The better way to measure cosmic time

For some reason, when we talk about the age of stars, galaxies, and the Universe, we use "years" to measure time. Can we do better?

 Today, we can trace the Big Bang back to having occurred some 13.8 billion years ago, with the size of the observable Universe stretching to 46.1 billion light-years.  

• But not only are units like "years" and "light-years" completely arbitrary and Earth-centric, they haven't even had consistent definitions over the history of Earth. 
• There might be better ways to measure time, especially for the Universe, but every alternative has its drawbacks, too.
• • • There are a number of grand questions we can ask about the Universe that cut right to the very core of what reality actually is, and were some of the biggest head-scratchers for all of human history. Questions like, “What is the Universe?” “How big is it?” and “Was it eternal, or did it spring into existence, and if so, when?” used to be some of the greatest philosophical mysteries, and yet the last 100 years have provided firm, scientific answers. We know what the Universe is, we know that the part observable to us is a hair over 92 billion light-years in diameter, and we know that the hot Big Bang, which started off the Universe as-we-know-it, occurred precisely 13.8 billion years ago, with an uncertainty in these values of just ~1% or so.
    • • • But why, of all the ways there are to measure time and distance, do we use such an Earth-centric set of units, like “years” and “light-years”? Isn’t there a better, more objective, more universal way to do it? Surely there is. At least, that’s what Jerry Bear thinks, writing in to ask:

          “Why do cosmological calculations, such as the age or scale of the universe, utilize the0 provincial and wildly, woefully unequal to the task parameter of ‘year’? A year’s value as a measurement is so narrowly defined as to render it inappropriate to my mind. I mean, the basis of ‘year’ has only even existed for the most recent 30% of the universe’s age! And obviously the critical concept of a light-year is also tied to this parochial measurement.”

          All of these are excellent points and are worth both expanding on and considering the alternatives to these somewhat arbitrary definitions. Let’s look at the science behind measuring cosmic time.

        • There are really only two ways, here on Earth, to make sense of the concept of the passage of time, and both make use of the regular recurrence of phenomena that are essential to not only human activity, but all biological activity. On shorter timescales, we have the concept of days, which are important for a number of reasons, including:

          • they mark sunrise and sunset,
          • they correspond to (roughly) a single complete rotation of Earth about its axis,
          • they correspond to the period where most plants and animals experience both activity and dormancy,

          all followed by a repeat of all of these phenomena, and more, on the next day. Meanwhile, on longer timescales, it’s very apparent that there are substantial differences between subsequent days, that themselves repeat if we wait long enough. Over the course of a year, days change in a variety of ways, including:

          • sunrise and sunset times advance and retreat,
          • the duration of daylight waxes and wanes,
          • the Sun reaches a maximum in its height above the horizon, followed by a minimum, and a return to its original position again,
          • the seasons change in a cycle,
          • and the biological activity of plants, animals, and other living creatures change along with them.