslash pi\; G\}\{c^4\}$, with $G$ the gravitational constantNote however that it is different from the effective constant measured with Cavendish-type experiments (see also scalar–tensor theory) and $c$ the velocity of light in vacuum, $V(\backslash Phi)$ is the pressuron potential and $\backslash mathcal\{L\}\_m$ is the matter LagrangianSee also Electroweak lagrangian and Quantum chromodynamics lagrangian and $\backslash Psi$ represents the non-gravitational fields. The gravitational field equations therefore write

:$R\_\{\backslash mu\; \backslash nu\}-\backslash frac\{1\}\{2\}g\_\{\backslash mu\; \backslash nu\}R=\; \backslash kappa~\; \backslash frac\{1\}\{\backslash sqrt\{\backslash Phi\}\}T\_\{\backslash mu\; \backslash nu\}+\; \backslash frac\{1\}\{\backslash Phi\}\; [\backslash nabla\_\{\backslash mu\}\; \backslash nabla\_\{\backslash nu\}\; -g\_\{\backslash mu\; \backslash nu\}\backslash Box]\backslash Phi$

+\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

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

where $T\_\{\backslash mu\backslash nu\}$ is the stress–energy tensor of the matter field,

and $T\; =\; g^\{\backslash mu\backslash nu\}\; T\_\{\backslash mu\backslash nu\}$ is its trace.

If one considers a pressure-free perfect fluid (also known as a dust solution), the effective material Lagrangian becomes $\backslash mathcal\{L\}\_m\; =\; -\; c^2\; \backslash sum\_i\; \backslash mu\_i\; \backslash delta(x^\backslash alpha\_i)$,{{cite journal

|author=Minazzoli, O.

|date=July 2013

|title=Conservation laws in theories with universal gravity/matter coupling

|journal=Physical Review D

|volume=88

|issue=2

|pages=027506

|doi=10.1103/PhysRevD.88.027506

|bibcode= 2013PhRvD..88b7506M

|arxiv = 1307.1590|s2cid=119589077

}} where $\backslash mu\_i$ is the mass of the ith particle, $x^\backslash alpha\_i$ its position, and $\backslash delta(x^\backslash alpha\_i)$ the Dirac delta function, while at the same time the trace of the stress-energy tensor reduces to $T\; =\; -\; c^2\; \backslash sum\_i\; \backslash mu\_i\; \backslash delta(x^\backslash alpha\_i)$. Thus, there is an exact cancellation of the pressuron material source term $\backslash left(\; T\; -\; \backslash mathcal\{L\}\_m\; \backslash right)$, 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.

The pressuron shares some characteristics with the hypothetical string dilaton,{{cite journal|author=Minazzoli O. |date=July 2014 |title= On the cosmic convergence mechanism of the massless dilaton|journal=Physics Letters B |volume=735 |issue= 2 |pages=119–121 |doi= 10.1016/j.physletb.2014.06.027|bibcode= 2014PhLB..735..119M|arxiv = 1312.4357|s2cid=119219205 }} and can actually be viewed as a special case of the wider family of possible dilatons.{{cite journal|author=Gasperini, M.|author2=Piazza, F.|author3=Veneziano, G.|name-list-style=amp |date=December 2001 |title= Quintessence as a runaway dilaton |journal=Physical Review D |volume=65 |issue= 2 |pages=023508 |doi= 10.1103/PhysRevD.65.023508|bibcode= 2001PhRvD..65b3508G|arxiv = gr-qc/0108016|s2cid=15787261}} 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.

According to Minazzoli and Hees, post-Newtonian tests of gravitation in the Solar System should lead to the same results as what is expected from general relativity, except for gravitational redshift experiments, which should deviate from general relativity with a relative magnitude of the order of $\backslash frac\{1\}\{\backslash omega\_0\}\; \backslash frac\{P\}\{c^2\; \backslash rho\}\; \backslash sim\; \backslash frac\{10^\{-6\}\}\{\backslash omega\_0\}$, where $\backslash omega\_0$ is the current cosmological value of the scalar-field function $\backslash omega(\backslash Phi)$, and $P$ and $\backslash rho$ are respectively the mean pressure and density of the Earth (for instance). Current best constraints on the gravitational redshift come from gravity probe A and are at the $10^\{-4\}$ level only. Therefore, the scalar–tensor theory that involves the pressuron is weakly constrained by Solar System experiments.

Because of its non-minimal couplings, the pressuron leads to a variation of the fundamental coupling constantsNote that this is a classical effect, and it should not be confused with the quantum running of the coupling constants in regimes where it effectively couples to matter. However, since the pressuron decouples in both the matter-dominated era (which is essentially driven by pressure-less material fields) and the dark-energy-dominated era (which is essentially driven by dark energyIn the context of the pressuron, dark energy can either be a cosmological constant or due to a non-vanishing scalar potential $V(\backslash Phi)$), the pressuron is also weakly constrained by current cosmological tests on the variation of the coupling constants.

Although no calculations seem to have been performed regarding this issue, it has been argued that binary pulsars should give greater constraints on the existence of the pressuron because of the high pressure of bodies involved in such systems.

• List of hypothetical particles

{{reflist}}

{{Theories of gravitation|selected=GR alternatives}}

Category:Bosons

Category:Gravity

Category:Hypothetical elementary particles

Category:Physical cosmology

Category:Physics beyond the Standard Model

Category:String theory

Category:Subatomic particles with spin 0

Category:Dark energy

Category:Force carriers