We discuss the horizon problem in a universe dominated by fluid with negative pressure .
We show that for generally accepted value of nonrelativistic matter energy density parameter \Omega _ { m 0 } < 1 , the horizon problem can be solved only if the fluid influencing negative pressure ( the so-called “ X ” component ) violates the point-wise strong energy condition and if its energy density is sufficiently large ( \Omega _ { X 0 } > 1 ) .
The calculated value of the \Omega _ { X 0 } parameter allowing for the solution of the horizon problem is confronted with some recent observational data .
Assuming that p _ { X } / \rho _ { X } < -0.6 we find that the required amount of the “ X ” component is not ruled out by the supernova limits .
Since the value of energy density parameter \Omega _ { v 0 } for cosmological constant larger than 1 is excluded by gravitational lensing observations the value of the ratio p _ { X } / \rho _ { X } should lie between the values -1 and -0.6 if the model has to be free of the horizon problem beeing at the same time consistent with observations .
The value of \Omega _ { X 0 } + \Omega _ { m 0 } in the model is consistent with the constraints 0.2 < \Omega _ { \text { tot } } < 1.5 following from cosmic microwave background observations provided that \Omega _ { m 0 } is low ( < 0.2 ) .