[Paper Review] Evolution Of Gravitational Potential In The Quasilinear And Nonlinear Regimes

J. S. Bagla, Τ. Padmanabhan|arXiv (Cornell University)|Mar 21, 1995

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper investigates the evolution of gravitational potential power spectra in nonlinear and quasilinear regimes within an Ω=1 matter-dominated universe. Using N-body simulations, it finds that for power spectra with index n = -1 or n = -2, the potential evolves only weakly in quasilinear phases and not at all in extreme nonlinear phases, leading to suppressed evolution in CDM-like models due to a conspiracy between amplitude and spectral index.

ABSTRACT

We study the evolution of the power spectrum of gravitational potential during the nonlinear clustering in an $Ω=1$ matter dominated phase. N-body simulations suggest that the potential does not evolve in time even in the quasilinear phase for an $n=-1$ power spectrum. For $n=-2$, the potential evolves in the quasilinear phase but not in the extreme nonlinear phase. Becauase of these facts, the evolution of the gravitational potential in spectra like CDM is less than what would have been expected naively. We discuss a class of CDM like models in which such an interesting conspiracy between the amplitude and local index occurs.

Motivation & Objective

• To understand the time evolution of the gravitational potential power spectrum during nonlinear clustering in a matter-dominated universe.
• To investigate why the gravitational potential evolves less than naively expected in CDM-like models.
• To explore the role of initial power spectrum index (n) and amplitude in suppressing potential evolution.
• To identify conditions under which the amplitude and local spectral index conspire to reduce potential evolution.
• To provide a theoretical framework for understanding the observed suppression of potential evolution in cosmological simulations.

Proposed method

• Conduct N-body simulations for an Ω=1 matter-dominated universe with initial power spectra of index n = -1 and n = -2.
• Compute the power spectrum of the gravitational potential at different redshifts to track its temporal evolution.
• Compare the simulated evolution with predictions from linear and quasilinear theory to identify deviations.
• Analyze the behavior of the potential in both quasilinear and extreme nonlinear regimes.
• Identify the conditions under which the amplitude and local spectral index lead to suppressed potential evolution.
• Use the results to construct a class of CDM-like models where such suppression occurs naturally.

Experimental results

Research questions

• RQ1 How does the gravitational potential power spectrum evolve in the quasilinear and nonlinear regimes for n = -1 and n = -2 initial power spectra?
• RQ2 Why is the evolution of the gravitational potential in CDM-like models less than expected from naive theoretical estimates?
• RQ3 What is the role of the spectral index and amplitude in suppressing potential evolution in nonlinear clustering?
• RQ4 In what class of CDM-like models does the amplitude-spectral index conspiracy lead to minimal potential evolution?
• RQ5 How do N-body simulations challenge the standard expectation of growing potential power in nonlinear structures?

Key findings

• For an n = -1 power spectrum, the gravitational potential shows no significant evolution in time, even in the quasilinear regime.
• For an n = -2 power spectrum, the potential evolves weakly in the quasilinear phase but remains nearly constant in the extreme nonlinear phase.
• The suppression of potential evolution in CDM-like models arises from a delicate balance between the amplitude and the local spectral index of the power spectrum.
• This behavior implies that the potential power spectrum evolves less than predicted by simple extrapolations of linear theory.
• The findings suggest that the observed weak evolution in CDM models is not accidental but results from a specific conspiracy between amplitude and spectral index.
• The study identifies a class of CDM-like models where such suppression is a natural outcome of the initial power spectrum parameters.