Recently we showed that in FLRW cosmology, the contribution from higher
curvature terms in any generic metric gravity theory to the energy-momentum
tensor is of the perfect fluid form. Such a geometric perfect fluid can be
interpreted as a fluid remaining from the beginning of the universe where the
string theory is thought to be effective. Just a short time after the beginning
of the Universe, it is known that the Einstein-Hilbert action is assumed to be
modified by adding all possible curvature invariants. We propose that the
observed late-time accelerating expansion of the Universe can be solely driven
by this geometric fluid. To support our claim, we specifically study the
quadratic gravity field equations in $D$-dimensions. We show that the field
equations of this theory for the FLRW metric possess a geometric perfect fluid
source containing two critical parameters $sigma_1$ and $sigma_2$. To analyze
this theory concerning its parameter space $(sigma_1, sigma_2)$, we obtain
the general second-order nonlinear differential equation governing the
late-time dynamics of the deceleration parameter $q$. Hence using some
present-day cosmological data as our initial conditions, our findings for the
$sigma_2=0$ case are as follows: $ (i)$ In order to have a positive energy
density for the geometric fluid $rho_g$, the parameter $sigma_1$ must be
negative for all dimensions up to $D = 11$, $(ii)$ For a suitable choice of
$sigma_1$, the deceleration parameter experiences signature changes in the
past and future, and in the meantime it lies within a negative range which
means that the current observed accelerated expansion phase of the Universe can
be driven solely by the curvature of the spacetime, $(iii)$ $q$ experiences a
signature change and as the dimension $D$ of spacetime increases, this
signature change happens at earlier and later times, in the past and future,
respectively.
Conclusions
The article presents a proposal that the observed late-time accelerating expansion of the Universe can be explained solely by the presence of a geometric perfect fluid, which is a remnant from the beginning of the universe when string theory is effective. The authors specifically analyze the quadratic gravity field equations in $D$-dimensions and find that the field equations possess a geometric perfect fluid source with two critical parameters, $sigma_1$ and $sigma_2$. They study the dynamics of the deceleration parameter $q$ and find that with suitable choices of $sigma_1$, $q$ experiences signature changes in the past and future, indicating a potential explanation for the current accelerated expansion phase of the Universe driven by spacetime curvature.
Future Roadmap
While the proposal presented in this article provides an intriguing explanation for the late-time acceleration of the Universe, there are several challenges and potential opportunities on the horizon.
Challenges
- The validity of the proposal relies on the assumption that the contribution from higher curvature terms in any generic metric gravity theory takes the form of a geometric perfect fluid. This assumption may need to be further tested and supported by additional theoretical and observational evidence.
- The parameter space $(sigma_1, sigma_2)$ governing the late-time dynamics of the deceleration parameter $q$ needs to be thoroughly explored. The authors have only considered the case where $sigma_2 = 0$, and it remains to be seen how varying values of $sigma_2$ may affect the results.
- Further investigations are needed to understand the implications of this proposal in the context of other cosmological theories and models. The authors have focused on FLRW cosmology and quadratic gravity field equations, but it would be valuable to explore its compatibility with different frameworks.
Opportunities
- Experimental and observational tests can be conducted to gather data that can support or challenge the proposal. Analyzing present and future cosmological data can provide insights into the behavior of the deceleration parameter $q$ and help validate the theoretical predictions.
- Exploring the dependence of the proposal on the dimension of spacetime ($D$) can open up new avenues for research. Investigating how the signature change of $q$ varies with increasing dimensions can lead to a deeper understanding of the relationship between curvature and the observed accelerated expansion.
- This proposal has the potential to bridge the gap between string theory and cosmology, as it suggests that the geometric perfect fluid originates from the beginning of the universe when string theory is effective. Further exploration of this connection may offer new insights into the fundamental nature of our universe.
Note: The roadmap outlined above is based on the information presented in the article. It is important to conduct further research and analysis to address the challenges and explore the opportunities discussed.