Final Report Summary - D.E.E.O.S. (The search for the nature of dark energy and its equation of state)
The project objectives were to test the effect of inhomogeneities on cosmological observations and inferred values of cosmological parameters. The standard analysis of cosmological observations is usually done under the assumption of homogeneity and isotropy of the Universe. Since the real Universe is inhomogeneous there exists a bias due to the inhomogeneities being not taken into account. This project tested this bias using different methods, based on various inhomogeneous models.
The inhomogeneous bias has two sources. The first source of the bias comes from the fact that our Universe is approximated by a homogeneous model. Thus, the cosmological model recovers average properties of the Universe. This relates to the operation of averaging and the relation between the average and the actual quantities. The problem of the relation between the average quantities and local inhomogeneities has been done in following papers: Bolejko & Sussman (PLB, 697, 265, 2011) and Sussman & Bolejko (CQG, 29, 065018, 2012).
The second source of inhomogeneous bias is related to the fact that inhomogeneities affect optical properties of the Universe. In other words light propagation in the averaged cosmological model is different than in the real inhomogeneous Universe. The light-propagation effect within inhomogeneous models have been studied in following papers: Bolejko (MNRAS, 412, 1937, 2011) Krasinski & Bolejko (PRD 83, 083503); Bolejko & Ferreira (JCAP, in press, 2012), Krasinski & Bolejko (PRD in press 2012).
The way the inhomogeneous bias affects the observations has been studied in Bolejko JCAP, 02, 025 (2011) and in Bolejko (to be submitted to JCAP).
Also, the assumption of homogeneity has been tested - in the standard approach to cosmology we model the complex structure such as our Universe using just homogeneous solutions of the Einstein equations. In the standard approach one fits the model to the data, and thus the questions of validity of the assumption of homogeneity are never addressed. This problem was analysed in the paper by Bolejko, Hellaby & Alfedeel (JCAP, 09, 011, 2011).
During the project the review paper on the role of inhomogeneity has been written, and published in CQG 28, 164002, 2011. Also, 2 popular articles published in Polish science popular magazine has been published Bolejko & Wojciechowska (WZ 3, 29, 2011), and Bolejko (WZ, 3, 13, 2011).
During the project the following findings has been reported:
(1) Due to the presence of inhomogeneities trajectories of photons emitted by a cosmological object at one instant is different than the trajectory of photons emitted at another instant. Thus, the position on the observed object changes in the sky. This effect is related to the presence of inhomogeneity, and in the limit of homogeneity vanishes. Thus, by measuring the speed of the position change we can study the degree of inhomogeneity of our Universe.
(2) The assumption of the homogeneity has been tested. It has been shown that the assumption of homogeneity is consistent with the present data. It has also been shown that a range of inhomogeneous model that deviates from homogeneity are also consistent with the data.
(3) The optical properties of the inhomogeneous universe has been studied. Using various inhomogeneous methods it has been found that inhomogeneities affect the distance-redshift relation at the level of a few percent. However, if the average evolution of the universe does not deviates from the initial background than the average of the distance should coincide at the percentage level with the background model.
(4) The inhomogeneous bias on cosmological parameters has been estimated to be at the level of a few percent.
(5) The dark energy equation of state is more sensitive to the inhomogeneous bias and is affected at the level of 10 %.
The results of this project show that the inhomogeneous bias affects the observables at the level of a few percent. The amplitude of the inhomogeneous bias is thus comparable with the precision of present observations. In the near future however the precision of measurements will increase and thus as this project shows the inhomogeneous bias will need to be taken into account. Otherwise the results will be misinterpreted. Thus, it will have a huge impact on how we deal with future observations. This project shows that unless the observational data are properly interpreted, all the very expensive and precise observational missions could be futile. In a way disregarding inhomogeneous bias would be like spending a lot of money on very large telescopes in countries with bad atmospheric conditions. Therefore the impact of this project will not be limited to the area of inhomogeneous cosmology, but will have much broader impact including the way we will design and perform the analysis of future space or ground-based missions.
The inhomogeneous bias has two sources. The first source of the bias comes from the fact that our Universe is approximated by a homogeneous model. Thus, the cosmological model recovers average properties of the Universe. This relates to the operation of averaging and the relation between the average and the actual quantities. The problem of the relation between the average quantities and local inhomogeneities has been done in following papers: Bolejko & Sussman (PLB, 697, 265, 2011) and Sussman & Bolejko (CQG, 29, 065018, 2012).
The second source of inhomogeneous bias is related to the fact that inhomogeneities affect optical properties of the Universe. In other words light propagation in the averaged cosmological model is different than in the real inhomogeneous Universe. The light-propagation effect within inhomogeneous models have been studied in following papers: Bolejko (MNRAS, 412, 1937, 2011) Krasinski & Bolejko (PRD 83, 083503); Bolejko & Ferreira (JCAP, in press, 2012), Krasinski & Bolejko (PRD in press 2012).
The way the inhomogeneous bias affects the observations has been studied in Bolejko JCAP, 02, 025 (2011) and in Bolejko (to be submitted to JCAP).
Also, the assumption of homogeneity has been tested - in the standard approach to cosmology we model the complex structure such as our Universe using just homogeneous solutions of the Einstein equations. In the standard approach one fits the model to the data, and thus the questions of validity of the assumption of homogeneity are never addressed. This problem was analysed in the paper by Bolejko, Hellaby & Alfedeel (JCAP, 09, 011, 2011).
During the project the review paper on the role of inhomogeneity has been written, and published in CQG 28, 164002, 2011. Also, 2 popular articles published in Polish science popular magazine has been published Bolejko & Wojciechowska (WZ 3, 29, 2011), and Bolejko (WZ, 3, 13, 2011).
During the project the following findings has been reported:
(1) Due to the presence of inhomogeneities trajectories of photons emitted by a cosmological object at one instant is different than the trajectory of photons emitted at another instant. Thus, the position on the observed object changes in the sky. This effect is related to the presence of inhomogeneity, and in the limit of homogeneity vanishes. Thus, by measuring the speed of the position change we can study the degree of inhomogeneity of our Universe.
(2) The assumption of the homogeneity has been tested. It has been shown that the assumption of homogeneity is consistent with the present data. It has also been shown that a range of inhomogeneous model that deviates from homogeneity are also consistent with the data.
(3) The optical properties of the inhomogeneous universe has been studied. Using various inhomogeneous methods it has been found that inhomogeneities affect the distance-redshift relation at the level of a few percent. However, if the average evolution of the universe does not deviates from the initial background than the average of the distance should coincide at the percentage level with the background model.
(4) The inhomogeneous bias on cosmological parameters has been estimated to be at the level of a few percent.
(5) The dark energy equation of state is more sensitive to the inhomogeneous bias and is affected at the level of 10 %.
The results of this project show that the inhomogeneous bias affects the observables at the level of a few percent. The amplitude of the inhomogeneous bias is thus comparable with the precision of present observations. In the near future however the precision of measurements will increase and thus as this project shows the inhomogeneous bias will need to be taken into account. Otherwise the results will be misinterpreted. Thus, it will have a huge impact on how we deal with future observations. This project shows that unless the observational data are properly interpreted, all the very expensive and precise observational missions could be futile. In a way disregarding inhomogeneous bias would be like spending a lot of money on very large telescopes in countries with bad atmospheric conditions. Therefore the impact of this project will not be limited to the area of inhomogeneous cosmology, but will have much broader impact including the way we will design and perform the analysis of future space or ground-based missions.