The screening is possible when you have positive and negative charges. In gravity we only have positive mass so far.

Even if you turn to dark energy - it is not compact by nature, so can not screen particular objects inside the Universe.

Thank you very much Alexander Tevzadze-Srinivas

Please keep in mind that there are Collective Effects in Gravitational Systems due to the 1/R^2 "long range" nature of gravity. An interesting and plasma--like (if I may use the Term) kinetic analysis may be found in the following article (I cite using the BibTex record with the web link, the later is in line tagged adsurl):

@ARTICLE{1966SvA.....9..549L,

author = {{Lebedev}, V.~I. and {Maksumov}, M.~N. and {Marochnik}, L.~S.},

title = "{Collective Processes in Gravitating Systems. I.}",

journal = {\sovast},

year = 1966,

month = feb,

volume = 9,

pages = {549},

adsurl = {http://adsabs.harvard.edu/abs/1966SvA.....9..549L},

adsnote = {Provided by the SAO/NASA Astrophysics Data System}}

I suspect, there is some sort of Debye Length despite the lack of the 'Neutralizing Background" of a typical plasma since there are oscillation frequencies and you may envision debye length as We/Vth (longitudinal eigenfrequency over thermal speed).

Best Regards

Roughly speaking, the quantity which plays for gravitation a role similar to Debye length for electrostatics is Jeans' length. Just like Debye length is the ratio of sound speed and Langmuir frequency, Jeans' length is the ratio of sound speed and a characteristic frequency. The latter is proportional to the square root of mass density, just like Langmuir frequency is proportional to the square root of electron density. Basically (and provided that dimensionless proportionality coefficients of order unity are dropped) Jeans' length is the radius of a spherical cloud made of massive particles where thermal energy per particle equals gravitational energy per particle. Analogously, the electrostatic energy of an electron displaced from its equilibrium position in a quasi-neutral plasma by a displacement equal to Debye's length is equal to the thermal energy of the electron.