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A cosmological model based on two scalar fields is proposed. The first of
these, \$varphi\$, has mass \$mu\$, while the second, \$chi\$, is massless. The
pair are coupled through a “Higgs portal”. First, we show how the model
reproduces the Friedmann equations if the square of the mass of \$varphi\$ is
proportional to the cosmological constant and \$chi\$ represents the
quintessence field. Quantum corrections break the conformal symmetry and \$chi\$
acquires a mass that is equal to \$sqrt{3g Lambda}\$. Using dimensional
analysis, we estimate the coupling constant and the mass of \$chi\$ and obtain
that \$gsim 10^{-26}\$ and \$m_chi sim 4.5times10^{-10},\$ eV, which is in
accordance with what is expected in the quintessence scenario. the acceleration
of the universe is proportional to \$chi^2\$, we conclude that for very long
times, the solution of the equation of motion goes to
\${m_chi}/{{sqrtlambda}}\$ and the universe, although it continues to
accelerate, the acceleration is constant

A cosmological model based on two scalar fields is proposed in this text. The first scalar field, denoted as \$varphi\$, has a mass of \$mu\$, while the second scalar field, denoted as \$chi\$, is massless. The two fields are coupled through a “Higgs portal”. The model is shown to reproduce the Friedmann equations if the square of the mass of \$varphi\$ is proportional to the cosmological constant and \$chi\$ represents the quintessence field. Quantum corrections are taken into account, which break the conformal symmetry and cause \$chi\$ to acquire a mass equal to \$sqrt{3gLambda}\$, where \$g\$ is the coupling constant and \$Lambda\$ is the cosmological constant.

Dimensional analysis is used to estimate the values of the coupling constant and the mass of \$chi\$. It is found that \$g approx 10^{-26}\$ and \$m_chi approx 4.5times10^{-10},\$ eV, which aligns with expectations in the quintessence scenario. It is observed that the acceleration of the universe is proportional to \$chi^2\$. For very long times, it is concluded that the solution of the equation of motion approaches \${m_chi}/{{sqrtlambda}}\$, and although the universe continues to accelerate, the acceleration remains constant.

### Potential Challenges:

• Testing and Verification: The proposed cosmological model based on two scalar fields needs extensive testing and verification against observational data and existing cosmological models.
• Quantum Corrections: Further research and analysis are required to understand and explore the quantum corrections that break the conformal symmetry and lead to the acquisition of mass by \$chi\$. This may involve complex calculations and theoretical investigations.
• Constraints and Boundaries: It is important to determine the constraints and boundaries within which the model is valid. This involves investigating its applicability to different cosmological scenarios and understanding the limitations of the model.

### Potential Opportunities:

• Understanding Dark Energy and Quintessence: The proposed model provides a potential framework for understanding dark energy and quintessence. Further exploration of the model may lead to insights into the nature of these phenomena and their role in the acceleration of the universe.
• Confronting Observational Data: The model can be confronted with observational data to test its validity and make predictions. This presents an opportunity to refine the model and potentially uncover new aspects of cosmology.
• Theoretical Advancements: Further investigation of the proposed model may contribute to theoretical advancements in cosmology and our understanding of fundamental physics. It opens up possibilities for exploring new connections between different fields and theories.

## Conclusion:

The cosmological model based on two scalar fields, presented in this text, offers a potential approach to understanding the acceleration of the universe and the role of dark energy. While there are challenges ahead to test and verify the model, as well as explore quantum corrections and determine its boundaries, there are exciting opportunities to deepen our knowledge of cosmology and contribute to theoretical advancements. Continued research and investigation in this area hold promise for uncovering new insights into the nature of the universe.