Could there exist a "locality" field? What I mean is (and I'm a layperson on the subject), can there exist a field that pervades the universe - like the Higgs field - that interacts with particles to give them "distance" or "space" between one another, in a similar way that the Higgs field give particles their mass?
And could an excitation or de-excitation of this "locality" field affect the space in between two particles in space? If such a field could even be possible, that is. 
 A: According to General Relativity, there is a dynamic field, called the “metric field”, that pervades the universe and determines its geometry. The spacetime distance between events is determined by this field. It determines which events can causally influence other events. Its influence on particles is what we know as gravity.
Ripples in this field are called gravitational waves. They were first detected in 2015.
Quantum excitations in this field are called gravitons. They are theoretical and have not been observed. We may never be able to detect them because they are so weak.
A: Would like to point out the similarity and dissimilarity between "Higgs field" and the "locality field" (a.k.a. metric):


*

*Like the Higgs field, the "locality field" also acquires a non-zero
vacuum expectation value (Minkowski metric) that breaks the local
Lorentz gauge symmetry and diffeomorphism invariance. There is nothing, I mean NOTHING, in the general relativity that tells you that the vacuum should be Minkowskian. Within the framework of general relativity, it's perfect fine that the vacuum metric is $g_{\mu\nu}=0$, which preserves both the local Lorentz gauge symmetry and diffeomorphism invariance. The non-zero Minkowskian metric $g_{\mu\nu}=\eta_{\mu\nu}$ is accidental, in the sense that it happens to be determined by the evolutionary history of our Universe.

*Gravitons are Nambu-Goldston bosons, which are "excitation or de-excitation" from the symmetry breaking Minkowskian VEV. Whereas, for the Higgs field, the Nambu-Goldston boson is "eaten" by the Higgs mechanism. The tricky part of the story is that metric field is a tensor while Higgs is a scalar, which makes the NG boson analogy only partially correct.

*The gauge field acquires mass via the kinetic term $(D\phi)^2$ of the Higgs field. For the "locality field", the situation is a bit different: the covariant derivative $De$ of the tetrad $e$ (in lieu of the "locality field" $g_{\mu\nu}$) vanishes, since the zero torsion condition enforces that $De = de + \omega e = 0$, where $\omega$ is the spin connection (which is the Lorentz "gauge field" in gravity). 

