## Title: Exploring Gravity Models with Bose Gases: Tabletop Experiments and Seismic Waves

Utilizing the recently established connection between Palatini-like gravity

and linear Generalized Uncertainty Principle (GUP) models, we have formulated

an approach that facilitates the examination of Bose gases. Our primary focus

is on the ideal Bose-Einstein condensate and liquid helium, chosen as

illustrative examples to underscore the feasibility of tabletop experiments in

assessing gravity models. The non-interacting Bose-Einstein condensate imposes

constraints on linear GUP and Palatini $f(R)$ gravity (Eddington-inspired

Born-Infeld gravity) within the ranges of $-10^{12}lesssimsigmalesssim

3times 10^{24}{text{ s}}/{text{kg m}}$ and

$-10^{-1}lesssimbarbetalesssim 10^{11} text{ m}^2$

($-4times10^{-1}lesssimepsilonlesssim 4times 10^{11} text{ m}^2$),

respectively. In contrast, the properties of liquid helium suggest more

realistic bounds, specifically $-10^{23}lesssimsigmalesssim 10^{23}{text{

s}}/{text{kg m}}$ and $-10^{9}lesssimbarbetalesssim 10^{9} text{ m}^2$.

Additionally, we argue that the newly developed method employing Earth seismic

waves provides improved constraints for quantum and modified gravity by

approximately one order of magnitude.

**Conclusions:**

The article concludes by stating that the recently established connection between Palatini-like gravity and linear Generalized Uncertainty Principle (GUP) models has allowed for the examination of Bose gases. The ideal Bose-Einstein condensate and liquid helium are used as examples to demonstrate the feasibility of conducting tabletop experiments to assess gravity models.

The non-interacting Bose-Einstein condensate sets constraints on linear GUP and Palatini $f(R)$ gravity, with specific ranges for the parameters $sigma$ and $barbeta$. On the other hand, properties of liquid helium provide more realistic bounds for these parameters.

Furthermore, the article suggests that using Earth seismic waves as a method can greatly improve constraints for quantum and modified gravity by approximately one order of magnitude.

## Future Roadmap:

- Further exploration of the connection between Palatini-like gravity and linear GUP models to examine other interesting phenomena and systems.
- Conducting more tabletop experiments to validate and refine the constraints on gravity models using ideal Bose-Einstein condensate and liquid helium.
- Exploring other systems or materials that can provide even more realistic bounds for the parameters $sigma$ and $barbeta$.
- Continued research into the use of Earth seismic waves as a method to improve constraints for quantum and modified gravity.
- Collaboration with experts in the field to gather more data and insights for a comprehensive understanding of gravity models.

## Potential Challenges:

- Obtaining accurate and precise measurements in tabletop experiments to validate the constraints on gravity models.
- Identifying suitable systems or materials that can provide more realistic bounds for the parameters $sigma$ and $barbeta$.
- Addressing any limitations or assumptions that may affect the applicability of the connection between Palatini-like gravity and linear GUP models.
- Overcoming technical challenges in utilizing Earth seismic waves as a method to improve constraints for quantum and modified gravity.

## Opportunities on the Horizon:

- Potential advancements in technology and measurement techniques that can enhance the accuracy and precision of tabletop experiments.
- Discovery of new systems or materials that can provide even stronger constraints on gravity models.
- Further development of the connection between Palatini-like gravity and linear GUP models, leading to a deeper understanding of quantum and modified gravity.
- Possible collaborations and interdisciplinary research opportunities with experts in different fields to expand knowledge and capabilities in gravity modeling.