Based on the entropy$-$area relation from Nouicer’s generalised uncertainty
principle (GUP), we derive the GUP modified Friedmann equations from the first
law of thermodynamics at apparent horizon. We find a minimum apparent horizon
due to the minimal length notion of GUP. We show that the energy density of
universe has a maximum and finite value at the minimum apparent horizon. Both
minimum apparent horizon and maximum energy density imply the absence of the
Big Bang singularity. Moreover, we investigate the GUP effects on the
deceleration parameter for flat case. Finally, we examine the validity of
generalised second law (GSL) of thermodynamics. We show that GSL always holds
in a region enclosed by apparent horizon for the GUP effects. We also
investigate the GSL in $Lambda CDM$ cosmology and find that the total entropy
change of universe has a maximum value in the presence of GUP effects.
Conclusions
Based on the entropy$-$area relation from Nouicer’s generalized uncertainty principle (GUP), the authors of this study derived the GUP modified Friedmann equations from the first law of thermodynamics at apparent horizon. They found that there is a minimum apparent horizon due to the minimal length notion of GUP, and this minimum apparent horizon leads to a maximum and finite value for the energy density of the universe. Both the minimum apparent horizon and maximum energy density suggest the absence of the Big Bang singularity.
The authors also investigated the effects of GUP on the deceleration parameter for the flat case. Finally, they examined the validity of the generalized second law (GSL) of thermodynamics. They showed that GSL always holds in a region enclosed by the apparent horizon for the GUP effects. Additionally, they explored the GSL in $Lambda CDM$ cosmology and found that the total entropy change of the universe has a maximum value in the presence of GUP effects.
Future Roadmap
Looking ahead, exploring and understanding the implications of GUP in cosmology can lead to significant advancements in our understanding of the universe’s evolution and fundamental physics. Researchers should focus on addressing the following challenges and opportunities:
1. Experimental Verification
One crucial step in validating the conclusions drawn from this study is experimental verification. Designing and implementing experiments that can test the predicted effects of GUP on the energy density and apparent horizon will provide empirical evidence for its existence and impact. Overcoming technological limitations and designing robust experiments will be a significant challenge in this regard.
2. Cosmological Observations
Observational data from cosmological observations can provide invaluable insights into GUP effects. Analyzing data from large-scale surveys, such as those conducted by current and upcoming telescopes, can help detect signatures of GUP on the energy density and deceleration parameter of the universe. Collaborating with observational astronomers and cosmologists will be crucial for interpreting and utilizing the data effectively.
3. Theoretical Frameworks
Developing theoretical frameworks that incorporate GUP effects into existing cosmological models, such as the $Lambda CDM$ model, is essential. Exploring how GUP modifies other fundamental principles and equations in cosmology can deepen our understanding of the universe’s behavior. This will require interdisciplinary collaborations between theoretical physicists and cosmologists.
4. Implications for Fundamental Physics
Studying the implications of GUP effects on the absence of the Big Bang singularity has profound implications for fundamental physics. It challenges our current understanding of the universe’s origin and evolution. Researchers should explore the consequences of GUP on other areas of physics, such as quantum gravity and black hole physics, to establish a more comprehensive understanding of the fundamental laws governing our universe.
5. Philosophical and Conceptual Implications
The potential absence of the Big Bang singularity and the introduction of a minimal length concept through GUP raise philosophical and conceptual questions about the nature of space, time, and the beginning of the universe. Exploring these implications and engaging in interdisciplinary discussions with philosophers, theologians, and other experts can provide deeper insights into these profound questions.
In conclusion, investigating the consequences of GUP in cosmology presents numerous challenges and opportunities. From experimental verification to theoretical advancements and philosophical implications, researchers have a rich roadmap ahead that can revolutionize our understanding of the universe.