MULTIVERSE: SCIENCE OR SCIENCE FICTION?

Many people consider the concept of the Multiverse to be exotic and far from reality. The original Big Bang model probably has a lot to do with this: an initial "big bang" created space-time and matter, producing only the expanding Universe we observe today. However, we have long known that this model is incomplete. Our standard cosmological model, the one accepted by the scientific community, tells us that before the Big Bang, the Universe underwent a very brief period of exponential expansion: cosmic inflation. At this level, we suddenly encounter the Multiverse: most cosmic inflation models predict the creation of an enormous number of Universes, not just the Universe we observe.

In addition to this, we know that our standard cosmological model is, in turn, incomplete. We know that the Universe at the fundamental level is quantum, but our cosmological model is classical. At this new level, we encounter the Multiverse again: quantum mechanics and quantum cosmology include Feynmann sum-of-history descriptions or Everett's many-worlds interpretation, which imply the existence of other "Universes."

We still don't have a complete theory of quantum gravity; by far the most promising candidate for a quantum theory of gravity is superstring theory. And again, at this final level, we find a multiverse: string theory predicts, in a general way, the existence of a "landscape" that implies the existence of a huge number of distinct universes.

So it seems that rather than asking whether our fundamental theories admit the existence of a Multiverse, we should ask whether there is any way to avoid the Multiverse in modern Physics.

Of course, the million-dollar question is whether this Multiverse can be experimentally detected. The most widely held view is that the Multiverse is impossible to verify experimentally because it is causally disconnected from our observable Universe. While this is true at the classical level, it is not true at the quantum level. In this article, we will see that, incredible as it may seem, the Multiverse is, in principle, experimentally detectable.

Quantum cosmology

Next, we will see how, using the principles of quantum cosmology, we can experimentally observe the traces of the Multiverse.

As we saw in the previous article , quantizing the equations of general relativity gives us the Wheeler-DeWitt equation. This equation can also be written as:

Where:

and:

phi represents the wave function of the Universe behaving as a scalar field, w2 is the oscillation frequency of the scalar field and the term V represents the potential of the scalar field.

Next, we will apply the process known as "third quantization." This consists of quantizing the psi scalar field (the wave function of the Universe) following the methodology of quantum field theory. In this way, we obtain the dynamics of a harmonic oscillator, and the different modes of this oscillator can be interpreted as different Universes. Applying this method, we obtain the following density for the Hamiltonian:

Interactions in the Multiverse

The key idea is the following: depending on whether the different modes of the Hamiltonian obtained from the wave function of the Universe (representing different Universes) are entangled or not, the shape of the potential V will be slightly different, that is, the entanglement between different Universes would have a measurable effect: it would slightly modify the minimum of the potential of the wave function.

TO We'll see why this is so below. Suppose there is entanglement between the different modes, then the total Hamiltonian will consist of two terms:

The H0n term represents the non-interacting portion, while the HIn term represents the entangled modes. We will decompose the full Hamiltonian with interactions into its various Fourier modes and compare the result with the results obtained without the interaction term. The full Hamiltonian can be expressed through the following Fourier transformation:

This transformation represents N Universes with Hamiltonian:

Where:

And whose effective frequency value is given by:

Where:

With a new effective potential given by:

The new term to the right of V implies a modification of the potential, which means that the interaction between N Universes produces a modification of the value of the minimum of the potential:

Figure 1: The interaction (entanglement) between different Universes would result in the modification of the shape of the potential of the scalar field that represents the wave function of the Universe.

Measurable effects of the Multiverse

Although it may seem incredible, this small modification in the value of the vacuum potential, despite not modifying the equations of motion, could have an experimentally measurable effect. As we can see in the equation for the frequency w2, as the scale factor "a" increases, the effects of the Multiverse quickly fade away. However, for small values of a, comparable to the Hubble radius, the effects would be significant. The highest modes of the CMB are sensitive to large scales of the Universe, while the lowest modes would be sensitive to the earliest moments of the Universe. Therefore, possible "fingerprints" of the Multiverse would be hidden in the lowest modes, resulting in a suppression of the values of these modes.

The following figure is an example of how different models can affect the value of the CMB's low modes. This figure is taken from studies of the effect of domain walls and cosmic strings during inflation:

Figure 2: The black line represents the values measured by Planck, the blue line represents the values predicted by a domain wall network, and the red line represents the effects of cosmic strings.

To analyze the possible effects of the Multiverse on the modes of the CMB we will distinguish three possible cases:

1st) Pre-inflationary stage leading to initial stages dominated by radiation

If the type of interaction between Universes "f" is of the type f=a2 then the solution to the Wheeler-DeWitt equation would be of the type:

a(t)=(sinh2Ht)1/2

This solution leads to a Friedmann equation that coincides with that of an initial stage dominated by radiation so the effects of the interaction between Universes would be difficult to distinguish from the effects caused by radiation.

2nd) Pre-inflationary stage leading to initial stages dominated by matter

If the type of interaction between Universes "f" is of the type f=a2 then the solution to the Wheeler-DeWitt equation would be of the type:

a(t)=(sinh3/2Ht)2/3

This solution leads to a Friedmann equation that coincides with that of an initial stage dominated by matter, so the effects of the interaction between Universes would be difficult to distinguish from the effects caused by matter.

3rd) Pre-inflationary stage dominated by the effects of the Multiverse

If the type of interaction between Universes "f" is of the type f=1/a then the solution to the Wheeler-DeWitt equation would be of the type:

a(t)=(sinh3Ht)1/3

In this case, the effects of the Multiverse would be distinguishable from the two previous cases. This is the most favorable case for enabling Multiverse detection:

Figure 3: The effects of the Multiverse would be better distinguished from other causes for the case represented by the green line.

The CMB results presented by the Planck satellite show a small discrepancy with theoretical models for the lowest modes (see Figure 2). Although more precise measurements are needed to increase reliability, it appears that a radiation-dominated Universe best fits the data, and that a Universe with effects due to the Multiverse could provide an even better fit.

It should be noted that in addition to the method outlined in this article, there are other possible ways to search for the "fingerprint" of the Multiverse in the CMB data: collisions between bubbles during inflation, transitions between false voids in the pre-inflationary epoch, or the mass spectrum of black holes due to the Multiverse.

Conclusions

From a theoretical perspective, there are very good reasons to believe in the existence of a multiverse-like structure. From a classical perspective, this structure would be undetectable because it is causally disconnected from our universe. However, from a quantum perspective, the multiverse could be detectable through the effect of quantum entanglement. Since we know that the universe is quantum at a fundamental level, the multiverse is, in principle, detectable and therefore susceptible to study by scientific methods. This statement is valid, in principle, regardless of the fact that, in practice, detecting the multiverse could be very technologically difficult.

Sources: Observational consequences of an interacting Multiverse