We further investigate novel features of the $T-$vacuum state, originally
defined in the context of quantum field theory in a (1+1) dimensional radiation
dominated universe [Modak, JHEP 12, 031 (2020)]. Here we extend the previous
work to a realistic (3+1) dimensional set up and show that $T-$vacuum causes an
emph{anisotropic particle creation} in the radiation dominated early universe.
Unlike the Hawking or Unruh effect, where the particle content is thermal and
asymptotically defined, here it is non-thermal and time dependent. This novel
example of particle creation is interesting because these particles are
detected in the frame of physical/cosmological observers, who envision the
$T-$vacuum as a particle excited state, and therefore may eventually be
compared with observations.

The article explores the concept of the $T-$vacuum state in quantum field theory and its implications for particle creation in the early universe. Building upon previous research conducted in a (1+1) dimensional radiation dominated universe, the authors extend the study to a more realistic (3+1) dimensional setup and demonstrate that the $T-$vacuum leads to anisotropic particle creation.

Unlike the Hawking or Unruh effect, where the particle content is thermal and consistently defined, the particle creation in the $T-$vacuum is non-thermal and varies with time. This unique characteristic makes it particularly intriguing, as these particles can be observed by physical and cosmological observers who perceive the $T-$vacuum as an excited state of particles. Consequently, there is potential for a comparison between these detected particles and actual observations.

Roadmap for the Future

1. Further Experimental Investigations

  • Experimental studies should be carried out to validate the predicted anisotropic particle creation induced by the $T-$vacuum in a (3+1) dimensional universe.
  • Developing advanced detectors capable of measuring and observing these non-thermal particles is crucial.

2. Comparison with Observations

  • Physicists and cosmologists should analyze the detected particles and compare them with observational data to determine the compatibility of the $T-$vacuum model with real-world observations.
  • This comparison could shed light on the accuracy and feasibility of the $T-$vacuum as an explanation for early universe phenomena.

3. Theoretical Developments

  • Further exploration and theoretical developments are essential to better understand the nature of the $T-$vacuum and its implications.
  • Investigating the potential cosmological consequences of the $T-$vacuum and its role in the evolution of the early universe could unveil new insights into quantum field theory and cosmology.

Challenges and Opportunities


  1. Developing experiments with sufficient sensitivity to detect non-thermal particles created by the $T-$vacuum.
  2. Ensuring the accuracy of observational data and minimizing potential sources of error during the comparison process.
  3. Dealing with complex mathematical models and calculations involved in analyzing the $T-$vacuum and its impact on particle creation.


  1. Successful experimental verification of anisotropic particle creation could confirm the existence of the $T-$vacuum and promote further exploration of its properties.
  2. Discovery of a non-thermal particle signature consistent with the $T-$vacuum would provide support for the model and open avenues for developing new theories and expanding our understanding of the early universe.
  3. Improvements in detector technologies driven by the need to observe non-thermal particles may have broader applications in other fields of research.

In summary, the extension of the $T-$vacuum concept to a (3+1) dimensional universe reveals an intriguing phenomenon of anisotropic particle creation in the radiation dominated early universe. The non-thermal nature and observability of these particles offer opportunities for experimental investigations, as well as comparisons with observational data. While there are challenges to overcome, such as developing sensitive detectors and ensuring accuracy in analysis, successful validation of the $T-$vacuum model could lead to theoretical advancements and a deeper understanding of quantum field theory and cosmology.

Read the original article