I will argue that irrespective of inflationary cosmology or quantum gravity, in our universe time had to have a beginning.
Let’s go by parts. Where does time come into the game here? We need to make a distinction between classical and quantum theories. Einstein’s theory of general relativity (GR), used to study the Big Bang model including its inflationary phase, is a classical theory, in the sense that the field it describes, the gravitational field, is a continuous entity and not quantized, that is, made of little discrete pellets.
Think of sand dunes seen from afar: you see them as a smooth continuum. This is the classical space that GR describes: Gravity is seen as a distortion in the continuous geometry of space caused by the presence of a mass; the bigger the mass, the stronger the curvature. Likewise, time is also affected by mass: more mass, more gravity and time runs slower. These are not speculations; these are measured facts.
Back to the sand dunes analogy, the quantum realm would be apparent as we come closer. We first see the granularity, then the individual grains of sand, the “quanta” of the beach field. Taking this image to describe space, in a quantum as opposed to classical theory of gravity, both space and time would be granular, discontinuous. You couldn’t think of a distance between two points or of a time interval between two events. Everything fluctuates wildly. Physics as we know it falls apart.
So, people attempt to construct alternative theories where gravity and thus space and time can be described as quantized fields. However, irrespective of these ideas, there is always a transition from the quantum to the classical realm. Even if linear flowing time wouldn’t make sense in a quantum space-time, it has to as the quantum cosmos transitions to the classical cosmos we live in. In a sense, as Saint Augustine had remarked some 16 centuries ago, space and time emerge with Creation. Here, Creation is precisely this transition from a quantum to a classical time. Time begins when it starts ticking, that is, when physical processes take place in the background of a classical space-time. Anything that happened before has been erased from cosmic memory.
Now, inflationary cosmology... The idea there, and in some versions of superstring theories, is that our universe is not unique: there are many, possibly infinitely many universes out there, bubbles sprouting from an eternal realm called the multiverse. There is no time in the multiverse itself. But each one of these baby universes that transitions to a large, classical universe will have a well-defined arrow of time. Ours happens to be one of the babies that worked out, and kept growing and growing and is still doing so after 13.7 billion years.
So, within our universe, time had a beginning.
In a real sense, the only time that exists is classical time.
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