In this manuscript, we show that three fundamental building blocks are
supporting the Cosmological Principle. The first of them states that there is a
special frame in the universe where the spatial geometry is intrinsically
homogeneous and isotropic. The second demands the existence of a fiducial
observer to whom the Hubble parameter is isotropic. The last piece states that
matter and radiation behave as a perfect fluid. We show that these three
hypotheses give us the Friedmann-Lema^itre-Robertson-Walker (FLRW) spacetimes,
the central pillar of the standard model of Cosmology. We keep with the first
of them and start to investigate the so-called intrinsically homogeneous and
isotropic spacetimes. They emerge after the decoupling of the CMB with the
geometric frame of reference. Furthermore, a “$Lambda$CDM-like” effective
theory arises naturally in those backgrounds, together with some new density
parameters relating to the local inhomogeneities, the internal energy density,
and the local and global magnitudes of the Hubble anisotropy. All those
properties make this class of inhomogeneous models, which roughly speaking,
keeps “1/3” of the Cosmological Principle, worth investigating in applications
to Cosmology, for it can accommodate the same ingredients of the standard
model, as a geometric frame and a free-falling isotropic cosmic background
radiation, and reduce to the latter when some observable parameters vanish.
Based on the conclusions of the text, a future roadmap for readers can be outlined as follows:
- Investigating intrinsically homogeneous and isotropic spacetimes: The first fundamental building block of the Cosmological Principle suggests the existence of a special frame in the universe where spatial geometry is homogeneous and isotropic. This should be further explored to understand the implications and properties of these spacetimes.
- Emergence of “ΛCDM-like” effective theory: In the intrinsically homogeneous and isotropic backgrounds, a new effective theory similar to ΛCDM (Lambda Cold Dark Matter) arises naturally. This theory should be studied to understand its implications and how it relates to the standard model of Cosmology.
- Properties of inhomogeneous models: The class of inhomogeneous models that approximately satisfy 1/3 of the Cosmological Principle is worth investigating. These models should be analyzed to understand their properties, such as the relation to local inhomogeneities, internal energy density, and the magnitudes of Hubble anisotropy at local and global scales.
- Application to Cosmology: The inhomogeneous models can potentially be applied to Cosmology to study various phenomena. These models have the advantage of accommodating the same ingredients as the standard model, such as a geometric frame and a free-falling isotropic cosmic background radiation. Additionally, they reduce to the standard model when certain observable parameters vanish.
Potential Challenges and Opportunities:
- Challenges: One of the challenges in investigating intrinsically homogeneous and isotropic spacetimes may be the complexity of the mathematical equations involved. Additionally, understanding the implications and behavior of the “ΛCDM-like” effective theory and inhomogeneous models may require advanced mathematical and computational techniques.
- Opportunities: The exploration of intrinsically homogeneous and isotropic spacetimes, as well as the study of inhomogeneous models, presents an opportunity to expand our understanding of the universe beyond the standard model of Cosmology. These investigations may lead to new insights and discoveries regarding the nature of spatial geometry, cosmic background radiation, and the overall structure of the universe.
Overall, further research and analysis should be conducted to investigate the proposed building blocks of the Cosmological Principle and their implications. This will require a combination of theoretical and observational studies, as well as collaborations between researchers from various disciplines such as mathematics, physics, and astrophysics.