  In this paper we present a scale free method to determine the cosmological
parameters (Omega_m, Omega_Lambda). The method is based on the requirement of
isotropy of the distribution of orientations of cosmological filaments. The
current structure formation paradigm predicts that the first structures to form
are voids and filaments, causing a web-like structure of the matter
distribution at high redshifts. Recent observational evidence suggests that the
threads, or filaments, of the cosmic web most easily are mapped in Ly-alpha
emission. We describe how such a 3D map can be used to constrain the
cosmological parameters in a way which, contrary to most other cosmological
tests, does not require the use of a standard rod or a standard candle. We
perform detailed simulations in order to define the optimal survey parameters
for the definition of an observing programme aimed to address this test, and to
investigate how statistical and observational errors will influence the
results. We conclude that observations should target filaments of comoving size
15-50 Mpc in the redshift range 2-4, and that each filament must be defined by
at least four Ly-alpha emitters. Detection of 20 filaments will be sufficient
to obtain a result, while 50 filaments will make it possible to place
significant new constraints on the values of Omega_m and Omega_Lambda permitted
by the current supernova observations. In a future paper we study how robust
these conclusions are to systematic velocities in the survey box.
