How to make value in a row equal to now() in postgres
You can use now(), CURRENT_DATE and their friends wherever an expresison is accepted.  That means, you can define your table like

CREATE TABLE experiment (
    e_id text PRIMARY KEY,
    e_started date NOT NULL DEFAULT CURRENT_DATE,
    e_ended date
);


Here, when you insert an experiment, it is enough to insert its ID:

INSERT INTO experiment (e_id) VALUES ('this_experiment_about_AAAAA');


Still, the start date will be the day when this INSERT was issued.  The end date is left to NULL - this is the usual way of having undefined values.  You will find the running experiments like

SELECT e_id, e_started FROM experiments WHERE e_ended IS NULL;


When one finishes, you update the given row and set the end date as necessary (to CURRENT_DATE, for example).

Notes:


I used different column names than you.  I'd advise to use snake_case instead of CamelCase - the latter often leads to confusion.
another naming consideration is that the table defines the data type, no need to reflect this in the column name.
the last naming thing: I prefixed the column names with the table name acronym.  You don't have to do this, it's a matter of taste more than anything else.