The solubility of alkali metal carbonates in water is an important concept in inorganic chemistry. The solubility of these compounds generally increases down the group in the periodic table due to the increase in the ionic nature and the lattice energy trend.

Alkali metals in Group 1 of the periodic table include: Lithium (Li), Sodium (Na), Potassium (K), Rubidium (Rb), and Cesium (Cs). Their carbonates are represented as $Li_2CO_3$, $Na_2CO_3$, $K_2CO_3$, $Rb_2CO_3$, and $Cs_2CO_3$ respectively.

Here's the explanation for the order of solubility:

1. As we move down the group from Li to Cs, the atomic size increases, leading to lower lattice energy of the carbonate salts. Lower lattice energy means the salts can dissolve more easily in water.
2. The solubility trend is closely tied to the hydration energy of the ions. Smaller ions like Li⁺ have higher hydration energy compared to larger ions like Cs⁺. However, the lattice energy effect predominates in carbonates.
3. Therefore, the correct order of increasing solubility from lowest to highest is: $Li_2CO_3$, $Na_2CO_3$, $K_2CO_3$, $Rb_2CO_3$, $Cs_2CO_3$.

Based on these observations, the solubility order is observed as \(Cs_2CO_3 > Rb_2CO_3 > K_2CO_3 > Na_2CO_3 > Li_2CO_3\).

Hence, the correct answer is: $Cs_2CO_3 > Rb_2CO_3 > K_2CO_3 > Na_2CO_3 > Li_2CO_3$.

This order aligns with the general trend of increasing solubility as one moves down the group in the periodic table due to the predominant effect of decreasing lattice energy.