Cosmology faces complex challenges that transcend the limits of traditional mathematics. By going back Albert Einstein’s theory of relativity to the moment of the Big Bang, the formulas converge to a singular point, where density and temperature reach infinite values, making current physics ineffective in describing the scenario.
This limitation has turned questions about the initial formation of the cosmos into a scientific impasse. Questions such as the existence of something before the Big Bang, the possibility of the universe having sprouted from a previous phase, or whether cosmic inflation started from a homogeneous or chaotic state, were previously debated predominantly in the field of speculation, with few avenues for robust empirical or theoretical verification.
However, recent research suggests that this situation may be in the process of changing. According to a study published in the journal *Living Reviews in Relativity*, researchers Eugene Lim, from King’s College London, Katy Clough, from Queen Mary University of London, and Josu Aurrekoetxea, from the University of Oxford, propose that numerical relativity can enable cosmologists to study areas previously unreachable by conventional calculations.
Numerical relativity uses the power of supercomputers to estimate solutions to Einstein’s equations in highly complex scenarios, where analytical mathematics becomes unfeasible. This approach is already consolidated in black hole physics, contributing to the modeling of mergers of these cosmic objects and the resulting gravitational waves.
How traditional simplifications of cosmology prove insufficient
In most cosmological investigations, scholars choose to simplify matters by postulating that the universe presents homogeneity in large dimensions and a uniform appearance in all directions. Such a model, present in the Robertson-Walker description of the cosmos, is effective for the currently observable portion of the universe.
However, it is unlikely that the universe in its initial stages would have such a degree of organization.
These conventional simplifications lose their validity when the gravitational force is intense, the distribution of matter is excessively heterogeneous and the structure of space-time undergoes drastic changes. According to the analysis, under these conditions, simulations that fully consider relativity may be the only way to understand the phenomena.
“It is possible to investigate close to the lamp post, but you cannot go much further, where there is darkness, as the equations cannot be solved”, explains Lim. He adds that “numerical relativity makes it possible to explore areas that transcend the limits of illumination”.
This methodological transformation is crucial, since the biggest questions in cosmology are located exactly in this obscure area. The theory of inflation, for example, is widely accepted to elucidate the current homogeneity and flatness of the universe, but the mechanism triggering this accelerated expansion has not yet been identified. Simulations that do not require perfect symmetry can help reveal which initial conditions actually generate inflation and which do not.
The study emphasizes the relevance of this approach, especially when heterogeneities are pronounced, covering extensions the size of a cosmological horizon and cannot be considered as mere discrete fluctuations in a simplified background scenario.
Numerical relativity: from studying black holes to exploring cosmic origins
Numerical relativity has a long history, but it has solidified its contemporary prominence in the field of black holes. Pioneering research in the 1960s and 1970s already indicated its potential, and the discipline gained significant momentum when physicists needed accurate models for the gravitational waves predicted from the merger of compact celestial bodies.
In 2005, simulations reached the level of precision necessary to elucidate the issue of black hole mergers. This advance was crucial for subsequent detections carried out by the LIGO observatory, demonstrating the ability of computing to resolve aspects of general relativity that traditional calculation methods were unable to address.
Recent analysis points out that cosmology now finds itself at a similar juncture. Although researchers already have the computational tools, collaboration between cosmologists and experts in numerical relativity is still restricted. One of the purposes of the article is precisely to encourage a common dialogue between these two areas, ranging from the selection of gauges and boundary conditions to the interpretation of results in a highly irregular space-time continuum.
These technical details are not trivial. The authors allocate a considerable portion of the review to practical challenges, such as defining initial conditions that meet the restrictions proposed by Einstein, imposing limits on a simulated universe, the stability of coordinate choices and the differentiation between a result that represents real physics and a mere failure in data segmentation.
The possibilities of investigating a universe with a multiple past
Among the most intriguing perspectives, the opportunity to analyze models that suggest a universe without a singular starting point stands out. Some hypotheses conceive the cosmos as a cyclical system, alternating stages of contraction and expansion. Other theories, in turn, seek to replace the concept of a single Big Bang with a cosmic “rebound” event.
Such scenarios are complex due to the involvement of conditions of extreme gravity and strong irregularities, which nullify conventional approximations. The review indicates that numerical relativity may be one of the rare instruments capable of verifying the viability of models like these.
The same principle extends to other ancient conceptions that lie on the border between observation and theory. The researchers mention cosmic strings, bubble shocks, primordial black holes, the post-inflationary preheating period, and the tenuous impacts of general relativity on the late universe as questions that could be elucidated by comprehensive simulations.
In certain situations, the benefit may manifest itself in the ability to observe. Simulations can help predict the marks that bubble collisions would leave in the cosmic microwave background radiation, or the patterns of gravitational waves that could emerge from cosmic strings or violent events subsequent to the inflation phase.
It is important to emphasize that the article does not suggest the existence of ready-made answers. The majority of the review acts as a guide to a developing field of research, not as the solution to an unraveled enigma. The text also highlights that complete simulations of general relativity are costly, technically challenging and only become justifiable when more simplified approaches prove ineffective.
Despite this, the authors maintain that the field of study has reached a stage where such endeavors are no longer considered premature.
The rigorous test for current cosmological theories
A point frequently made in the review is the ability of numerical relativity to convert comprehensive narratives about the genesis of the universe into models that should support concrete assessments. It is distinct to propose that inflation mitigates a disorderly beginning, or that a contracting universe can continually expand, actually construct a spacetime with these characteristics, without assuming symmetries, and then verify the soundness of the theory.
A “stress testing” method like this would have the potential to reduce the number of theories considered plausible.
Furthermore, such progress could intensify discussions already underway. The study highlights that previous numerical work has been used to question the resilience of inflation in the face of challenging initial conditions, the ability of a slow contraction to homogenize an irregular cosmos, and the degree to which integral general relativity modifies projections for the late universe compared to standard estimates.
Lim and his collaborators express the expectation that the article will contribute to the formation of a more comprehensive and collaborative field of research around these questions.
“We aim to strengthen the intersection between cosmology and numerical relativity so that specialists in numerical relativity, who want to apply their skills in exploring cosmological problems, have this opportunity,” says Lim. He adds: “And, likewise, so that cosmologists, interested in solving questions that are inaccessible to them, can employ numerical relativity.”
The relevant practical implications of this new research method
The immediate result does not lie in the exact revelation of what preceded the Big Bang. Instead, the significant advance is that certain questions previously considered unattainable by science can now be reformulated as computational challenges.
If simulations demonstrate which models of the universe in its primordial phase remain stable, which collapse and which generate observable evidence, scientists will have a more precise method to analyze theories about the origin of the cosmos.
With the constant advancement of computer processing capacity, this approach could establish a link between abstract theories and detectable signals in phenomena such as gravitational waves, cosmic microwave background radiation or the configuration of the universe itself.
