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Spherical collapse model with non-clustering dark energy

Spherical collapse model with non-clustering dark energy We investigate a spherical overdensity model for thenon-clustering dark energy (DE) with the constant equation of state,de in a flat universe. In this case, the exact solution for theevolution of the scale factor is obtained for general de. Wealso obtain the exact (when de = 1/3) and theapproximate (when de1/3) solutions for the ratioof the overdensity radius to its value at the turnaround epoch (yR/Rta) for general cosmological parameters. Alsothe exact and approximate solutions of the overdensity at theturnaround epoch = (cluster/m)|z = zta are obtained for general de. Thus, we areable to obtain the non-linear overdensity 1NL = (x/y)3 at any epoch forthe given DE model. The non-linear overdensity at the virial epochvir = (xvir/yvir)3 isobtained by using the virial theorem and the energyconservation. The non-linear overdensity of every DE model convergesto that of the Einstein de Sitter universe virEdS = 182((1/2)(3/4))2 147 whenzvir increases. We find that the observed quantities at highredshifts are insensitive to the different de models. Thelow-redshift cluster (zvir 0.04, i.e., zta 0.7) shows the most model dependent feature and it should be asuitable object for testing DE models. Also as M0 increases, themodel dependence of the observed quantities decreases. The error inthe approximate solutions is at most 2 for a wide range of theparameter space. Even though the analytic forms of y and are obtained for the constant de, they can be generalized tothe slowly varying de. Thus, these analytic forms of the scalefactor, y, and provide a very accurate and useful tool formeasuring the properties of DE. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Cosmology and Astroparticle Physics IOP Publishing

Spherical collapse model with non-clustering dark energy

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Copyright
Copyright © IOP Publishing Ltd
eISSN
1475-7516
DOI
10.1088/1475-7516/2010/10/028
Publisher site
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Abstract

We investigate a spherical overdensity model for thenon-clustering dark energy (DE) with the constant equation of state,de in a flat universe. In this case, the exact solution for theevolution of the scale factor is obtained for general de. Wealso obtain the exact (when de = 1/3) and theapproximate (when de1/3) solutions for the ratioof the overdensity radius to its value at the turnaround epoch (yR/Rta) for general cosmological parameters. Alsothe exact and approximate solutions of the overdensity at theturnaround epoch = (cluster/m)|z = zta are obtained for general de. Thus, we areable to obtain the non-linear overdensity 1NL = (x/y)3 at any epoch forthe given DE model. The non-linear overdensity at the virial epochvir = (xvir/yvir)3 isobtained by using the virial theorem and the energyconservation. The non-linear overdensity of every DE model convergesto that of the Einstein de Sitter universe virEdS = 182((1/2)(3/4))2 147 whenzvir increases. We find that the observed quantities at highredshifts are insensitive to the different de models. Thelow-redshift cluster (zvir 0.04, i.e., zta 0.7) shows the most model dependent feature and it should be asuitable object for testing DE models. Also as M0 increases, themodel dependence of the observed quantities decreases. The error inthe approximate solutions is at most 2 for a wide range of theparameter space. Even though the analytic forms of y and are obtained for the constant de, they can be generalized tothe slowly varying de. Thus, these analytic forms of the scalefactor, y, and provide a very accurate and useful tool formeasuring the properties of DE.

Journal

Journal of Cosmology and Astroparticle PhysicsIOP Publishing

Published: Oct 1, 2010

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