> I assume that Einstein originally set the constant to exactly balance the expansion, but later set it to zero.
Einstein didn't include the constant at all in his original equation, published in 1915.
In (IIRC) 1917, he realized that his original equation did not allow a static solution for the universe as a whole. He also realized that including the cosmological constant term in his equation would be mathematically valid, and that if he picked just the right value for the constant, he could obtain a static solution for the universe. At that time, it was generally believed that the universe was static on large scales.
Then, later, when it was discovered that the universe is expanding, Einstein dropped the cosmological constant term. He later called including that term in 1917 "the greatest blunder of my life", because if he had just gone with his original field equation, without the constant, he could have predicted the expansion of the universe more than a decade before it was discovered.
> In bot cases you are picking arbitrar values
When the expansion of the universe was discovered, yes, it was already recognized that it is valid to include the constant in the Einstein Field Equation, so it couldn't just be un-included. Its value was just assumed to be zero since that was consistent with all observations that were known then.
In Einstein's original 1915 field equation, however, the constant wasn't "set to zero". It wasn't included at all; nobody even realized at that time that it was valid to include it.
Einstein didn't include the constant at all in his original equation, published in 1915.
In (IIRC) 1917, he realized that his original equation did not allow a static solution for the universe as a whole. He also realized that including the cosmological constant term in his equation would be mathematically valid, and that if he picked just the right value for the constant, he could obtain a static solution for the universe. At that time, it was generally believed that the universe was static on large scales.
Then, later, when it was discovered that the universe is expanding, Einstein dropped the cosmological constant term. He later called including that term in 1917 "the greatest blunder of my life", because if he had just gone with his original field equation, without the constant, he could have predicted the expansion of the universe more than a decade before it was discovered.
> In bot cases you are picking arbitrar values
When the expansion of the universe was discovered, yes, it was already recognized that it is valid to include the constant in the Einstein Field Equation, so it couldn't just be un-included. Its value was just assumed to be zero since that was consistent with all observations that were known then.
In Einstein's original 1915 field equation, however, the constant wasn't "set to zero". It wasn't included at all; nobody even realized at that time that it was valid to include it.