“I believe the Big Bang never happened,” said Juliano César Silva Neves, a physicist at the University of Campinas’s Mathematics, Statistics & Scientific Computation Institute (IMECC-UNICAMP) in São Paulo State, Brazil.

Although for five decades, the Big Bang theory has been the best known and most accepted explanation for the beginning and evolution of the Universe, it is hardly a consensus among scientists, according to Neves, part of a group of researchers who dare to imagine a different origin.

In a study recently published in the journal General Relativity and Gravitation, Neves suggests the elimination of a key aspect of the standard cosmological model: the need for a spacetime singularity known as the Big Bang.

In raising this possibility, Neves challenges the idea that time had a beginning and reintroduces the possibility that the current expansion was preceded by contraction.

For Neves, the fast spacetime expansion stage does not exclude the possibility of a prior contraction phase. Moreover, the switch from contraction to expansion may not have destroyed all traces of the preceding phase.

“Who knows, there may be remains of black holes in the ongoing expansion that date from the prior contraction phase and passed intact through the bottleneck of the bounce,” Neves told Agência FAPESP.

It is precisely in black holes that Neves locates the starting point for his investigations into what he calls the “bouncing Universe”, in which contraction is followed by expansion.

“The inspiration for the bouncing Universe came from a mathematical trick to avoid the formation of singularities in black holes,” he said. “There are two kinds of singularity in the Universe. One is the alleged cosmological singularity, or Big Bang. The other hides behind the event horizon of a black hole.”

Black holes are the most mysterious cosmic objects. A black hole consists of the imploded core remaining after a giant star explodes. The core contracts to form a singularity, a point with infinite density and the strongest gravitational attraction known to exist. Nothing escapes from it, not even light.

The singularity is located at the center of the black hole, hidden behind the event horizon, a membrane that indicates the point of no return from which nothing escapes the inexorable destiny of being swallowed up and destroyed by the singularity.

“But not all black holes have to contain a singularity. At least, not in theory. There are no singularities in so-called regular black holes,” Neves said.

In 1968, US physicist James Bardeen used a mathematical trick to modify the solution to the general relativity equations that describe black holes.

The trick consisted of thinking of the mass of a black hole not as a constant, as had previously been the case, but as a function that depends on the distance to the center of the black hole. With this change, a different black hole, termed a regular black hole, emerged from the solution to the equations.

“What defines a black hole isn’t a singularity but an event horizon,” Neves said. “Outside the event horizon of a regular black hole, there are no major changes, but inside it, the changes are deep-seated. There’s a different spacetime that avoids the formation of a singularity. Regular black holes are permitted, since they don’t violate general relativity. The concept isn’t new and has frequently been revisited in recent decades.”

If the insertion of a mathematical trick into the general relativity equations prevents the formation of singularities in regular black holes, could a similar artifice be created to eliminate the singularity in a regular bounce?

“In order to measure the rate at which the Universe is expanding with the standard cosmology, the model in which there’s a Big Bang, a mathematical function is used that depends only on cosmological time,” Neves explained.

This is where the mathematical trick comes in. Neves and his postdoctoral supervisor Alberto Vazques Saa, Full Professor at IMECC-UNICAMP, introduced a “scale factor” that makes the rate at which the Universe is expanding depend not only on time but also on cosmological scale into the solutions to the general relativity equations that describe the geometry of the cosmos.

This is the proposal presented in the recently published article, which is part of the Thematic Project “Physics and geometry of spacetime”, with Saa as principal investigator. Neves’s postdoctoral research was supported by a scholarship from FAPESP.

#### Vestiges of contraction

What are the consequences of the mathematical trick involving the scale factor? The cosmological singularity, or Big Bang, ceases to exist. It ceases to be a necessary condition for the cosmos to begin universal expansion.

“Eliminating the singularity or Big Bang brings back the bouncing Universe on to the theoretical stage of cosmology. The absence of a singularity at the start of spacetime opens up the possibility that vestiges of a previous contraction phase may have withstood the phase change and may still be with us in the ongoing expansion of the Universe,” Neves said.

“Did the Universe have a beginning, or did it not? Does the world end inside a black hole? Today, we know the theory of general relativity permits a non-singular cosmology, with no Big Bang, at least in theory.”

In modern science, a theory is worthless if cannot be verified, however beautiful and inspiring it may be. How do you test the hypothesis of a Big Bang that did not start with a singularity?

“By looking for traces of the events in a contraction phase that may have remained in the ongoing expansion phase. What traces? The candidates include remnants of black holes from a previous phase of universal contraction that may have survived the bounce,” Neves said.

#### Big Bang

The Big Bang theory began to be formulated in the late 1920s, when US astronomer Edwin Hubble discovered that almost all galaxies are moving away from each other at ever-faster velocities.

This means they were much closer together in the remote past. More precisely, 13.8 billion years ago all the matter and energy in the Universe were compressed into an initial state with infinite density and temperature, where the traditional laws of physics no longer apply.

To define this state cosmologists paradoxically borrowed the concept of singularity from mathematics, where it refers to indefinition. In this case, there was a primordial cosmological singularity that began expanding 13.8 billion years ago. The initial singularity became known as the Big Bang. The hundreds of billions of galaxies in the cosmos were formed from the matter and energy ejected by this initial explosion.

Guided by Einstein’s theory of general relativity, which is used to explain cosmic phenomena, from the 1940s onward, scientists constructed a detailed model of the evolution of the Universe since the Big Bang. The model was based on the assumption that the expansion might eventually decelerate in response to the gravitational attraction exerted by the mass of the Universe.

This assumption could lead to three possible outcomes: the Universe would expand infinitely at ever-higher velocities; the expansion would cease, and the Universe would thereafter remain static; or the expansion would go into reverse, giving way to a contraction in which the galaxies would move closer together at ever-higher velocities until they merged in a future Big Crunch.

If this were the case, when matter and energy reached an extreme temperature and density in the Big Crunch, the process might again go into reverse, giving way to expansion in another bounce and producing a new cycle in the Universe, and so on without end.

“This image of an eternal succession of universes with alternating expansion and contraction phases was called the cyclical Universe, which derives from bouncing cosmologies,” Neves said.

Publication: J. C. S. Neves, “Bouncing cosmology inspired by regular black holes,” *General Relativity and Gravitation*, 2017; doi:10.1007/s10714-017-2288-6

The correct cosmology is given by Dewey B. Larson in his book ‘Nothing But Motion’.