Gravitational clustering of galaxies in an expanding universe

Iqbal, Naseer; Ahmad, Farooq; Khan, Mohammad Shafi

doi:10.1007/bf02709363

Cited by 16 publications

(29 citation statements)

References 7 publications

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“…The effect of corrections on the power law of the correlation function is also discussed and it has been found that it behaves as ξ 2 ∼ R −2 at leading order in a certain approximation, which is consistent with the result obtained in Ref. [3].…”

Section: Discussionsupporting

confidence: 89%

“…The calculation of the power law of the correlation function is based on the assumption that the conversion of the initial primordial matter into the observed many-body galaxies took place at the stage of evolution of the Universe and these galaxies are coupled to the expansion of the Universe. The theories of the many-body (galaxies) distribution function have been developed mainly from a thermodynamic point of view [3][4][5][6][7][8]. Theses theories utilize only the first two laws of thermodynamics to derive the exact equations of state of the expanding Universe (a quasiequilibrium evolution).…”

Section: Overview and Motivationmentioning

confidence: 99%

“…Although there are corrections to the power law behavior, the correlation function obeys the original result (as in Refs. [1][2][3]) under certain approximations.…”

Section: Overview and Motivationmentioning

confidence: 99%

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Thermodynamics and galactic clustering with a modified gravitational potential

Upadhyay

2017

Phys. Rev. D

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Based on thermodynamics, we study the galactic clustering of an expanding Universe by considering the logarithmic and volume (quantum) corrections to Newton's law along with the repulsive effect of a harmonic force induced by the cosmological constant (Λ) in the formation of the large scale structure of the Universe. We derive the N -body partition function for extended-mass galaxies (galaxies with halos) analytically. For this partition function, we compute the exact equations of states, which exhibit the logarithmic, volume and cosmological constant corrections. In this setting, a modified correlation (clustering) parameter (due to these corrections) emerges naturally from the exact equations of state. We compute a corrected grand canonical distribution function for this system. Furthermore, we obtain a deviation in differential forms of the two-point correlation functions for both the point-mass and extended-mass cases. The consequences of these deviations on the correlation function's power law are also discussed.Keywords: Cosmology; Modified gravity; Galaxies cluster; Large scale structure of universe;Correlation function; Distribution function. I. OVERVIEW AND MOTIVATIONThe characterization of galactic clusters on very large scales under the influence of their mutual gravitational interaction is a matter of vast interest. The importance of such a process can be exaggerated as the evolution and distribution of the galaxies throughout the Universe are the main manifestations of this. The analysis of the correlation functions is one of the standard ways to study the formation of the Universe. The observation tells us that the power law of two-point correlation function scales as (intergalactic distance) −1.6 to (intergalactic distance) −1.8 [1], which has also been approved by N -body computer simulations [2] and by the analytic gravitational quasiequilibrium thermodynamics [3]. The calculation of the power law of the correlation function is based on the assumption that the conversion of the initial primordial matter into the observed many-body galaxies took place at the stage of evolution of the Universe and these galaxies are coupled to the expansion of the Universe. The theories of the many-body (galaxies) distribution function have been developed mainly from a thermodynamic point of view [3][4][5][6][7][8]. Theses theories utilize only the first two laws of thermodynamics to derive the exact equations of state of the expanding Universe (a quasiequilibrium evolution).The relation between thermodynamics and relativity was originated in the work of Bekenstein [9], Hawking [10], and Unruh [11]. Later, Jacobson established an important connection between thermodynamics and general relativity, by which the Einstein equations themselves can be viewed as a thermodynamic equation of state under a set of minimal assumptions involving the equivalence principle and the identification of the area of a causal horizon with entropy [12][13][14][15][16]. Recently, Verlinde proposed a constructive idea stating that gravity...

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Section: Discussionsupporting

confidence: 89%

Section: Overview and Motivationmentioning

confidence: 99%

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Thermodynamics and galactic clustering with a modified gravitational potential

Upadhyay

2017

Phys. Rev. D

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“…This then yields, as in Saslaw & Ahmed (),

p = \frac{italicNT}{V} (1 - b),

where

b = \frac{2 π {italicGm}^{2} \overset{true‾}{n}}{3 T} \int_{0}^{normal∞} ζ (\overset{true‾}{n}, T, r) rdr

and ζ is the two particle correlation function (Iqbal et al ). The two particle correlation function in this context is the probability of finding two particles together within a given volume.…”

Section: Methods To Study the Gravitational Phase Transition Of Galaxymentioning

confidence: 91%

Thermodynamics and phase transitions in galaxy clustering

Demir

Iqbal

2019

Astron Nachr

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The phenomenon of galaxy clustering was studied from the perspective of the gravitational phase transition, which is somewhat different from a phase transition in materials science. There is evidence that the phase transition describing galaxy clustering in an expanding universe is a first‐order phase transition exhibiting a mixed phase. As such, the Clausius–Clapeyron equation is relevant for studying such a system. In this work, we derive a general analog of the Clausius–Clapeyron equation that applies not only toward the coexistence curve in pressure–temperature space, but to a more general parameter space. One key finding is that a cusp exists at the critical point in this mixed phase when viewed in this more general parameter space. We extend this formalism to derive an equation for the curvature of the phase coexistence curve in pressure–temperature space and a more general parameter space. We also verify previous findings of hysteresis in the system via an independent free energy analysis.

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“…We apply the same techniques to a system made up of many galaxies in gravitational interaction, subject to fluctuations emerging from the intrinsic properties of the gravitational interaction. A number of theories of the cosmological many‐body problem have been developed mainly from the thermodynamic point of view (Saslaw & Hamilton 1984; Saslaw 2000; Iqbal, Ahmad & Khan 2006). The theory makes use of the equations of state along with the correlation functions for the extended mass structures for the development of a semi‐analytical model.…”

Section: Introductionmentioning

confidence: 99%

Correlation functions for extended mass galaxy clusters

Iqbal

Ahmad

Hamid

et al. 2012

Monthly Notices of the Royal Astronomical Society: Letters

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The phenomenon of clustering of galaxies on the basis of correlation functions in an expanding Universe is studied by using equation of state, taking gravitational interaction between galaxies of extended nature into consideration. The partial differential equation for the extended mass structures of a two-point correlation function developed earlier by Iqbal, Ahmad and Khan is studied on the basis of assigned boundary conditions. The solution for the correlation function for extended structures satisfies the basic boundary conditions, which seem to be sufficient for understanding the phenomena, and provides a new insight into the gravitational clustering problem for extended mass structures.Comment: 3 pages, no figure

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Gravitational clustering of galaxies in an expanding universe

Cited by 16 publications

References 7 publications

Thermodynamics and galactic clustering with a modified gravitational potential

Thermodynamics and galactic clustering with a modified gravitational potential

Thermodynamics and phase transitions in galaxy clustering

Correlation functions for extended mass galaxy clusters

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