What if stillness as we know it didn’t exist at the core of the universe’s fabric, propelling us into a realm where motion is the eternal law governing everything from microscopic particles to the colossal galaxies? This provocative notion shakes the foundation of our understanding of reality, suggesting a cosmos pulsating with unceasing activity. It’s a concept that doesn’t just expand our knowledge but revolutionizes it, inviting us to view the universe not as a static void but as a dynamic, ever-moving tapestry. Such a perspective doesn’t only promise to unlock new cosmic mysteries but also offers a deeper insight into the essence of all existence, challenging us to reimagine the fundamental principles that orchestrate the universe’s vast expanse.

The enigmatic nature of the cosmological constant, a significant element in understanding the universe’s accelerated expansion, has captivated the scientific community for decades. Dr. Cláudio Nassif Cruz from The Federal University of Ouro Preto has introduced a groundbreaking approach to this puzzle through the lens of Symmetrical Special Relativity (SSR). His research, published in Reviews in Physics, provides new insights into the possible origins of the cosmological constant, offering fresh perspectives on the cosmos.

At the heart of his investigation is the introduction of an invariant minimum speed within the SSR framework, challenging the traditional views of space-time and introducing a novel concept of the universe’s structure. This idea, emerging from quantum mechanics and thermodynamic principles, suggests that absolute rest is unachievable, prompting a reevaluation of our fundamental understanding of physics.

Dr. Cruz states, “The advantage of Symmetrical Special Relativity (SSR) as a theory of Modified Relativity is its kinematic basis that is based on new relativistic effects as a consequence of an invariant minimum speed that prevents rest.” This introduction of a minimum speed not only tackles the quantum vacuum energy puzzle but also offers a new angle on the cosmological constant problem, bridging the gap between quantum mechanics and cosmological observations.

“The implications of our findings extend across the spectrum of theoretical physics, potentially revolutionizing our understanding of the universe,” Dr. Cruz remarks, emphasizing the significance of their findings in providing a coherent explanation for dark energy and the universe’s accelerated expansion.

Moreover, the study carefully aligns the SSR model with the de-Sitter metric, commonly used to describe a universe under the influence of a positive cosmological constant. Through this alignment, Dr. Cruz affirms the model’s applicability to current astrophysical observations and its role in comprehending the universe’s accelerated expansion. “We aim to investigate a modified space–time with the presence of a minimum speed, which is a kinematic invariant at lower energies as is also the speed of light for higher energies, by forming a fundamental symmetry of motion,” Dr. Cruz elaborates, shedding light on the research’s methodological foundation.

This research not only challenges the existing paradigms but also opens the door to future explorations into the universe’s most profound mysteries. Dr. Cruz’s innovative approach promises to enhance our understanding of the cosmos, offering insights into the fundamental forces shaping the universe’s expansion. Ultimately, this study marks a significant advancement in theoretical physics, providing a compelling explanation for the cosmological constant. As we continue our quest to decode the universe’s secrets, the insights provided by Dr. Cruz’s research underscore the vast potential for discovery in our journey to understand the cosmos fully.


Cláudio Nassif Cruz, “A brief review of a modified relativity that explains cosmological constant,” Reviews in Physics, 2023.

DOI: https://doi.org/10.1016/j.revip.2023.100088


Prof. Cláudio Nassif Cruz

Cláudio Nassif Cruz is retired Professor of Physics, Federal University of Ouro Preto (UFOP) , Ouro Preto, Minas Gerais, Brazil. He was born in Além Paraíba, Minas Gerais, in August 1967.

He got his bachelor’s degree of Physics (1992) in Federal University of Juiz de Fora (UFJF), Minas Gerais, Brazil.

His master’s degree (1992) and Ph.D degree (2002) of Physics was in Federal University of Minas Gerais (UFMG), Belo Horizonte, Minas Gerais, Brazil.

He has long experience in the area of Condensed Matter Physics, with emphasis on State Equation, Phase Equilibrium and Phase Transitions, focusing on the following topics as a line of work, namely Thompsons approach, Renormalization Group, dynamical and stationary critical exponents for various systems, diffusion-limited chemical reactions, polymers, surface growth, N-vector model without random field. Also some topics in field theories, such as Quantum Electrodynamics (QED) and Quantum Chromodynamics (QCD) are treated on Thompsons approach.

In another line of original research that he himself introduced, he works on the exploration of another possibility of Lorentz symmetry breaking for a Deformed Special Relativity with an invariant minimum speed (Symmetrical Special Relativity), where a background field is generated by a non-Lorentzian dynamics at low energies, thus explaining the tiny positive value of the cosmological constant and also explaining the principle of quantum uncertainty, allowing us to make a connection between quantum physics and cosmology.