https://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric
The FLRW model is an exact solution of the Einstein field equations. It requires that the mass-energy density ϱ and the pressure p are uniform throughout the space.
In our previous post we stressed that it is not known if the Einstein equations have a solution for a realistic, nonuniform mass-energy density. That is, we do not know if a modified FLRW model can describe a realistic universe.
A hybrid FLRW & Newton model might not be a general relativistic model at all
However, if we ignore the Einstein equations, we may simply assume that
1. the uniform, symmetric FLRW metric is a practical approximate model for our universe, and
2. we may combine the newtonian gravity to that model,
and we get a hybrid FLRW & Newton model.
Cosmologists use such hybrid models to simulate the evolution of the universe.
We do not know if any solution of the Einstein equations is close to the hybrid model. Thus, it may be that the hybrid model has nothing to do with general relativity.
Simulations with hybrid models have been moderately successful in explaining galaxy formation. Lots of open problems remain, though.
Dark energy
Observations suggest that the expansion of the universe has accelerated in the past 5 billion years or so. The standard ΛCDM cosmological model explains this with a positive cosmological constant Λ.
The FLRW model includes a cosmological constant, the same which appears in the Einstein equations. The model is an exact solution of the equations then.
The need to set the cosmological constant non-zero can be seen as a weakness of the ΛCDM model: the more adjustable parameters you have, the less predictive is the theory.
The inflation hypothesis
The inflation hypothesis claims that there was a scalar field in a higher energy state in the first moments of the universe. The field caused an exponentially fast expansion.
The field decayed or "rolled" to a lower energy state after a short period of time.
The energy density of the field was equal to the negative pressure that the field caused.
The FLRW model allows the energy density as well as the pressure to vary during the evolution of the universe. However, they have to be uniform throughout the space.
Let us list some of the problems involved with the inflaton field:
1. The inflaton field is "exotic matter". The negative pressure causes negative gravity which exceeds the positive gravity of the energy density. It breaks the strong energy condition:
http://cds.cern.ch/record/424782/files/0001099.pdf
(Visser and Barcelo 1999).
(Visser and Barcelo 1999).
2. Suppose that we in a Minkowski space have matter which breaks the strong energy condition. If such matter allows light to propagate faster than in the surrounding Minkowski space, then we face the paradoxes of closed timelike curves. Visser and Barcelo write about this problem in connection with wormholes, but the problem of closed timelike curves is possible in an asymptotic Minkowski space, too.
3. Why would the pressure be uniform throughout space when the inflaton field decays to a lower energy state? If the pressure is not uniform, does there exist a solution of the Einstein field equations?
4. What is the status of the "quantum fluctuations" which the fast expansion of the universe supposedly magnified to astronomical dimensions? Such quantum fluctuations are not a concept of standard quantum mechanics.
5. Can an expanding universe magnify quantum phenomena? We would need a theory of quantum gravity to answer that question. Why would a growing spatial metric cause the scalar field to expand? If we have an electric field of an electron, the electric field probably does not expand with the spatial metric. Why would a scalar field be different from an electric field?
6. The only known scalar field in the standard model is the Higgs field. We do not have any empirical observation of other scalar fields. Why would there exist a scalar field which can roll down to a lower energy state?
https://www.scientificamerican.com/article/cosmic-inflation-theory-faces-challenges/
Paul Steinhardt explained in a 2017 Scientific American article some other problems of the inflation hypothesis. It looks like the inflaton field has to be fine-tuned to make it consistent with observations. A prime motivation for the inflation hypothesis was to do away with the fine tuning required to get a flat spatial metric in the current observable universe. If the fine tuning problem comes back in the fine tuning of the inflation process, what is the benefit?
The flatness is at least partially explained by the anthropic principle: if the universe would collapse in a short time, or expand so fast that stars cannot form, then there would not exist intelligent observers in the universe.
4. What is the status of the "quantum fluctuations" which the fast expansion of the universe supposedly magnified to astronomical dimensions? Such quantum fluctuations are not a concept of standard quantum mechanics.
5. Can an expanding universe magnify quantum phenomena? We would need a theory of quantum gravity to answer that question. Why would a growing spatial metric cause the scalar field to expand? If we have an electric field of an electron, the electric field probably does not expand with the spatial metric. Why would a scalar field be different from an electric field?
6. The only known scalar field in the standard model is the Higgs field. We do not have any empirical observation of other scalar fields. Why would there exist a scalar field which can roll down to a lower energy state?
https://www.scientificamerican.com/article/cosmic-inflation-theory-faces-challenges/
Paul Steinhardt explained in a 2017 Scientific American article some other problems of the inflation hypothesis. It looks like the inflaton field has to be fine-tuned to make it consistent with observations. A prime motivation for the inflation hypothesis was to do away with the fine tuning required to get a flat spatial metric in the current observable universe. If the fine tuning problem comes back in the fine tuning of the inflation process, what is the benefit?
The flatness is at least partially explained by the anthropic principle: if the universe would collapse in a short time, or expand so fast that stars cannot form, then there would not exist intelligent observers in the universe.
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