  We investigate the role of the cosmological constant in the holographic
description of a radiation-dominated universe $C_2/R^4$ with a positive
cosmological constant $\Lambda$. In order to understand the nature of
cosmological term, we first study the newtonian cosmology. Here we find two
aspects of the cosmological term: entropy ($\Lambda \to S_{\rm \Lambda}$) and
energy ($\Lambda \to E_{\rm \Lambda}$). Also we solve the Friedmann equation
parametrically to obtain another role. In the presence of the cosmological
constant, the solutions are described by the Weierstrass elliptic functions on
torus and have modular properties. In this case one may expect to have a
two-dimensional Cardy entropy formula but the cosmological constant plays a
role of the modular parameter $\tau(C_2,\Lambda)$ of torus. Consequently the
entropy concept of the cosmological constant is very suitable for establishing
the holographic entropy bounds in the early universe. This contrasts to the
role of the cosmological constant as a dark energy in the present universe.
